From a7b976320f4a854b21777162d1ec897211b9a5be Mon Sep 17 00:00:00 2001 From: ToikY <27568617+ToikY@users.noreply.github.com> Date: Tue, 3 Nov 2026 15:46:05 -0800 Subject: [PATCH] Prove positive common-covector correlation over every finite field (no kappa) --- .../CASES.json | 834 ++++ .../common-covector-all-field-positive/NOTICE | 19 + .../ORACLE.json | 4335 +++++++++++++++++ .../PROOF.md | 112 + .../README.md | 83 + .../RESULT.json | 1 + .../RUN-RECORDS.json | 521 ++ .../SCHEMA.json | 50 + .../SOURCE-PINS.json | 26 + .../SOURCES.json | 18 + .../SOURCES.md | 25 + .../TASK.json | 111 + .../VALIDATION.md | 69 + .../VERIFY.json | 63 + .../inputs/4807-PROOF.md | 139 + .../inputs/4807-README.md | 104 + .../oracle.py | 284 ++ .../verify.py | 223 + 18 files changed, 7017 insertions(+) create mode 100644 research/common-covector-all-field-positive/CASES.json create mode 100644 research/common-covector-all-field-positive/NOTICE create mode 100644 research/common-covector-all-field-positive/ORACLE.json create mode 100644 research/common-covector-all-field-positive/PROOF.md create mode 100644 research/common-covector-all-field-positive/README.md create mode 100644 research/common-covector-all-field-positive/RESULT.json create mode 100644 research/common-covector-all-field-positive/RUN-RECORDS.json create mode 100644 research/common-covector-all-field-positive/SCHEMA.json create mode 100644 research/common-covector-all-field-positive/SOURCE-PINS.json create mode 100644 research/common-covector-all-field-positive/SOURCES.json create mode 100644 research/common-covector-all-field-positive/SOURCES.md create mode 100644 research/common-covector-all-field-positive/TASK.json create mode 100644 research/common-covector-all-field-positive/VALIDATION.md create mode 100644 research/common-covector-all-field-positive/VERIFY.json create mode 100644 research/common-covector-all-field-positive/inputs/4807-PROOF.md create mode 100644 research/common-covector-all-field-positive/inputs/4807-README.md create mode 100644 research/common-covector-all-field-positive/oracle.py create mode 100644 research/common-covector-all-field-positive/verify.py diff --git a/research/common-covector-all-field-positive/CASES.json b/research/common-covector-all-field-positive/CASES.json new file mode 100644 index 0000000000..c931d07187 --- /dev/null +++ b/research/common-covector-all-field-positive/CASES.json @@ -0,0 +1,834 @@ +{ + "schema_version": 1, + "scope": "Exact parameter algebra only; only primepower q rows have a finite-field interpretation. The all-field theorem rests on the written inequality proof and cited count, not this finite table.", + "non_prime_power_q": [ + 6, + 10, + 12, + 14, + 15 + ], + "case_count": 205, + "cases": [ + { + "q": 2, + "n": 1 + }, + { + "q": 2, + "n": 2 + }, + { + "q": 2, + "n": 3 + }, + { + "q": 2, + "n": 4 + }, + { + "q": 2, + "n": 5 + }, + { + "q": 2, + "n": 6 + }, + { + "q": 2, + "n": 7 + }, + { + "q": 2, + "n": 8 + }, + { + "q": 2, + "n": 9 + }, + { + "q": 2, + "n": 10 + }, + { + "q": 2, + "n": 11 + }, + { + "q": 2, + "n": 12 + }, + { + "q": 3, + "n": 1 + }, + { + "q": 3, + "n": 2 + }, + { + "q": 3, + "n": 3 + }, + { + "q": 3, + "n": 4 + }, + { + "q": 3, + "n": 5 + }, + { + "q": 3, + "n": 6 + }, + { + "q": 3, + "n": 7 + }, + { + "q": 3, + "n": 8 + }, + { + "q": 3, + "n": 9 + }, + { + "q": 3, + "n": 10 + }, + { + "q": 3, + "n": 11 + }, + { + "q": 3, + "n": 12 + }, + { + "q": 4, + "n": 1 + }, + { + "q": 4, + "n": 2 + }, + { + "q": 4, + "n": 3 + }, + { + "q": 4, + "n": 4 + }, + { + "q": 4, + "n": 5 + }, + { + "q": 4, + "n": 6 + }, + { + "q": 4, + "n": 7 + }, + { + "q": 4, + "n": 8 + }, + { + "q": 4, + "n": 9 + }, + { + "q": 4, + "n": 10 + }, + { + "q": 4, + "n": 11 + }, + { + "q": 4, + "n": 12 + }, + { + "q": 5, + "n": 1 + }, + { + "q": 5, + "n": 2 + }, + { + "q": 5, + "n": 3 + }, + { + "q": 5, + "n": 4 + }, + { + "q": 5, + "n": 5 + }, + { + "q": 5, + "n": 6 + }, + { + "q": 5, + "n": 7 + }, + { + "q": 5, + "n": 8 + }, + { + "q": 5, + "n": 9 + }, + { + "q": 5, + "n": 10 + }, + { + "q": 5, + "n": 11 + }, + { + "q": 5, + "n": 12 + }, + { + "q": 6, + "n": 1 + }, + { + "q": 6, + "n": 2 + }, + { + "q": 6, + "n": 3 + }, + { + "q": 6, + "n": 4 + }, + { + "q": 6, + "n": 5 + }, + { + "q": 6, + "n": 6 + }, + { + "q": 6, + "n": 7 + }, + { + "q": 6, + "n": 8 + }, + { + "q": 6, + "n": 9 + }, + { + "q": 6, + "n": 10 + }, + { + "q": 6, + "n": 11 + }, + { + "q": 6, + "n": 12 + }, + { + "q": 7, + "n": 1 + }, + { + "q": 7, + "n": 2 + }, + { + "q": 7, + "n": 3 + }, + { + "q": 7, + "n": 4 + }, + { + "q": 7, + "n": 5 + }, + { + "q": 7, + "n": 6 + }, + { + "q": 7, + "n": 7 + }, + { + "q": 7, + "n": 8 + }, + { + "q": 7, + "n": 9 + }, + { + "q": 7, + "n": 10 + }, + { + "q": 7, + "n": 11 + }, + { + "q": 7, + "n": 12 + }, + { + "q": 8, + "n": 1 + }, + { + "q": 8, + "n": 2 + }, + { + "q": 8, + "n": 3 + }, + { + "q": 8, + "n": 4 + }, + { + "q": 8, + "n": 5 + }, + { + "q": 8, + "n": 6 + }, + { + "q": 8, + "n": 7 + }, + { + "q": 8, + "n": 8 + }, + { + "q": 8, + "n": 9 + }, + { + "q": 8, + "n": 10 + }, + { + "q": 8, + "n": 11 + }, + { + "q": 8, + "n": 12 + }, + { + "q": 9, + "n": 1 + }, + { + "q": 9, + "n": 2 + }, + { + "q": 9, + "n": 3 + }, + { + "q": 9, + "n": 4 + }, + { + "q": 9, + "n": 5 + }, + { + "q": 9, + "n": 6 + }, + { + "q": 9, + "n": 7 + }, + { + "q": 9, + "n": 8 + }, + { + "q": 9, + "n": 9 + }, + { + "q": 9, + "n": 10 + }, + { + "q": 9, + "n": 11 + }, + { + "q": 9, + "n": 12 + }, + { + "q": 10, + "n": 1 + }, + { + "q": 10, + "n": 2 + }, + { + "q": 10, + "n": 3 + }, + { + "q": 10, + "n": 4 + }, + { + "q": 10, + "n": 5 + }, + { + "q": 10, + "n": 6 + }, + { + "q": 10, + "n": 7 + }, + { + "q": 10, + "n": 8 + }, + { + "q": 10, + "n": 9 + }, + { + "q": 10, + "n": 10 + }, + { + "q": 10, + "n": 11 + }, + { + "q": 10, + "n": 12 + }, + { + "q": 11, + "n": 1 + }, + { + "q": 11, + "n": 2 + }, + { + "q": 11, + "n": 3 + }, + { + "q": 11, + "n": 4 + }, + { + "q": 11, + "n": 5 + }, + { + "q": 11, + "n": 6 + }, + { + "q": 11, + "n": 7 + }, + { + "q": 11, + "n": 8 + }, + { + "q": 11, + "n": 9 + }, + { + "q": 11, + "n": 10 + }, + { + "q": 11, + "n": 11 + }, + { + "q": 11, + "n": 12 + }, + { + "q": 12, + "n": 1 + }, + { + "q": 12, + "n": 2 + }, + { + "q": 12, + "n": 3 + }, + { + "q": 12, + "n": 4 + }, + { + "q": 12, + "n": 5 + }, + { + "q": 12, + "n": 6 + }, + { + "q": 12, + "n": 7 + }, + { + "q": 12, + "n": 8 + }, + { + "q": 12, + "n": 9 + }, + { + "q": 12, + "n": 10 + }, + { + "q": 12, + "n": 11 + }, + { + "q": 12, + "n": 12 + }, + { + "q": 13, + "n": 1 + }, + { + "q": 13, + "n": 2 + }, + { + "q": 13, + "n": 3 + }, + { + "q": 13, + "n": 4 + }, + { + "q": 13, + "n": 5 + }, + { + "q": 13, + "n": 6 + }, + { + "q": 13, + "n": 7 + }, + { + "q": 13, + "n": 8 + }, + { + "q": 13, + "n": 9 + }, + { + "q": 13, + "n": 10 + }, + { + "q": 13, + "n": 11 + }, + { + "q": 13, + "n": 12 + }, + { + "q": 14, + "n": 1 + }, + { + "q": 14, + "n": 2 + }, + { + "q": 14, + "n": 3 + }, + { + "q": 14, + "n": 4 + }, + { + "q": 14, + "n": 5 + }, + { + "q": 14, + "n": 6 + }, + { + "q": 14, + "n": 7 + }, + { + "q": 14, + "n": 8 + }, + { + "q": 14, + "n": 9 + }, + { + "q": 14, + "n": 10 + }, + { + "q": 14, + "n": 11 + }, + { + "q": 14, + "n": 12 + }, + { + "q": 15, + "n": 1 + }, + { + "q": 15, + "n": 2 + }, + { + "q": 15, + "n": 3 + }, + { + "q": 15, + "n": 4 + }, + { + "q": 15, + "n": 5 + }, + { + "q": 15, + "n": 6 + }, + { + "q": 15, + "n": 7 + }, + { + "q": 15, + "n": 8 + }, + { + "q": 15, + "n": 9 + }, + { + "q": 15, + "n": 10 + }, + { + "q": 15, + "n": 11 + }, + { + "q": 15, + "n": 12 + }, + { + "q": 16, + "n": 1 + }, + { + "q": 16, + "n": 2 + }, + { + "q": 16, + "n": 3 + }, + { + "q": 16, + "n": 4 + }, + { + "q": 16, + "n": 5 + }, + { + "q": 16, + "n": 6 + }, + { + "q": 16, + "n": 7 + }, + { + "q": 16, + "n": 8 + }, + { + "q": 16, + "n": 9 + }, + { + "q": 16, + "n": 10 + }, + { + "q": 16, + "n": 11 + }, + { + "q": 16, + "n": 12 + }, + { + "q": 25, + "n": 1 + }, + { + "q": 25, + "n": 2 + }, + { + "q": 25, + "n": 3 + }, + { + "q": 25, + "n": 8 + }, + { + "q": 25, + "n": 16 + }, + { + "q": 27, + "n": 1 + }, + { + "q": 27, + "n": 2 + }, + { + "q": 27, + "n": 3 + }, + { + "q": 27, + "n": 8 + }, + { + "q": 27, + "n": 16 + }, + { + "q": 32, + "n": 1 + }, + { + "q": 32, + "n": 2 + }, + { + "q": 32, + "n": 3 + }, + { + "q": 32, + "n": 8 + }, + { + "q": 32, + "n": 16 + }, + { + "q": 49, + "n": 1 + }, + { + "q": 49, + "n": 2 + }, + { + "q": 49, + "n": 3 + }, + { + "q": 49, + "n": 8 + }, + { + "q": 49, + "n": 16 + }, + { + "q": 64, + "n": 1 + }, + { + "q": 64, + "n": 2 + }, + { + "q": 64, + "n": 3 + }, + { + "q": 64, + "n": 8 + }, + { + "q": 64, + "n": 16 + } + ] +} diff --git a/research/common-covector-all-field-positive/NOTICE b/research/common-covector-all-field-positive/NOTICE new file mode 100644 index 0000000000..417fc4e09b --- /dev/null +++ b/research/common-covector-all-field-positive/NOTICE @@ -0,0 +1,19 @@ +Common-covector all-field positive sign corollary +Prepared for ToikY with substantial OpenAI Codex assistance; Apache-2.0. +Separate AI primary, independent oracle and static review are not independent +human acceptance or formal proof-kernel checking. + +Nick Petalas, PR4807: exact all-field common-covector count, orbit and dependent- +pair subtraction; binary strict-positive theorem; explicit odd-field sign +question and suggested q*delta-alpha^2=q-1 identity. This package adds only the +quantified remaining sign proof, not a new count or generic correlation principle. +Nick Petalas PR4227: marginal law; PR4261: partial-sum/header counting method; +PR4778: two-way-coupling question; PR4769/4274: one-way comparison context. +Cinna Davis: BIT request context. source527, commdata2338, Jose Manuel and all +retained normalizer/recursive-closure lineage retain predecessor credit. +Two exact source prose objects and their original notices remain in inputs/. +No predecessor program is copied, imported or executed. + +Classical elementary polynomial identities and rational inequalities are used. +Douglas Colkitt and other repository contributors retain task/replay-framework +credit. No supplier, physical caller, kappa or selected-frontier change follows. diff --git a/research/common-covector-all-field-positive/ORACLE.json b/research/common-covector-all-field-positive/ORACLE.json new file mode 100644 index 0000000000..3a0ca22d75 --- /dev/null +++ b/research/common-covector-all-field-positive/ORACLE.json @@ -0,0 +1,4335 @@ +{ + "case_manifest_sha256": "a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b", + "cases": [ + { + "joint": [ + 1, + 3 + ], + "lower_bound": [ + 1, + 1 + ], + "marginal": [ + 1, + 2 + ], + "n": 1, + "positive": true, + "q": 2, + "ratio": [ + 4, + 3 + ] + }, + { + "joint": [ + 4, + 21 + ], + "lower_bound": [ + 35, + 27 + ], + "marginal": [ + 9, + 28 + ], + "n": 2, + "positive": true, + "q": 2, + "ratio": [ + 448, + 243 + ] + }, + { + "joint": [ + 7, + 60 + ], + "lower_bound": [ + 95, + 63 + ], + "marginal": [ + 9, + 40 + ], + "n": 3, + "positive": true, + "q": 2, + "ratio": [ + 560, + 243 + ] + }, + { + "joint": [ + 34, + 465 + ], + "lower_bound": [ + 403, + 243 + ], + "marginal": [ + 81, + 496 + ], + "n": 4, + "positive": true, + "q": 2, + "ratio": [ + 269824, + 98415 + ] + }, + { + "joint": [ + 1441, + 31248 + ], + "lower_bound": [ + 1477, + 837 + ], + "marginal": [ + 27, + 224 + ], + "n": 5, + "positive": true, + "q": 2, + "ratio": [ + 645568, + 203391 + ] + }, + { + "joint": [ + 133, + 4572 + ], + "lower_bound": [ + 12065, + 6561 + ], + "marginal": [ + 729, + 8128 + ], + "n": 6, + "positive": true, + "q": 2, + "ratio": [ + 17296384, + 4782969 + ] + }, + { + "joint": [ + 37969, + 2072640 + ], + "lower_bound": [ + 175015, + 92583 + ], + "marginal": [ + 729, + 10880 + ], + "n": 7, + "positive": true, + "q": 2, + "ratio": [ + 826205440, + 202479021 + ] + }, + { + "joint": [ + 353, + 30660 + ], + "lower_bound": [ + 644371, + 334611 + ], + "marginal": [ + 6561, + 130816 + ], + "n": 8, + "positive": true, + "q": 2, + "ratio": [ + 2955395072, + 645700815 + ] + }, + { + "joint": [ + 138103, + 19117824 + ], + "lower_bound": [ + 6537311, + 3352671 + ], + "marginal": [ + 6561, + 174592 + ], + "n": 9, + "positive": true, + "q": 2, + "ratio": [ + 48223357952, + 9427231899 + ] + }, + { + "joint": [ + 55151, + 12183744 + ], + "lower_bound": [ + 10797925, + 5491557 + ], + "marginal": [ + 59049, + 2096128 + ], + "n": 10, + "positive": true, + "q": 2, + "ratio": [ + 1849656885248, + 324270949293 + ] + }, + { + "joint": [ + 24325489, + 8583644160 + ], + "lower_bound": [ + 3463915, + 1751787 + ], + "marginal": [ + 19683, + 931840 + ], + "n": 11, + "positive": true, + "q": 2, + "ratio": [ + 45334927339520, + 7137447668847 + ] + }, + { + "joint": [ + 83657, + 47180160 + ], + "lower_bound": [ + 9493369, + 4782969 + ], + "marginal": [ + 531441, + 33550336 + ], + "n": 12, + "positive": true, + "q": 2, + "ratio": [ + 89815054680064, + 12709329141645 + ] + }, + { + "joint": [ + 5, + 12 + ], + "lower_bound": [ + 8, + 7 + ], + "marginal": [ + 7, + 12 + ], + "n": 1, + "positive": true, + "q": 3, + "ratio": [ + 60, + 49 + ] + }, + { + "joint": [ + 10, + 39 + ], + "lower_bound": [ + 65, + 49 + ], + "marginal": [ + 49, + 117 + ], + "n": 2, + "positive": true, + "q": 3, + "ratio": [ + 3510, + 2401 + ] + }, + { + "joint": [ + 457, + 2808 + ], + "lower_bound": [ + 6320, + 4459 + ], + "marginal": [ + 343, + 1080 + ], + "n": 3, + "positive": true, + "q": 3, + "ratio": [ + 2467800, + 1529437 + ] + }, + { + "joint": [ + 338, + 3267 + ], + "lower_bound": [ + 3509, + 2401 + ], + "marginal": [ + 2401, + 9801 + ], + "n": 4, + "positive": true, + "q": 3, + "ratio": [ + 9938214, + 5764801 + ] + }, + { + "joint": [ + 63775, + 972972 + ], + "lower_bound": [ + 430664, + 290521 + ], + "marginal": [ + 2401, + 12636 + ], + "n": 5, + "positive": true, + "q": 3, + "ratio": [ + 805860900, + 443889677 + ] + }, + { + "joint": [ + 333610, + 8056503 + ], + "lower_bound": [ + 15974195, + 10706059 + ], + "marginal": [ + 117649, + 796797 + ], + "n": 6, + "positive": true, + "q": 3, + "ratio": [ + 2392375024530, + 1259557135291 + ] + }, + { + "joint": [ + 40951513, + 1568096496 + ], + "lower_bound": [ + 1347023840, + 900132499 + ], + "marginal": [ + 823543, + 7173360 + ], + "n": 7, + "positive": true, + "q": 3, + "ratio": [ + 1468799726468400, + 741297818623957 + ] + }, + { + "joint": [ + 1116986, + 67877919 + ], + "lower_bound": [ + 354167749, + 236356841 + ], + "marginal": [ + 5764801, + 64566801 + ], + "n": 8, + "positive": true, + "q": 3, + "ratio": [ + 2812688298489654, + 1362550153353641 + ] + }, + { + "joint": [ + 59273761445, + 5718810698172 + ], + "lower_bound": [ + 595409386088, + 397119846487 + ], + "marginal": [ + 40353607, + 581120892 + ], + "n": 9, + "positive": true, + "q": 3, + "ratio": [ + 34445221123113608940, + 16025218217036728609 + ] + }, + { + "joint": [ + 7635270550, + 1169809562889 + ], + "lower_bound": [ + 284255114575, + 189540892079 + ], + "marginal": [ + 282475249, + 5230147077 + ], + "n": 10, + "positive": true, + "q": 3, + "ratio": [ + 119800763847560047050, + 53540610685697652671 + ] + }, + { + "joint": [ + 148999647743, + 36254469946968 + ], + "lower_bound": [ + 37526299332080, + 25019680229677 + ], + "marginal": [ + 282475249, + 6724500120 + ], + "n": 11, + "positive": true, + "q": 3, + "ratio": [ + 5009740745638806145800, + 2150960122584726710957 + ] + }, + { + "joint": [ + 852664202, + 329500919223 + ], + "lower_bound": [ + 10608952598459, + 7072897759711 + ], + "marginal": [ + 13841287201, + 423644039001 + ], + "n": 12, + "positive": true, + "q": 3, + "ratio": [ + 3251034958021600879818, + 1341068619663964900807 + ] + }, + { + "joint": [ + 1, + 2 + ], + "lower_bound": [ + 15, + 13 + ], + "marginal": [ + 13, + 20 + ], + "n": 1, + "positive": true, + "q": 4, + "ratio": [ + 200, + 169 + ] + }, + { + "joint": [ + 1, + 3 + ], + "lower_bound": [ + 1071, + 845 + ], + "marginal": [ + 169, + 336 + ], + "n": 2, + "positive": true, + "q": 4, + "ratio": [ + 37632, + 28561 + ] + }, + { + "joint": [ + 859, + 3808 + ], + "lower_bound": [ + 20145, + 15379 + ], + "marginal": [ + 2197, + 5440 + ], + "n": 3, + "positive": true, + "q": 4, + "ratio": [ + 46729600, + 33787663 + ] + }, + { + "joint": [ + 7063, + 46376 + ], + "lower_bound": [ + 37851, + 28561 + ], + "marginal": [ + 28561, + 87296 + ], + "n": 4, + "positive": true, + "q": 4, + "ratio": [ + 19730292736, + 13867422257 + ] + }, + { + "joint": [ + 444355, + 4333056 + ], + "lower_bound": [ + 12959415, + 9739301 + ], + "marginal": [ + 28561, + 107520 + ], + "n": 5, + "positive": true, + "q": 4, + "ratio": [ + 477770496000, + 328739480563 + ] + }, + { + "joint": [ + 1253281, + 18174208 + ], + "lower_bound": [ + 418045011, + 313742585 + ], + "marginal": [ + 4826809, + 22368256 + ], + "n": 6, + "positive": true, + "q": 4, + "ratio": [ + 448539363966976, + 302875106592253 + ] + }, + { + "joint": [ + 9058528753, + 195453820928 + ], + "lower_bound": [ + 456794481795, + 342669651337 + ], + "marginal": [ + 62748517, + 357908480 + ], + "n": 7, + "positive": true, + "q": 4, + "ratio": [ + 32421242570225254400, + 21502012442303817229 + ] + }, + { + "joint": [ + 102305537, + 3285126144 + ], + "lower_bound": [ + 279504468747, + 209642795297 + ], + "marginal": [ + 815730721, + 5726601216 + ], + "n": 8, + "positive": true, + "q": 4, + "ratio": [ + 262466629639304380416, + 171012068560077219137 + ] + }, + { + "joint": [ + 25498833457, + 1218624225280 + ], + "lower_bound": [ + 137275778424675, + 102959084412457 + ], + "marginal": [ + 10604499373, + 91625881600 + ], + "n": 9, + "positive": true, + "q": 4, + "ratio": [ + 23363530952692006912000, + 14956569124610333286157 + ] + }, + { + "joint": [ + 1637223064757, + 116456578809856 + ], + "lower_bound": [ + 5840564524164381, + 4380453578501975 + ], + "marginal": [ + 137858491849, + 1466015154176 + ], + "n": 10, + "positive": true, + "q": 4, + "ratio": [ + 38403101179203785391603712, + 24155308957873496086716071 + ] + }, + { + "joint": [ + 30976398243694289, + 3279420191315853312 + ], + "lower_bound": [ + 11173314706987545, + 8380004144025163 + ], + "marginal": [ + 137858491849, + 1804326666240 + ], + "n": 11, + "positive": true, + "q": 4, + "ratio": [ + 558915413751675075730971033600, + 345421165162120067490432519713 + ] + }, + { + "joint": [ + 3964246775712049, + 624651604633059328 + ], + "lower_bound": [ + 97323801851666703, + 72992900688732973 + ], + "marginal": [ + 23298085122481, + 375299963355136 + ], + "n": 12, + "positive": true, + "q": 4, + "ratio": [ + 47609013428974337001390759477248, + 28910111830909347880727940522221 + ] + }, + { + "joint": [ + 17, + 30 + ], + "lower_bound": [ + 8, + 7 + ], + "marginal": [ + 7, + 10 + ], + "n": 1, + "positive": true, + "q": 5, + "ratio": [ + 170, + 147 + ] + }, + { + "joint": [ + 187, + 465 + ], + "lower_bound": [ + 1612, + 1323 + ], + "marginal": [ + 441, + 775 + ], + "n": 2, + "positive": true, + "q": 5, + "ratio": [ + 724625, + 583443 + ] + }, + { + "joint": [ + 13379, + 46500 + ], + "lower_bound": [ + 118768, + 95697 + ], + "marginal": [ + 3087, + 6500 + ], + "n": 3, + "positive": true, + "q": 5, + "ratio": [ + 1130525500, + 886249917 + ] + }, + { + "joint": [ + 71077, + 346125 + ], + "lower_bound": [ + 727892, + 583443 + ], + "marginal": [ + 194481, + 488125 + ], + "n": 4, + "positive": true, + "q": 5, + "ratio": [ + 1908195334375, + 1475091515079 + ] + }, + { + "joint": [ + 1394993837, + 9533081250 + ], + "lower_bound": [ + 63255128, + 50629887 + ], + "marginal": [ + 64827, + 193750 + ], + "n": 5, + "positive": true, + "q": 5, + "ratio": [ + 270280055918750, + 206777572126587 + ] + }, + { + "joint": [ + 12422388121, + 119200134375 + ], + "lower_bound": [ + 209349117172, + 167501234313 + ], + "marginal": [ + 85766121, + 305171875 + ], + "n": 6, + "positive": true, + "q": 5, + "ratio": [ + 18954817374316484375, + 14365931129738109873 + ] + }, + { + "joint": [ + 11057383451747, + 149009323125000 + ], + "lower_bound": [ + 14656622765408, + 11725686764757 + ], + "marginal": [ + 600362847, + 2543125000 + ], + "n": 7, + "positive": true, + "q": 5, + "ratio": [ + 28120308290724089375000, + 21119000067359195349537 + ] + }, + { + "joint": [ + 24603443642767, + 465659856796875 + ], + "lower_bound": [ + 44394213598276, + 35515664939979 + ], + "marginal": [ + 37822859361, + 190734765625 + ], + "n": 8, + "positive": true, + "q": 5, + "ratio": [ + 23463660283855299857421875, + 17462952001783914902814447 + ] + }, + { + "joint": [ + 4609942229308403, + 122542368738281250 + ], + "lower_bound": [ + 161596275252669928, + 129277285141539087 + ], + "marginal": [ + 264760015527, + 1589457031250 + ], + "n": 9, + "positive": true, + "q": 5, + "ratio": [ + 7327305090030540973058593750, + 5404335161267730800020642713 + ] + }, + { + "joint": [ + 14173501477311457, + 529160488735546875 + ], + "lower_bound": [ + 2313769374635486612, + 1851016431793899573 + ], + "marginal": [ + 16679880978201, + 119209287109375 + ], + "n": 10, + "positive": true, + "q": 5, + "ratio": [ + 42240325173849304749552490234375, + 30874733771016554206915596208173 + ] + }, + { + "joint": [ + 693793180872372449567, + 36379787176847460937500 + ], + "lower_bound": [ + 84838249637509193488, + 67870608059069977077 + ], + "marginal": [ + 5559960326067, + 47305273437500 + ], + "n": 11, + "positive": true, + "q": 5, + "ratio": [ + 32820076130240473516108613476562500, + 23773546951211752867985849540668017 + ] + }, + { + "joint": [ + 237490765585994835497, + 17490282640434228515625 + ], + "lower_bound": [ + 10792405438379320442012, + 8633924608972604033673 + ], + "marginal": [ + 7355827511386641, + 74505805908203125 + ], + "n": 12, + "positive": true, + "q": 5, + "ratio": [ + 88472204428703487041947629586181640625, + 63509660169918827440939200374086362393 + ] + }, + { + "joint": [ + 13, + 21 + ], + "lower_bound": [ + 35, + 31 + ], + "marginal": [ + 31, + 42 + ], + "n": 1, + "positive": true, + "q": 6, + "ratio": [ + 1092, + 961 + ] + }, + { + "joint": [ + 416, + 903 + ], + "lower_bound": [ + 7955, + 6727 + ], + "marginal": [ + 961, + 1548 + ], + "n": 2, + "positive": true, + "q": 6, + "ratio": [ + 7727616, + 6464647 + ] + }, + { + "joint": [ + 414349, + 1202796 + ], + "lower_bound": [ + 1531985, + 1281013 + ], + "marginal": [ + 29791, + 55944 + ], + "n": 3, + "positive": true, + "q": 6, + "ratio": [ + 46360680912, + 38162658283 + ] + }, + { + "joint": [ + 2795728, + 10874115 + ], + "lower_bound": [ + 7751675, + 6464647 + ], + "marginal": [ + 923521, + 2015280 + ], + "n": 4, + "positive": true, + "q": 6, + "ratio": [ + 270440386744320, + 220898778697219 + ] + }, + { + "joint": [ + 2162939753, + 11282746608 + ], + "lower_bound": [ + 344601355, + 287215031 + ], + "marginal": [ + 923521, + 2340576 + ], + "n": 5, + "positive": true, + "q": 6, + "ratio": [ + 10125049750635456, + 8222722491968681 + ] + }, + { + "joint": [ + 6047009306, + 42315590457 + ], + "lower_bound": [ + 1419601613105, + 1183042406773 + ], + "marginal": [ + 887503681, + 2612129472 + ], + "n": 6, + "positive": true, + "q": 6, + "ratio": [ + 9098249025980659064832, + 7349681435530957819891 + ] + }, + { + "joint": [ + 280399265048461, + 2632423105867968 + ], + "lower_bound": [ + 1848405166613705, + 1540348726232557 + ], + "marginal": [ + 27512614111, + 94036940928 + ], + "n": 7, + "positive": true, + "q": 6, + "ratio": [ + 52735778247233484228623616, + 42379020101206723585811827 + ] + }, + { + "joint": [ + 117564164939546, + 1480743139695939 + ], + "lower_bound": [ + 9292063585844555, + 7743397728926839 + ], + "marginal": [ + 852891037441, + 3385331553024 + ], + "n": 8, + "positive": true, + "q": 6, + "ratio": [ + 305659143993417946562678095872, + 244358157326679715381054822963 + ] + }, + { + "joint": [ + 7268298020805978637, + 122818830070902577920 + ], + "lower_bound": [ + 63948088445651234825, + 53290089610096666669 + ], + "marginal": [ + 26439622160671, + 121871945986560 + ], + "n": 9, + "positive": true, + "q": 6, + "ratio": [ + 1771603247611774359051970498237440, + 1408969834199255237932200648374899 + ] + }, + { + "joint": [ + 110814045934171463, + 2512203584718354408 + ], + "lower_bound": [ + 216260877654093719585, + 180217408856477581477 + ], + "marginal": [ + 819628286980801, + 4387390115982336 + ], + "n": 10, + "positive": true, + "q": 6, + "ratio": [ + 186694828739941034537502145258586112, + 147711286105153354927260926812223077 + ] + }, + { + "joint": [ + 14492432230046821944961, + 440787383133413085084672 + ], + "lower_bound": [ + 3102873653723390655745, + 2585728075750690820357 + ], + "marginal": [ + 819628286980801, + 5095033694779392 + ], + "n": 11, + "positive": true, + "q": 6, + "ratio": [ + 1919825193816280471443724590296787136512, + 1511086477681225214297430024409462727341 + ] + }, + { + "joint": [ + 2025418068095499331201, + 82647634558993781932368 + ], + "lower_bound": [ + 122214702437006983798865, + 101845585606643272647061 + ], + "marginal": [ + 787662783788549761, + 5686057605550583808 + ], + "n": 12, + "positive": true, + "q": 6, + "ratio": [ + 26534347339424219668620018807642085924012032, + 20776974166155457163102778102414944325727039 + ] + }, + { + "joint": [ + 37, + 56 + ], + "lower_bound": [ + 48, + 43 + ], + "marginal": [ + 43, + 56 + ], + "n": 1, + "positive": true, + "q": 7, + "ratio": [ + 2072, + 1849 + ] + }, + { + "joint": [ + 407, + 798 + ], + "lower_bound": [ + 4275, + 3698 + ], + "marginal": [ + 1849, + 2793 + ], + "n": 2, + "positive": true, + "q": 7, + "ratio": [ + 7957257, + 6837602 + ] + }, + { + "joint": [ + 1029451, + 2606800 + ], + "lower_bound": [ + 1759200, + 1510633 + ], + "marginal": [ + 79507, + 137200 + ], + "n": 3, + "positive": true, + "q": 7, + "ratio": [ + 141240677200, + 120105897931 + ] + }, + { + "joint": [ + 14667059, + 48037150 + ], + "lower_bound": [ + 7974447, + 6837602 + ], + "marginal": [ + 3418801, + 6725201 + ], + "n": 4, + "positive": true, + "q": 7, + "ratio": [ + 690472438977013, + 584410013880050 + ] + }, + { + "joint": [ + 217785651197, + 923074188456 + ], + "lower_bound": [ + 11171364336, + 9576061601 + ], + "marginal": [ + 3418801, + 7663992 + ], + "n": 5, + "positive": true, + "q": 7, + "ratio": [ + 1669107488488598424, + 1407761906035097243 + ] + }, + { + "joint": [ + 687126629519, + 3769439303966 + ], + "lower_bound": [ + 12050488609275, + 10329107222066 + ], + "marginal": [ + 6321363049, + 16148148793 + ], + "n": 6, + "positive": true, + "q": 7, + "ratio": [ + 77670761371737786143969, + 65294036722727049839234 + ] + }, + { + "joint": [ + 15295672663525753, + 108605989522200800 + ], + "lower_bound": [ + 43527088381915200, + 37309007104713499 + ], + "marginal": [ + 271818611107, + 791260114400 + ], + "n": 7, + "positive": true, + "q": 7, + "ratio": [ + 12102855701566340026126143200, + 10141282492984418611334233393 + ] + }, + { + "joint": [ + 978128212626191, + 8989357798426950 + ], + "lower_bound": [ + 32754221959784247, + 28075057066797602 + ], + "marginal": [ + 11688200277601, + 38771751370401 + ], + "n": 8, + "positive": true, + "q": 7, + "ratio": [ + 9822249661894207018387246101069, + 8203672245045191212412027820050 + ] + }, + { + "joint": [ + 3225650782105069609, + 38370580873993261432 + ], + "lower_bound": [ + 23062046994953271888, + 19767470020087972033 + ], + "marginal": [ + 502592611936843, + 1899815857503256 + ], + "n": 9, + "positive": true, + "q": 7, + "ratio": [ + 6128142506610991193266058824146904, + 5101748740183940334216344831889853 + ] + }, + { + "joint": [ + 924180428125936718537, + 14229381439078975154818 + ], + "lower_bound": [ + 26977879642532262370125, + 23123897068532507313518 + ], + "marginal": [ + 21611482313284249, + 93090977300134793 + ], + "n": 10, + "positive": true, + "q": 7, + "ratio": [ + 602230014791303007613089149187412304887, + 499741692510795775289470699478494177982 + ] + }, + { + "joint": [ + 75431607343263800558507153, + 1503248777963153980063141200 + ], + "lower_bound": [ + 8309187024427921372509600, + 7122160318719494565847793 + ], + "marginal": [ + 21611482313284249, + 106080416039161200 + ], + "n": 11, + "positive": true, + "q": 7, + "ratio": [ + 8001816289476071022478493475647458320063600, + 6618578995696394462361860264858613767435651 + ] + }, + { + "joint": [ + 9152644679646875232802031, + 236087147938096820963350550 + ], + "lower_bound": [ + 13787924084027148225002619, + 11818220646813596020901354 + ], + "marginal": [ + 39959630797262576401, + 223511436608353935601 + ], + "n": 12, + "positive": true, + "q": 7, + "ratio": [ + 14320045327795763277520026643264112548292039417, + 11806293343181425432969765178960883407733673850 + ] + }, + { + "joint": [ + 25, + 36 + ], + "lower_bound": [ + 21, + 19 + ], + "marginal": [ + 19, + 24 + ], + "n": 1, + "positive": true, + "q": 8, + "ratio": [ + 400, + 361 + ] + }, + { + "joint": [ + 725, + 1314 + ], + "lower_bound": [ + 33215, + 29241 + ], + "marginal": [ + 3249, + 4672 + ], + "n": 2, + "positive": true, + "q": 8, + "ratio": [ + 108390400, + 95004009 + ] + }, + { + "joint": [ + 960485, + 2186496 + ], + "lower_bound": [ + 1714895, + 1502121 + ], + "marginal": [ + 20577, + 33280 + ], + "n": 3, + "positive": true, + "q": 8, + "ratio": [ + 319649408000, + 278182294353 + ] + }, + { + "joint": [ + 12245105, + 35051328 + ], + "lower_bound": [ + 108557071, + 95004009 + ], + "marginal": [ + 10556001, + 19173376 + ], + "n": 4, + "positive": true, + "q": 8, + "ratio": [ + 15025920148766720, + 13037211382104117 + ] + }, + { + "joint": [ + 797665137625, + 2872095031296 + ], + "lower_bound": [ + 6274446871, + 5490293409 + ], + "marginal": [ + 1172889, + 2392064 + ], + "n": 5, + "positive": true, + "q": 8, + "ratio": [ + 3816132119535616000, + 3303465934794752313 + ] + }, + { + "joint": [ + 20291547082175, + 91909802041344 + ], + "lower_bound": [ + 1467842426308895, + 1284367653027801 + ], + "marginal": [ + 34296447249, + 78536507392 + ], + "n": 6, + "positive": true, + "q": 8, + "ratio": [ + 50996071597259293406003200, + 44049247460389912126969449 + ] + }, + { + "joint": [ + 3775411771722995, + 21512226446770176 + ], + "lower_bound": [ + 10624457519238745, + 9296406423463023 + ], + "marginal": [ + 217210832577, + 558482063360 + ], + "n": 7, + "positive": true, + "q": 8, + "ratio": [ + 21084997563054915499589632000, + 18173521612931166480629702439 + ] + }, + { + "joint": [ + 168064967376973105, + 1204685246482219008 + ], + "lower_bound": [ + 4695687892401526447, + 4108727310190812873 + ], + "marginal": [ + 111429157112001, + 321685685272576 + ], + "n": 8, + "positive": true, + "q": 8, + "ratio": [ + 6920204057724764551199711496765440, + 5951816272709077615673650816655349 + ] + }, + { + "joint": [ + 21888784136905904995225, + 197375642364331432083456 + ], + "lower_bound": [ + 15464467561392367543487, + 13531409313946405437753 + ], + "marginal": [ + 705717995042673, + 2287542665740288 + ], + "n": 9, + "positive": true, + "q": 8, + "ratio": [ + 100143055228702925996311214743460249600, + 85944231460260077513779614820322103921 + ] + }, + { + "joint": [ + 556795956406703263603625, + 6316020601981344807911424 + ], + "lower_bound": [ + 5769652370599529739015325, + 5048445835133579943039051 + ], + "marginal": [ + 362033331456891249, + 1317624576540147712 + ], + "n": 10, + "positive": true, + "q": 8, + "ratio": [ + 23476737160948765861359204223565789396992000, + 20104762308103852498418720504878760538811689 + ] + }, + { + "joint": [ + 725171055434256987801817445, + 10348168163773132284371140608 + ], + "lower_bound": [ + 56414378884331780029099655, + 49362581539309818493814193 + ], + "marginal": [ + 40225925717432361, + 164382013464248320 + ], + "n": 11, + "positive": true, + "q": 8, + "ratio": [ + 1192050781982771970121598737028710267879424000, + 1018641291107360036129791963118730059580732249 + ] + }, + { + "joint": [ + 709482258809908878607100255, + 12736206972257223881080700928 + ], + "lower_bound": [ + 203029274285297943173564327503, + 177650615007752515608067787817 + ], + "marginal": [ + 1176246293903439668001, + 5396990266126920318976 + ], + "n": 12, + "positive": true, + "q": 8, + "ratio": [ + 245060406066356395314269589487579229244352700088320, + 208960877512535675388191777054582145243492992543817 + ] + }, + { + "joint": [ + 13, + 18 + ], + "lower_bound": [ + 80, + 73 + ], + "marginal": [ + 73, + 90 + ], + "n": 1, + "positive": true, + "q": 9, + "ratio": [ + 5850, + 5329 + ] + }, + { + "joint": [ + 37, + 63 + ], + "lower_bound": [ + 29848, + 26645 + ], + "marginal": [ + 5329, + 7371 + ], + "n": 2, + "positive": true, + "q": 9, + "ratio": [ + 31909059, + 28398241 + ] + }, + { + "joint": [ + 57181, + 119556 + ], + "lower_bound": [ + 39799520, + 35400547 + ], + "marginal": [ + 389017, + 597780 + ], + "n": 3, + "positive": true, + "q": 9, + "ratio": [ + 170908290900, + 151334226289 + ] + }, + { + "joint": [ + 85853209, + 220610709 + ], + "lower_bound": [ + 31944968, + 28398241 + ], + "marginal": [ + 28398241, + 48426741 + ], + "n": 4, + "positive": true, + "q": 9, + "ratio": [ + 37418320046356821, + 33064863767657321 + ] + }, + { + "joint": [ + 12819325055, + 40493560338 + ], + "lower_bound": [ + 235805176880, + 209607416821 + ], + "marginal": [ + 28398241, + 53734590 + ], + "n": 5, + "positive": true, + "q": 9, + "ratio": [ + 44774676433964909250, + 39502834681247769623 + ] + }, + { + "joint": [ + 221223625411, + 859056327189 + ], + "lower_bound": [ + 807839531004184, + 718080903741305 + ], + "marginal": [ + 151334226289, + 317733162111 + ], + "n": 6, + "positive": true, + "q": 9, + "ratio": [ + 1897832214958402854070767, + 1671849507393788885941033 + ] + }, + { + "joint": [ + 644648054239846579, + 3077408354424035832 + ], + "lower_bound": [ + 7430532263888373440, + 6604919200011042487 + ], + "marginal": [ + 11047398519097, + 25736390913960 + ], + "n": 7, + "positive": true, + "q": 9, + "ratio": [ + 82954571629201903751799946714200, + 72967174588957332716930947874239 + ] + }, + { + "joint": [ + 11038243236902569, + 64779139340210169 + ], + "lower_bound": [ + 2976744909269703208, + 2645995561504479761 + ], + "marginal": [ + 806460091894081, + 2084647707077481 + ], + "n": 8, + "positive": true, + "q": 9, + "ratio": [ + 99613962957246746320542677276874681, + 87489482770971561306157405827980281 + ] + }, + { + "joint": [ + 131110433356717286293, + 945900143736289373610 + ], + "lower_bound": [ + 168809645383868579591600, + 150053018762180713744747 + ], + "marginal": [ + 58871586708267913, + 168856464660696450 + ], + "n": 9, + "positive": true, + "q": 9, + "ratio": [ + 110694221283735647439281713297093799250, + 97075376976868943679173983643784312121 + ] + }, + { + "joint": [ + 135784984600679586557411, + 1204294268798513816419089 + ], + "lower_bound": [ + 95784128000986371040417448, + 85141447159360349062692475 + ], + "marginal": [ + 4297625829703557649, + 13677373641003196851 + ], + "n": 10, + "positive": true, + "q": 9, + "ratio": [ + 16714637722992239750078251305663749813214849, + 14636243299616305265847216654972161852839651 + ] + }, + { + "joint": [ + 266606324298963547379282693, + 2906860257460762983230362092 + ], + "lower_bound": [ + 824576406879239871865721440, + 732956806167433693222463813 + ], + "marginal": [ + 4297625829703557649, + 15176263903460821980 + ], + "n": 11, + "positive": true, + "q": 9, + "ratio": [ + 262995715833027470712185564047878916636919489100, + 229948109463679644138250468499353519142115461501 + ] + }, + { + "joint": [ + 4809846107708056227876185659, + 64470007854998125660037929959 + ], + "lower_bound": [ + 12189663739484579730059755784, + 10835256657419145769783834873 + ], + "marginal": [ + 22902048046490258711521, + 89737248461446269904221 + ], + "n": 12, + "positive": true, + "q": 9, + "ratio": [ + 11653803591175388660420384929690895035528796081699253, + 10174132311134935427657040249242187358238779473545153 + ] + }, + { + "joint": [ + 41, + 55 + ], + "lower_bound": [ + 99, + 91 + ], + "marginal": [ + 91, + 110 + ], + "n": 1, + "positive": true, + "q": 10, + "ratio": [ + 9020, + 8281 + ] + }, + { + "joint": [ + 3772, + 6105 + ], + "lower_bound": [ + 100899, + 91091 + ], + "marginal": [ + 8281, + 11100 + ], + "n": 2, + "positive": true, + "q": 10, + "ratio": [ + 837384000, + 754324571 + ] + }, + { + "joint": [ + 10536467, + 20553500 + ], + "lower_bound": [ + 30966903, + 27882127 + ], + "marginal": [ + 753571, + 1111000 + ], + "n": 3, + "positive": true, + "q": 10, + "ratio": [ + 23412029674000, + 21011162325517 + ] + }, + { + "joint": [ + 15997006, + 37635125 + ], + "lower_bound": [ + 838091619, + 754324571 + ], + "marginal": [ + 68574961, + 111110000 + ], + "n": 4, + "positive": true, + "q": 10, + "ratio": [ + 5829961664244800000, + 5224505581804339831 + ] + }, + { + "joint": [ + 48229935811, + 136868550000 + ], + "lower_bound": [ + 846590043519, + 761936391671 + ], + "marginal": [ + 68574961, + 122100000 + ], + "n": 5, + "positive": true, + "q": 10, + "ratio": [ + 129555253575508200000, + 115968975835172659381 + ] + }, + { + "joint": [ + 4061354960419, + 13902776387500 + ], + "lower_bound": [ + 23369061533093613, + 21032173487842517 + ], + "marginal": [ + 567869252041, + 1111111000000 + ], + "n": 6, + "positive": true, + "q": 10, + "ratio": [ + 361009293714089240720000000, + 322797962901018387448346681 + ] + }, + { + "joint": [ + 14948896166751172121, + 61728388271605000000 + ], + "lower_bound": [ + 63797643727123556349, + 57417885297912007141 + ], + "marginal": [ + 51676101935731, + 111111110000000 + ], + "n": 7, + "positive": true, + "q": 10, + "ratio": [ + 3321976892724935656330728620000000, + 2967132493589011197831537595055071 + ] + }, + { + "joint": [ + 77453981505980631583, + 385802464891975312500 + ], + "lower_bound": [ + 574810557566189441859, + 517329508154704976731 + ], + "marginal": [ + 4702525276151521, + 11111111100000000 + ], + "n": 8, + "positive": true, + "q": 10, + "ratio": [ + 275391933968094755829402198816000000000, + 245708263907849990136368468959061042951 + ] + }, + { + "joint": [ + 27841453386874816518649, + 167285623289504500000000 + ], + "lower_bound": [ + 5870093265939580673347341, + 5283083946936526060126069 + ], + "marginal": [ + 427929800129788411, + 1111111111000000000 + ], + "n": 9, + "positive": true, + "q": 10, + "ratio": [ + 2536665752772705596396493893941198000000000, + 2260789057481441280257036717160052955186359 + ] + }, + { + "joint": [ + 94420492794274002807013, + 684350277770934275000000 + ], + "lower_bound": [ + 4370551268397455587315588389, + 3933496142213796385840295501 + ], + "marginal": [ + 38941611811810745401, + 111111111110000000000 + ], + "n": 10, + "positive": true, + "q": 10, + "ratio": [ + 4196466346370213239069789332085772000000000000, + 3736016581301092022759479068781517156315042461 + ] + }, + { + "joint": [ + 7060367886682680063380883246841, + 61728395061049382716050000000000 + ], + "lower_bound": [ + 480760639637937070250471472279, + 432684575682459214254243250511 + ], + "marginal": [ + 38941611811810745401, + 122100122100000000000 + ], + "n": 11, + "positive": true, + "q": 10, + "ratio": [ + 1724143562069748399388083166490261078572200000000000, + 1533298565269778047936377797641653057841235657641901 + ] + }, + { + "joint": [ + 8343375781453462376286660541, + 87992352408570666306250000000 + ], + "lower_bound": [ + 131392041483344552465851664230833, + 118252837335270373002664978077497 + ], + "marginal": [ + 322475487413604782665681, + 1111111111111000000000000 + ], + "n": 12, + "positive": true, + "q": 10, + "ratio": [ + 117178077641734687121417368957551526290084640000000000000, + 104094534517055041203579130721338194216864839386169954761 + ] + }, + { + "joint": [ + 101, + 132 + ], + "lower_bound": [ + 40, + 37 + ], + "marginal": [ + 37, + 44 + ], + "n": 1, + "positive": true, + "q": 11, + "ratio": [ + 4444, + 4107 + ] + }, + { + "joint": [ + 404, + 627 + ], + "lower_bound": [ + 40565, + 36963 + ], + "marginal": [ + 12321, + 16093 + ], + "n": 2, + "positive": true, + "q": 11, + "ratio": [ + 500621044, + 455421123 + ] + }, + { + "joint": [ + 140732693, + 259161672 + ], + "lower_bound": [ + 66675440, + 60631641 + ], + "marginal": [ + 455877, + 649528 + ], + "n": 3, + "positive": true, + "q": 11, + "ratio": [ + 91409824618904, + 82921711812471 + ] + }, + { + "joint": [ + 1794312268, + 3922743165 + ], + "lower_bound": [ + 500946025, + 455421123 + ], + "marginal": [ + 151807041, + 235793305 + ], + "n": 4, + "positive": true, + "q": 11, + "ratio": [ + 4653955018611423140, + 4217304118583149623 + ] + }, + { + "joint": [ + 35404129824961, + 91898837229276 + ], + "lower_bound": [ + 179288474120, + 162990159687 + ], + "marginal": [ + 50602347, + 85679132 + ], + "n": 5, + "positive": true, + "q": 11, + "ratio": [ + 3033395112617970413852, + 2746478977816306134537 + ] + }, + { + "joint": [ + 14983528358324, + 46178686791963 + ], + "lower_bound": [ + 13017518509187465, + 11834112871522647 + ], + "marginal": [ + 1870414552161, + 3452271037237 + ], + "n": 6, + "positive": true, + "q": 11, + "ratio": [ + 24466966066879947260816802724, + 22134696926811757518674290167 + ] + }, + { + "joint": [ + 222453502288407634037, + 814027448298417776016 + ], + "lower_bound": [ + 148347774434504909920, + 134861619489210515169 + ], + "marginal": [ + 69205338429957, + 139241604997616 + ], + "n": 7, + "positive": true, + "q": 11, + "ratio": [ + 30974782695978722708108945585455792, + 27999432053888695158441772777553199 + ] + }, + { + "joint": [ + 202411036553995537364, + 879440413007199382251 + ], + "lower_bound": [ + 556760190581822625545, + 506145630363069481803 + ], + "marginal": [ + 23045377697175681, + 50544702828493489 + ], + "n": 8, + "positive": true, + "q": 11, + "ratio": [ + 787772038270835866873204978023027170692, + 711523350511012464752413095396741603423 + ] + }, + { + "joint": [ + 279544217403282872193117989, + 1442099360397802262781272340 + ], + "lower_bound": [ + 11640156103356433314186200, + 10581960099634831115319447 + ], + "marginal": [ + 852678974795500197, + 2038636348201886620 + ], + "n": 9, + "positive": true, + "q": 11, + "ratio": [ + 569889002527982874970822763799024750060407180, + 514311848677760464096832043238826484966570363 + ] + }, + { + "joint": [ + 1424404854397462859506917388, + 8724701134076249116590093573 + ], + "lower_bound": [ + 40505997251322094706606798005, + 36823633866911371986989455923 + ], + "marginal": [ + 283942098606901565601, + 740024994423222267661 + ], + "n": 10, + "positive": true, + "q": 11, + "ratio": [ + 11595047138750824966439861564406125713916660884148, + 10455779878502988786990732147869941456347882504723 + ] + }, + { + "joint": [ + 351286725220180442370893024354261, + 2554766986177890565583776539377112 + ], + "lower_bound": [ + 2970439798684204382631833432240, + 2700399817001481311914860622887 + ], + "marginal": [ + 94647366202300521867, + 268897970947433051224 + ], + "n": 11, + "positive": true, + "q": 11, + "ratio": [ + 94460287632474977917077551071326614499824841535665464, + 85110048213997383994472341927690725583294725128619657 + ] + }, + { + "joint": [ + 49174877494381312533123508210924, + 424624732594229772977394098540277 + ], + "lower_bound": [ + 27196902113957086342166338789345, + 24724456467248733148359182116539 + ], + "marginal": [ + 3498450596935634189769921, + 10834705943388058361345353 + ], + "n": 12, + "positive": true, + "q": 11, + "ratio": [ + 5860748711991281662296619239922430262110335139334043597892, + 5276334658692081337198843419602430153234260356979348228559 + ] + }, + { + "joint": [ + 61, + 78 + ], + "lower_bound": [ + 143, + 133 + ], + "marginal": [ + 133, + 156 + ], + "n": 1, + "positive": true, + "q": 12, + "ratio": [ + 19032, + 17689 + ] + }, + { + "joint": [ + 4087, + 6123 + ], + "lower_bound": [ + 250415, + 229957 + ], + "marginal": [ + 17689, + 22608 + ], + "n": 2, + "positive": true, + "q": 12, + "ratio": [ + 4435147008, + 4067709373 + ] + }, + { + "joint": [ + 145758829, + 255696480 + ], + "lower_bound": [ + 402860315, + 369364009 + ], + "marginal": [ + 2352637, + 3257280 + ], + "n": 3, + "positive": true, + "q": 12, + "ratio": [ + 949554637050240, + 868979434041733 + ] + }, + { + "joint": [ + 4482037159, + 9210366360 + ], + "lower_bound": [ + 4437403223, + 4067709373 + ], + "marginal": [ + 312900721, + 469069056 + ], + "n": 4, + "positive": true, + "q": 12, + "ratio": [ + 201828954156388982784, + 184554433366372900285 + ] + }, + { + "joint": [ + 317347317801181, + 763981214750208 + ], + "lower_bound": [ + 7721575595591, + 7078127209741 + ], + "marginal": [ + 312900721, + 507866112 + ], + "n": 5, + "positive": true, + "q": 12, + "ratio": [ + 322339896890628366956544, + 294561897265271057393713 + ] + }, + { + "joint": [ + 6501247671115159, + 18335622329047296 + ], + "lower_bound": [ + 126080986753454315, + 115574264727550489 + ], + "marginal": [ + 5534900853769, + 9726654763008 + ], + "n": 6, + "positive": true, + "q": 12, + "ratio": [ + 9105896394107557745791858311168, + 8315997254685167108647994759533 + ] + }, + { + "joint": [ + 690432840301381965709, + 2281245546369819893760 + ], + "lower_bound": [ + 2615929664001078637355, + 2397935580709031097049 + ], + "marginal": [ + 736141813551277, + 1400638321704960 + ], + "n": 7, + "positive": true, + "q": 12, + "ratio": [ + 1934093389379432611058391130270433280, + 1765220647162280710381562345924881573 + ] + }, + { + "joint": [ + 10608213378637385688007, + 41062420972675394472960 + ], + "lower_bound": [ + 28793268534693818461031, + 26393829549782585056621 + ], + "marginal": [ + 97906861202319841, + 201691918755495936 + ], + "n": 8, + "positive": true, + "q": 12, + "ratio": [ + 410801454893778555206641062216931668393984, + 374699865917596472321595617636302824002845 + ] + }, + { + "joint": [ + 1502123020387372346763301501, + 6811762906047145501259071488 + ], + "lower_bound": [ + 6663338232105959701681690163, + 6108060047432298373711770673 + ], + "marginal": [ + 13021612539908538853, + 29043636305951195136 + ], + "n": 9, + "positive": true, + "q": 12, + "ratio": [ + 87254229381855509529347540256333503072105398272, + 79536791308158761126263766927035126226846458069 + ] + }, + { + "joint": [ + 92317977327737190683762107667, + 490446929329786294084994531328 + ], + "lower_bound": [ + 10634687822432314809700982376575, + 9748463837433822672251821661557 + ], + "marginal": [ + 1731874467807835667449, + 4182283628118889463808 + ], + "n": 10, + "positive": true, + "q": 12, + "ratio": [ + 18532798327624611729971815854182405075940364599164928, + 16883115620399633078994431299694142888889015279558093 + ] + }, + { + "joint": [ + 12917218962480398785539354099313, + 80394525903126937989273385697280 + ], + "lower_bound": [ + 504412070646229481171551155755, + 462377731426631409228575871961 + ], + "marginal": [ + 1731874467807835667449, + 4528186785337316474880 + ], + "n": 11, + "positive": true, + "q": 12, + "ratio": [ + 116983160418424686735772662858758944445994677179514880, + 106503764942911988750923533593629025279674762733166037 + ] + }, + { + "joint": [ + 2574991018342774313221673844434371, + 18775213895555353989109821139845120 + ], + "lower_bound": [ + 14370741102016733822095184720927123, + 13173179343517818943722165852543313 + ], + "marginal": [ + 30635127461052805121505361, + 86723833312789201227350016 + ], + "n": 12, + "positive": true, + "q": 12, + "ratio": [ + 64314170454726167066370174309468912386670171486673946246381568, + 58516494097116563326216819478002521293171031797426387059143985 + ] + }, + { + "joint": [ + 145, + 182 + ], + "lower_bound": [ + 168, + 157 + ], + "marginal": [ + 157, + 182 + ], + "n": 1, + "positive": true, + "q": 13, + "ratio": [ + 26390, + 24649 + ] + }, + { + "joint": [ + 11455, + 16653 + ], + "lower_bound": [ + 186660, + 172543 + ], + "marginal": [ + 24649, + 30927 + ], + "n": 2, + "positive": true, + "q": 13, + "ratio": [ + 4605494205, + 4253012407 + ] + }, + { + "joint": [ + 37903841, + 63792092 + ], + "lower_bound": [ + 255697680, + 236063473 + ], + "marginal": [ + 3869893, + 5228860 + ], + "n": 3, + "positive": true, + "q": 13, + "ratio": [ + 990969390256300, + 913540381718389 + ] + }, + { + "joint": [ + 4150442039, + 8089307863 + ], + "lower_bound": [ + 4607362428, + 4253012407 + ], + "marginal": [ + 607573201, + 883705901 + ], + "n": 4, + "positive": true, + "q": 13, + "ratio": [ + 47681011581096037807, + 43928278154232981719 + ] + }, + { + "joint": [ + 2047169120589725, + 4620935271976842 + ], + "lower_bound": [ + 20365470639864, + 18798922412141 + ], + "marginal": [ + 607573201, + 951252666 + ], + "n": 5, + "positive": true, + "q": 13, + "ratio": [ + 1947375083713851398456850, + 1793210270051338335434537 + ] + }, + { + "joint": [ + 49788380168751655, + 130156691969574361 + ], + "lower_bound": [ + 155377972893142380, + 143425839929787073 + ], + "marginal": [ + 14976071831449, + 25239591813787 + ], + "n": 6, + "positive": true, + "q": 13, + "ratio": [ + 16336299102876210707093104877305, + 15035689768920781827382005411439 + ] + }, + { + "joint": [ + 1473397926315984588767, + 4460887253932758011272 + ], + "lower_bound": [ + 13319314725659208614880, + 12294752201704485009199 + ], + "marginal": [ + 2351243277537493, + 4265491079278520 + ], + "n": 7, + "positive": true, + "q": 13, + "ratio": [ + 31423828554641511944623250686281924200, + 28907953463246961563777180666172398107 + ] + }, + { + "joint": [ + 26875345523148825129599, + 94236244732251390735603 + ], + "lower_bound": [ + 39977532428307577397388, + 36902337665917718348767 + ], + "marginal": [ + 369145194573386401, + 720867993213800601 + ], + "n": 8, + "positive": true, + "q": 13, + "ratio": [ + 251856493124597317273380365249469198156987, + 231579450504266032480884330952795939598639 + ] + }, + { + "joint": [ + 2945657321264553363775851745, + 11962139507012361510766000078 + ], + "lower_bound": [ + 6164890869320508565306427592, + 5690668495303297609989823213 + ], + "marginal": [ + 57955795548021664957, + 121826690863736800942 + ], + "n": 9, + "positive": true, + "q": 13, + "ratio": [ + 358859683868199781977604392512273422177568343790, + 329807219845366002623019237137971088014347246841 + ] + }, + { + "joint": [ + 175843382707529055714014889025, + 827018826903244342271245515083 + ], + "lower_bound": [ + 5147403654468710936481750210300, + 4751449527242060622679202908993 + ], + "marginal": [ + 9099059901039401398249, + 20588710756109377851047 + ], + "n": 10, + "positive": true, + "q": 13, + "ratio": [ + 47065051084235096157479602345048187189607516905769275, + 43233723865140854687514313581078342784880112496553257 + ] + }, + { + "joint": [ + 829586265584587762007337209775197, + 4518701423806830451034877010497156 + ], + "lower_bound": [ + 1472157445199267155296571509825360, + 1358914564800328397987291433370247 + ], + "marginal": [ + 9099059901039401398249, + 22162370176969917307140 + ], + "n": 11, + "positive": true, + "q": 13, + "ratio": [ + 91927989558078565493610641455550186823758761795015032900, + 84403507348067527872989221944380528044508577460842439477 + ] + }, + { + "joint": [ + 232023579190785747845330526886332359, + 1463682702862241045091863576287555343 + ], + "lower_bound": [ + 66069147796621717148380049979109764, + 60986905658423965489265325663855361 + ], + "marginal": [ + 224282727500720205065439601, + 588034167905566113995468101 + ], + "n": 12, + "positive": true, + "q": 13, + "ratio": [ + 1773691300211023989546667644957375223322231499274024682491543367, + 1627718835605151575751799002661437443133356700236764433520564359 + ] + }, + { + "joint": [ + 17, + 21 + ], + "lower_bound": [ + 65, + 61 + ], + "marginal": [ + 61, + 70 + ], + "n": 1, + "positive": true, + "q": 14, + "ratio": [ + 11900, + 11163 + ] + }, + { + "joint": [ + 3128, + 4431 + ], + "lower_bound": [ + 540371, + 502335 + ], + "marginal": [ + 33489, + 41356 + ], + "n": 2, + "positive": true, + "q": 14, + "ratio": [ + 3622123904, + 3364539363 + ] + }, + { + "joint": [ + 105363569, + 171089772 + ], + "lower_bound": [ + 464142835, + 431036919 + ], + "marginal": [ + 2042829, + 2702840 + ], + "n": 3, + "positive": true, + "q": 14, + "ratio": [ + 2847808688359600, + 2641604154611553 + ] + }, + { + "joint": [ + 4504271516, + 8386439523 + ], + "lower_bound": [ + 3623313551, + 3364539363 + ], + "marginal": [ + 1121513121, + 1589308336 + ], + "n": 4, + "positive": true, + "q": 14, + "ratio": [ + 801771742014449626112, + 743354883219919938831 + ] + }, + { + "joint": [ + 54875225730835, + 117157019848848 + ], + "lower_bound": [ + 16655720253965, + 15466039776297 + ], + "marginal": [ + 373837707, + 567404320 + ], + "n": 5, + "positive": true, + "q": 14, + "ratio": [ + 311364401406509362072000, + 288563825149233929418861 + ] + }, + { + "joint": [ + 12897179070893653, + 31573875256446726 + ], + "lower_bound": [ + 23426963037579759671, + 21753610213226138955 + ], + "marginal": [ + 37558352909169, + 61054981978816 + ], + "n": 6, + "positive": true, + "q": 14, + "ratio": [ + 176385896008218370071681407485952, + 163405953887370085284279537515679 + ] + }, + { + "joint": [ + 3456650984356632758321, + 9703537216967880963264 + ], + "lower_bound": [ + 20006630314330700370395, + 18577585413154650126879 + ], + "marginal": [ + 2291059527459309, + 3988925524420480 + ], + "n": 7, + "positive": true, + "q": 14, + "ratio": [ + 137883233405133497342634372274228140800, + 127687062173991133428205622764078999833 + ] + }, + { + "joint": [ + 18463763219663968953319, + 59434166014870922771622 + ], + "lower_bound": [ + 156112652660560716208127, + 144961748977967839035891 + ], + "marginal": [ + 1257791680575160641, + 2345488209835031296 + ], + "n": 8, + "positive": true, + "q": 14, + "ratio": [ + 38802658891053152482244410645357196351995904, + 35919341327624210510785683677737134244527807 + ] + }, + { + "joint": [ + 19794335873708291781748711313, + 73063133541328256220763841280 + ], + "lower_bound": [ + 131320402439731965841326592075, + 121940373699502059033685949391 + ], + "marginal": [ + 76725292515084799101, + 153238563049442393600 + ], + "n": 9, + "positive": true, + "q": 14, + "ratio": [ + 30332555858050874591383674025628283000301187968000, + 28067732524479145869809023573270999816769064892473 + ] + }, + { + "joint": [ + 7689585348976774699999024501, + 32546304942704344893164099232 + ], + "lower_bound": [ + 91757146658062573909434299557861, + 85203064754226819211244705611425 + ], + "marginal": [ + 42122185590781554706449, + 90104275073361382091776 + ], + "n": 10, + "positive": true, + "q": 14, + "ratio": [ + 155201651020481606261361192440469971244362111431245824, + 143557572259236826881358871387598624959191707557423193 + ] + }, + { + "joint": [ + 113351254879740835794764906716310513, + 550131494300621439679489084906392576 + ], + "lower_bound": [ + 4710200195144829484053592349277085, + 4373757324064350781374155406288633 + ], + "marginal": [ + 14040728530260518235483, + 32168375071735665674240 + ], + "n": 11, + "positive": true, + "q": 14, + "ratio": [ + 36463256818234108324680745296000204268461667009513452851200, + 33714495845189999782742729904583715827399611067397130441711 + ] + }, + { + "joint": [ + 32727986598377275841728443917570321, + 182138129869845089246708505003945408 + ], + "lower_bound": [ + 6725965037646640489880649067311671903, + 6245538963529172029650448203386767059 + ], + "marginal": [ + 1410629873249683485564270561, + 3461445831219101263123296256 + ], + "n": 12, + "positive": true, + "q": 14, + "ratio": [ + 50752196443266140941742270588037053093655877982918701655816142848, + 46908063129468263659340829674679635624804873462371900307610142419 + ] + }, + { + "joint": [ + 197, + 240 + ], + "lower_bound": [ + 224, + 211 + ], + "marginal": [ + 211, + 240 + ], + "n": 1, + "positive": true, + "q": 15, + "ratio": [ + 47280, + 44521 + ] + }, + { + "joint": [ + 10441, + 14460 + ], + "lower_bound": [ + 190631, + 178084 + ], + "marginal": [ + 44521, + 54225 + ], + "n": 2, + "positive": true, + "q": 15, + "ratio": [ + 8492448375, + 7928477764 + ] + }, + { + "joint": [ + 1868730377, + 2941164000 + ], + "lower_bound": [ + 2425446464, + 2263937371 + ], + "marginal": [ + 9393931, + 12204000 + ], + "n": 3, + "positive": true, + "q": 15, + "ratio": [ + 22805985520908000, + 21267271451495401 + ] + }, + { + "joint": [ + 46250925781, + 82744645500 + ], + "lower_bound": [ + 8494737251, + 7928477764 + ], + "marginal": [ + 1982119441, + 2745950625 + ], + "n": 4, + "positive": true, + "q": 15, + "ratio": [ + 1905041378327483446875, + 1775816460232348921412 + ] + }, + { + "joint": [ + 1498060937707687, + 3046567314150000 + ], + "lower_bound": [ + 115191511639904, + 107512140599281 + ], + "marginal": [ + 1982119441, + 2928150000 + ], + "n": 5, + "positive": true, + "q": 15, + "ratio": [ + 4386547134748763689050000, + 4087681977213728637484121 + ] + }, + { + "joint": [ + 271806969751967521, + 628355332329637500 + ], + "lower_bound": [ + 19231688848852394621, + 17949577105062118444 + ], + "marginal": [ + 88245939632761, + 139013932640625 + ], + "n": 6, + "positive": true, + "q": 15, + "ratio": [ + 1700323010295858442253554431328125, + 1583977297646900653996210044743884 + ] + }, + { + "joint": [ + 20751299737042370032391, + 54532271107656945000000 + ], + "lower_bound": [ + 34781887335627076303232, + 32463094967139954573373 + ], + "marginal": [ + 18619893262512571, + 31278135015000000 + ], + "n": 7, + "positive": true, + "q": 15, + "ratio": [ + 649061954911945246648715621270865000000, + 604459363258954992622135900968354371983 + ] + }, + { + "joint": [ + 105704476986046703210333, + 315765909908124443437500 + ], + "lower_bound": [ + 426212788036424015364283, + 397798602281959719006212 + ], + "marginal": [ + 3928797478390152481, + 7037580380937890625 + ], + "n": 8, + "positive": true, + "q": 15, + "ratio": [ + 11158556301214545753936959892295030857421875, + 10388489791025378033053244330385940510703108 + ] + }, + { + "joint": [ + 1280453296833989563515293040917, + 4348096581123892877559468750000 + ], + "lower_bound": [ + 2438925962773694342160720843104, + 2276330898639080007203949225331 + ], + "marginal": [ + 828976267940322173491, + 1583455585749468750000 + ], + "n": 9, + "positive": true, + "q": 15, + "ratio": [ + 2027540925163103323991552114232509452704762843750000, + 1887024292951064342879283862799095692659051633900521 + ] + }, + { + "joint": [ + 37161933904823297545074765461, + 143448934131702520062004687500 + ], + "lower_bound": [ + 175436378920994593694447743524601, + 163740620326536413984906983563164 + ], + "marginal": [ + 174913992535407978606601, + 356277506794207119140625 + ], + "n": 10, + "positive": true, + "q": 15, + "ratio": [ + 992997086944616871622439124352454894974324181396484375, + 923887923920608459622144949336731781870304311573898244 + ] + }, + { + "joint": [ + 11287145874432361949608225288059931097, + 49527537620732447934538503126562500000 + ], + "lower_bound": [ + 115788010088223514682749840910394944, + 108068809415688947222574017130294841 + ], + "marginal": [ + 174913992535407978606601, + 379916772647892187500000 + ], + "n": 11, + "positive": true, + "q": 15, + "ratio": [ + 4288176033020313915448366920411937014788625273534604687500000, + 3988479600847157481605943870934317483001871929796946036388051 + ] + }, + { + "joint": [ + 135105370509582943389431302143592469, + 673905174447634457202202617773437500 + ], + "lower_bound": [ + 6579728553189616814929095669518371037, + 6141079982977033835543306343472038268 + ], + "marginal": [ + 7787345861668898615544483121, + 18036548781458811347900390625 + ], + "n": 12, + "positive": true, + "q": 15, + "ratio": [ + 5811850534912085320593277392938616787089905269481400452091064453125, + 5403966658452372371929512888677885431330232225392679597740304410364 + ] + }, + { + "joint": [ + 113, + 136 + ], + "lower_bound": [ + 255, + 241 + ], + "marginal": [ + 241, + 272 + ], + "n": 1, + "positive": true, + "q": 16, + "ratio": [ + 61472, + 58081 + ] + }, + { + "joint": [ + 13673, + 18564 + ], + "lower_bound": [ + 1052415, + 987377 + ], + "marginal": [ + 58081, + 69888 + ], + "n": 2, + "positive": true, + "q": 16, + "ratio": [ + 61157031936, + 57347843537 + ] + }, + { + "joint": [ + 75964589, + 116320256 + ], + "lower_bound": [ + 1358606085, + 1273774411 + ], + "marginal": [ + 13997521, + 17895424 + ], + "n": 3, + "positive": true, + "q": 16, + "ratio": [ + 2718837058281472, + 2547097723890733 + ] + }, + { + "joint": [ + 8230053403, + 14215677440 + ], + "lower_bound": [ + 61170719775, + 57347843537 + ], + "marginal": [ + 3373402561, + 4581294080 + ], + "n": 4, + "positive": true, + "q": 16, + "ratio": [ + 53087647266012837969920, + 49718542099674576252049 + ] + }, + { + "joint": [ + 4207648244903933, + 8198544614227968 + ], + "lower_bound": [ + 50307757378515, + 47163541205341 + ], + "marginal": [ + 3373402561, + 4866441216 + ], + "n": 5, + "positive": true, + "q": 16, + "ratio": [ + 40952545682861123023405056, + 38343488175790251863070541 + ] + }, + { + "joint": [ + 1005978004557823, + 2211156147306496 + ], + "lower_bound": [ + 11131156335291466755, + 10435459374780333101 + ], + "marginal": [ + 195930594145441, + 300239974039552 + ], + "n": 6, + "positive": true, + "q": 16, + "ratio": [ + 2184315745723297562814377646620672, + 2044625755481322930924218420542541 + ] + }, + { + "joint": [ + 666472635989092619, + 1652520822885056512 + ], + "lower_bound": [ + 901356590612107109486415, + 845021805551485442237857 + ], + "marginal": [ + 47219273189051281, + 76861433622560768 + ], + "n": 7, + "positive": true, + "q": 16, + "ratio": [ + 102452084544657494356833935015542784, + 95875369701597056711165952452861323 + ] + }, + { + "joint": [ + 35602991704257875768893, + 99582909118482493734912 + ], + "lower_bound": [ + 13523856157998775898360415, + 12678615150141528030469009 + ], + "marginal": [ + 11379844838561358721, + 19676527011670523904 + ], + "n": 8, + "positive": true, + "q": 16, + "ratio": [ + 2331407862667891648634985845907882437001609216, + 2181184294490946227959225328968905023414765569 + ] + }, + { + "joint": [ + 82569396626325325935137393, + 260526032722173170580193280 + ], + "lower_bound": [ + 1489114807403636175733764590775, + 1396045131956843972451536846521 + ], + "marginal": [ + 2742542606093287451761, + 5037190915056373596160 + ], + "n": 9, + "positive": true, + "q": 16, + "ratio": [ + 831835629095624630910950571290864809494194421760, + 778035613578697468125631585729852007763897957361 + ] + }, + { + "joint": [ + 7544467058177585684595341918683, + 26853090823911745236777102737408 + ], + "lower_bound": [ + 939604368679795985093622815859705, + 880879095638023017964120309046167 + ], + "marginal": [ + 660952768068482275874401, + 1289520874255531152244736 + ], + "n": 10, + "positive": true, + "q": 16, + "ratio": [ + 622639856425805791978102132980636484695173306408115372032, + 582219476595612645010574997826611310508285358540202470967 + ] + }, + { + "joint": [ + 2096233452320958245014754206479679991, + 8416645983744443033957191947242176512 + ], + "lower_bound": [ + 826851844439548700565493029210864255, + 775173604162121208576494354236501361 + ], + "marginal": [ + 660952768068482275874401, + 1369781509582711896932352 + ], + "n": 11, + "positive": true, + "q": 16, + "ratio": [ + 5742763645515963817194600750887127338393664691897231069937664, + 5368569852021861420312718968245893617872527885583964333734887 + ] + }, + { + "joint": [ + 10019616775623751467642512421220032203, + 45382061861071507858390408764361539584 + ], + "lower_bound": [ + 10951812426139545283795928694652260015, + 10267324149505864788743377131649047617 + ], + "marginal": [ + 38388797722185519065061084481, + 84510040015215274668115099648 + ], + "n": 12, + "positive": true, + "q": 16, + "ratio": [ + 108385051474570941797234763569474547196626913049851927941262587461632, + 101296609090337216299194327749967958772503492621292334795176984066689 + ] + }, + { + "joint": [ + 577, + 650 + ], + "lower_bound": [ + 624, + 601 + ], + "marginal": [ + 601, + 650 + ], + "n": 1, + "positive": true, + "q": 25, + "ratio": [ + 375050, + 361201 + ] + }, + { + "joint": [ + 24811, + 30225 + ], + "lower_bound": [ + 4890312, + 4695613 + ], + "marginal": [ + 361201, + 406875 + ], + "n": 2, + "positive": true, + "q": 25, + "ratio": [ + 1766620734375, + 1696060111213 + ] + }, + { + "joint": [ + 41893787209, + 55185812500 + ], + "lower_bound": [ + 49069015008, + 47106750817 + ], + "marginal": [ + 217081801, + 254312500 + ], + "n": 3, + "positive": true, + "q": 25, + "ratio": [ + 10654113759588812500, + 10226018306612581417 + ] + }, + { + "joint": [ + 56540943484290813130615229011, + 110141173077141819891357421875 + ], + "lower_bound": [ + 45019331946538067989599719256, + 43218558668792068792629590269 + ], + "marginal": [ + 17021419531644106084801, + 24253192047271728515625 + ], + "n": 8, + "positive": true, + "q": 25, + "ratio": [ + 239977213150227385892434165459283161914356231689453125, + 230255701438853497176913227745814209294879542699659797 + ] + }, + { + "joint": [ + 22114875701280231642523063770180277955675909529522377087797781, + 80561775451492218689919661837436729041983373463153839111328125 + ], + "lower_bound": [ + 3439030080025360232849701317894092387477968282546815732735384, + 3301468876824345823535842451378587398722397316604076853227341 + ], + "marginal": [ + 289728722872235459745150239945139673003209601, + 564688631502866892712214030325412750244140625 + ], + "n": 16, + "positive": true, + "q": 25, + "ratio": [ + 312200472390298444504971638169469008978356389445452733713014656983619341709307379893143661320209503173828125, + 299394003082127174913233014528209888820366690538770321484177767043060306390444742070213597499438446319994533 + ] + }, + { + "joint": [ + 677, + 756 + ], + "lower_bound": [ + 728, + 703 + ], + "marginal": [ + 703, + 756 + ], + "n": 1, + "positive": true, + "q": 27, + "ratio": [ + 511812, + 494209 + ] + }, + { + "joint": [ + 119152, + 143073 + ], + "lower_bound": [ + 3591965, + 3459463 + ], + "marginal": [ + 494209, + 551853 + ], + "n": 2, + "positive": true, + "q": 27, + "ratio": [ + 1775368493712, + 1709697749767 + ] + }, + { + "joint": [ + 235890934373, + 304556633640 + ], + "lower_bound": [ + 273117113360, + 263003697739 + ], + "marginal": [ + 347428927, + 402320520 + ], + "n": 3, + "positive": true, + "q": 27, + "ratio": [ + 94903763380231233960, + 91375092502493096053 + ] + }, + { + "joint": [ + 1122278830594728533886239427952, + 2082877176854331883880985113865 + ], + "lower_bound": [ + 115227710954475256713738782737, + 110960017956308364703027746767 + ], + "marginal": [ + 59654416235884558133761, + 82834383195202897568241 + ], + "n": 8, + "positive": true, + "q": 27, + "ratio": [ + 2510008417044394400750831718942940610721401404517555664, + 2416028110297997993720423269549711206082667723774750755 + ] + }, + { + "joint": [ + 416082758153562693896981617988191585806426192073780033084765808, + 1380114389511224114383232796187670995578849080605322494899465945 + ], + "lower_bound": [ + 57099293006916074180231472454456306136029229478875183223949441, + 54984504377030293655038282894099265172513217099091447792887151 + ], + "marginal": [ + 3558649376444167173416649443111672743168005121, + 6607404111948863218416165262388359513904845281 + ], + "n": 16, + "positive": true, + "q": 27, + "ratio": [ + 74229127032641612525465815241226827761064757006562204015623102450424621790024052930212406891433054395691705296, + 71419758858624808825902783007928612186515409421488952074634691263869736979095571845424889022119049336231598915 + ] + }, + { + "joint": [ + 481, + 528 + ], + "lower_bound": [ + 341, + 331 + ], + "marginal": [ + 331, + 352 + ], + "n": 1, + "positive": true, + "q": 32, + "ratio": [ + 338624, + 328683 + ] + }, + { + "joint": [ + 34151, + 39864 + ], + "lower_bound": [ + 33586175, + 32539617 + ], + "marginal": [ + 986049, + 1082368 + ], + "n": 2, + "positive": true, + "q": 32, + "ratio": [ + 33119698812928, + 32085656803233 + ] + }, + { + "joint": [ + 471932942689, + 585777561600 + ], + "lower_bound": [ + 356113196725, + 344986005483 + ], + "marginal": [ + 326382219, + 369459200 + ], + "n": 3, + "positive": true, + "q": 32, + "ratio": [ + 348719934919047577600, + 337791893980463120331 + ] + }, + { + "joint": [ + 430446083176874097414780257143, + 726455720463446891014442188800 + ], + "lower_bound": [ + 33767315823803874464278818498751, + 32712087204319228096647143255841 + ], + "marginal": [ + 945352959132095589420801, + 1247923426698936583192576 + ], + "n": 8, + "positive": true, + "q": 32, + "ratio": [ + 1925194884039957204830962948604176482854896330844156198912, + 1864563538172947109397383428470349647314588637789053079825 + ] + }, + { + "joint": [ + 1224853595030732870931056374951712770303634345638738897481214555713, + 3379688484686570992194282903779295116785994788145147897385163161600 + ], + "lower_bound": [ + 2064626193875869258522831475361864615332734205023522630618555649231, + 2000106625317248344193994094616623595999220692619112981609600847121 + ], + "marginal": [ + 893692217339809593677055887744746833070651481601, + 1508646851438351399436061723806297968205182795776 + ], + "n": 16, + "positive": true, + "q": 32, + "ratio": [ + 1892220436086846137792860784846575944863787902167939070185484445012712227610503588205902486956533901481266230341926912, + 1832166718018210806240205065086933523534962244582392380844898468785017703248281924497173143484003205493531428953739025 + ] + }, + { + "joint": [ + 461, + 490 + ], + "lower_bound": [ + 2400, + 2353 + ], + "marginal": [ + 2353, + 2450 + ], + "n": 1, + "positive": true, + "q": 49, + "ratio": [ + 5647250, + 5536609 + ] + }, + { + "joint": [ + 542597, + 600495 + ], + "lower_bound": [ + 141295248, + 138415225 + ], + "marginal": [ + 5536609, + 5884851 + ], + "n": 2, + "positive": true, + "q": 49, + "ratio": [ + 156462022404303, + 153270196094405 + ] + }, + { + "joint": [ + 2003633111069, + 2308783976660 + ], + "lower_bound": [ + 10865316331200, + 10643582678209 + ], + "marginal": [ + 13027640977, + 14129644900 + ], + "n": 3, + "positive": true, + "q": 49, + "ratio": [ + 141553121846436146990500, + 138660773840722973370193 + ] + }, + { + "joint": [ + 16613689347274415147433714438803749, + 23426884329869407727108657845567485 + ], + "lower_bound": [ + 13824666525568734143263037604649968, + 13542530474026594845323112958792805 + ], + "marginal": [ + 939670120432694468626892161, + 1127436584124001634083939401 + ], + "n": 8, + "positive": true, + "q": 49, + "ratio": [ + 917813177202030666630628884079937332601613941367681088533103101, + 899019941237170491286536325661162690306768369113685061101154565 + ] + }, + { + "joint": [ + 220723414286614240730871613142111523644173515352153025692400851596800711269, + 429922780871590503673919579273009641801741654033679723710903808613473304485 + ], + "lower_bound": [ + 12697546290446375314622597776018512870779890117632301535618337150555149424, + 12438412692682163573507850887155823303424688784798140824943226790659988565 + ], + "marginal": [ + 882979935233994526703160487488167204587524477523249921, + 1245172164461582277224794151343358157141275599294278801 + ], + "n": 16, + "positive": true, + "q": 49, + "ratio": [ + 13467093924216085341798847217188497012065847046328305462641609113808552073341033013986659677921537616003807765401534220080236914981, + 13190425469391628902768450194684981632591841048953674289634018349639790412767522559018433277064607122055527867784809199456081191365 + ] + }, + { + "joint": [ + 397, + 416 + ], + "lower_bound": [ + 4095, + 4033 + ], + "marginal": [ + 4033, + 4160 + ], + "n": 1, + "positive": true, + "q": 64, + "ratio": [ + 16515200, + 16265089 + ] + }, + { + "joint": [ + 800749, + 865488 + ], + "lower_bound": [ + 1073999871, + 1057230785 + ], + "marginal": [ + 16265089, + 17043456 + ], + "n": 2, + "positive": true, + "q": 64, + "ratio": [ + 3493767769227264, + 3439190562312973 + ] + }, + { + "joint": [ + 8685021879343, + 9682682773504 + ], + "lower_bound": [ + 92427338379285, + 90983183160619 + ], + "marginal": [ + 65597103937, + 69810257920 + ], + "n": 3, + "positive": true, + "q": 64, + "ratio": [ + 6063036174377779501465600, + 5968233322306232708257003 + ] + }, + { + "joint": [ + 53952889301288300095367486586310242541, + 70234143356420202429557712027383758848 + ], + "lower_bound": [ + 15507024559886557920602856848097576627, + 15264727301138338460018473493728142861 + ], + "marginal": [ + 69988353395873511358695882241, + 80485752395443132135108509696 + ], + "n": 8, + "positive": true, + "q": 64, + "ratio": [ + 4446657422665976765457976694996413769317992706275661575387965621796864, + 4377042768872673849900289665332760499044562479780979860157000766659597 + ] + }, + { + "joint": [ + 27616014852411761613585075012173399712563034415124536835762079116265526800501533, + 46066874565547204266464201249059406971163840827680793966431010240146505606365184 + ], + "lower_bound": [ + 305487920822898179950240798065714560105830913216614206689442804114126932051353779, + 300714672060040395888518285597065400580595514985687925210614340128651540048006157 + ], + "marginal": [ + 4898369611065679269359671047322595842637172238649339182081, + 6376738270869009029928421001352562261397404509652454998016 + ], + "n": 16, + "positive": true, + "q": 64, + "ratio": [ + 360653002338838627034824931658938844563327594426395177593813031158848513304164856071791989299630767449342302715651737595008449620623275065344, + 354995798304136490386446688414908413807216804791338030409564456569459165812037303412789806988924397514444416917444289669030350570156929524797 + ] + } + ], + "identities": { + "A2_minus_q3_t": [ + 1, + 6, + 9, + 5, + 1 + ], + "A_minus_q_t": [ + 1, + 2, + 1 + ], + "qD_minus_A2_q": [ + -1, + 1 + ], + "twoA_minus_q_qplus1_t": [ + 0, + 1, + 1 + ] + }, + "schema_version": 1, + "source_manifest_sha256": "2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59" +} diff --git a/research/common-covector-all-field-positive/PROOF.md b/research/common-covector-all-field-positive/PROOF.md new file mode 100644 index 0000000000..9d39a64ba2 --- /dev/null +++ b/research/common-covector-all-field-positive/PROOF.md @@ -0,0 +1,112 @@ +# Strict positive correlation over every finite field + +This is a modest sign corollary of Nick Petalas's credited PR4807 formula, +closing its README Open next question2. It supplies no new counting law. +PR4807 already proves the binary sign and explicitly suggests the identity +q*delta-alpha^2=q-1 used below. Its marginal is predecessor PR4227. + +## Source model and claim + +Let K=F_q, q>=2 a prime power, m>=2. Let a,c be independent columns in +K^m and b a covector satisfying ba=bc=1. Write U=ab,V=cb and the corank-one +complements P=I-U,Q=I-V. Complete equally weighted headers G range over +GL_m(K). Event E_P (respectively E_Q) requires every leading principal +minor of GPG^{-1} (respectively GQG^{-1}) of orders1,...,m-1 to be nonzero. +These are full proper-minor events on the complements, not first-pivot +requests on U,V. Other two-way pairs and restricted headers are outside scope. + +We prove + + Pr(E_P and E_Q) > Pr(E_P) Pr(E_Q) = p(q,m)^2. (1) + +The source law and uniform conjugation make both marginals equal to p. +The algebra below holds for all integer parameters q>=2,n>=1; a field/count +interpretation is asserted only for finite-field prime-power q. + +## Credited formulas and exact cancellation + +Put n=m-1, A=q^2-q+1, D=q^2+(q-1)^3 and x=q^{n+1}. PR4807 proves + + p = (q-1) A^n / [(x-1) q^n], + J = (q-1)(D^n-A^n) / [(x-1)(x-q) q^{n-1}]. (2) + +Those formulas, their common-covector orbit count, dependent-pair subtraction +and finite source censuses are cited premises, not independently recounted +here. In particular the binary sign was already a theorem in that source. +All denominators in (2) and below are positive: q>=2,n>=1 imply x>q>1, +A>0 and p>0. Cancellation gives the exact ratio + + R = J/p^2 + = x(x-1)/[(q-1)(x-q)] * [D^n/A^{2n} - 1/A^n]. (3) + +The identity qD-A^2=q-1>0 shows D>A^2/q. Since n>=1 and all bases +are positive, replacing D^n by (A^2/q)^n strictly decreases (3). Therefore + + R > L = q(x-1)/[(q-1)(x-q)] * [1-(q/A)^n]. (4) + +It remains to prove L>=1. Strictness in (1) is already supplied by (4), +including any boundary equality for L. + +## Nonnegative coefficient certificates + +Set t=q-2>=0. Direct polynomial expansion gives + + qD-A^2 = q-1, + A-q = t^2+2t+1 > 0, + 2A-q(q+1) = t^2+t >= 0, + A^2-q^3 = t^4+5t^3+9t^2+6t+1 > 0. (5) + +The coefficient lists in RESULT.json are in increasing order: [-1,1] in q +for the first identity, and [1,2,1], [0,1,1], [1,6,9,5,1] in t for +the other three. Nonnegative coefficients and the positive constant terms +prove the strict signs stated in (5) throughout the quantified domain. +The written expansions establish identities; finite coefficient calculations +corroborate them and are not an inference from a numerical sign grid. + +If n=1, simplify (4) to + + L = (q^2-1)/A, + L-1 = (q-2)/A >= 0. + +Equivalently, clearing positive denominators before simplification gives +2A>=q(q+1), whose certificate is the third identity in (5). At q=2 this +lower bound is exactly one. The strict replacement in (4) still gives R>1. + +If n>=2, the second and fourth identities in (5) give A>q and A^2>q^3. +Consequently + + A^n = A^2 A^{n-2} > q^3 q^{n-2} = q^{n+1} = x. + +This step is strict also at n=2. It follows that (q/A)^n<1/q. Substituting +this strict bound in (4)'s expression for L gives + + L > q(x-1)/[(q-1)(x-q)] * (1-1/q) + = (x-1)/(x-q) > 1, + +because q>1. Thus R>L>=1 for all q>=2,n>=1. Since p>0, multiplying +by p^2 proves (1), in particular for every finite field and every m>=2. +No correlation-sign statement for a different pair orbit follows. + +## What is new and what remains + +PR4807 supplies both probabilities, their all-field validity, the binary +strict-positive theorem and the suggested qD-A^2 identity. PR4227 supplies +the marginal and PR4261 the partial-sum/header method. The increment here +is the short quantified sign proof for the remaining field sizes, using +these existing formulas. It is not a new orbit count, full audit of4807, +generic positive-correlation principle, larger-family law or physical saving. + +The program evaluates205 fixed parameter pairs exactly and obtains the four +actual coefficient arrays by degree-bounded rational interpolation. A separate +engine uses polynomial convolution and integer recurrences with Euclidean +rational normalization. Neither imports a predecessor or peer program. These +checks corroborate the algebra; no GL census or predecessor scientific checker +is run. Non-prime-power rows are explicitly parameter algebra, not field counts. + +The original hypotheses remain: independent a,c, ba=bc=1, one common covector, +corank-one full guards and a complete uniform header distribution. Independent +covectors/general two-way pairs, larger families and restricted headers remain +open here. Header production, selection, emission, dispatch, dirty restoration, +stock, precision, producer compatibility and the full physical caller bill are +unpriced. No supplier admission, selected-frontier change, kappa improvement, +complete multiplication theorem or human/formal-kernel acceptance is claimed. diff --git a/research/common-covector-all-field-positive/README.md b/research/common-covector-all-field-positive/README.md new file mode 100644 index 0000000000..8581d7b0d0 --- /dev/null +++ b/research/common-covector-all-field-positive/README.md @@ -0,0 +1,83 @@ +# A common-covector pair is positively correlated over every finite field + +This closes the odd-field sign question in Nick Petalas's [PR4807 README +question2](https://github.com/CrocSwap/integer-mult-bounds/pull/4807), as a modest +corollary of that source's exact all-field counting formula. It proves strict +`J>p^2` for every prime powerq>=2 and every dimensionm>=2. The count, marginal, +binary sign and suggested identityqD-A^2=q-1 remain predecessor credit. + +The model is precise: independent columns a,c with one covectorb satisfying +ba=bc=1; corank-one complementsI-ab,I-cb; all proper leading principal minors; +complete equally weightedGL_m(F_q) headers. Other two-way pairs, first-pivot +requests, larger families and restricted header distributions are separate. +No physical producer/caller, supplier admission, newkappa or frontier change. + +[PROOF.md](PROOF.md) cancels the credited ratio and proves `J/p^2>L>=1`. +It retains strictness at(q,m)=(2,2) and uses explicit positive-coefficient +polynomial identities to cover every dimension. This is a written universal +inequality proof, not extrapolation from finite field sizes. + +## Evidence and reproduction + +[CASES.json](CASES.json) freezes205 exact parameter pairs: q2..16 withn1..12, +andq25,27,32,49,64 withn1,2,3,8,16, wheren=m-1. Non-prime-power values +6,10,12,14,15 are explicitly algebra-only fixtures. No field arithmetic or +GL/header enumeration is claimed for this package. + +The primary uses Fraction closed formulas and exact degree-bounded interpolation +for the four coefficient arrays. The independent engine uses polynomial +convolution, integer recurrences and Euclidean rational normalization. After +separate blind first seals, it compares the submitted205 actual rows and all +coefficient arrays as data. Both source prose files remain inert; no predecessor +executable or peer code is imported or executed. [RUN-RECORDS.json](RUN-RECORDS.json) +and [VALIDATION.md](VALIDATION.md) distinguish first runs and later checks. + +From the repository root, CPython3.12, standard library only: + +```sh +python3.12 -I -W error -B research/common-covector-all-field-positive/verify.py +python3.12 -I -W error -B research/common-covector-all-field-positive/oracle.py --check-primary research/common-covector-all-field-positive/RESULT.json +python3.12 -W error -B scripts/research_package.py --package research/common-covector-all-field-positive +``` + +[VERIFY.json](VERIFY.json) also registers both optimized modes. Direct replay +is read-only and needs noGit/network/compiler/Lean/Docker. Source/case/schema +bytes authenticate before computation. Exact receipt keys, integer/rational +and boolean types, duplicate/nonfinite/float guards and complete typed retained +comparisons remain active under-O. Primary controls comprise14 intended +rejections and one boundary fixture. Loops are bounded by205rows, n<=16, +q<=64 and interpolation matrices at most5by5. All new functions are below50 +physical lines. CPython dynamic allocation, arbitrary-precision integers and +bounded recursive JSON comparison are declared managed-runtime deviations from +fixed allocation/no recursion. This is not formal verification. + +## Open next questions + +Structured copies are in [TASK.json](TASK.json). + +1. What is the law for two-way pairs with independent covectors? This is the + distinct PR4807 question1. Start with a normalized partial-Gram pair; the + common-covector orbit and formula used here do not transfer automatically. +2. Can a named actual producer and consumer use these headers profitably? + Pin its legal header distribution and charge selection, emission, dispatch, + restoration, stock, precision and the complete physical caller. Those costs + and compatibility remain unknown. +3. Which restricted header catalogues preserve this sign? Start by naming one + legal catalogue and its exact weights; complete uniform conjugation is an + essential current premise, so this theorem supplies no restricted law. + +## Credit + +Nick Petalas4807 supplies the all-field joint law, dependent-pair subtraction, +binary theorem, sign question and suggested identity;4227 supplies the marginal, +4261 the partial-sum/header method,4778 the motivating two-way question and +4769/4274 the contrasting one-way law. Cinna Davis supplies the BIT request +context. source527, commdata2338, Jose Manuel and the retained normalizer/ +recursive-closure lineage keep predecessor credit. The exact two prose sources +and original notices are preserved in inputs/ and [SOURCE-PINS.json](SOURCE-PINS.json). +Elementary polynomial expansion and rational inequalities are classical. + +Prepared for ToikY with substantial OpenAI Codex assistance and separate AI +primary/oracle/static review. Apache-2.0. Independent human and proof-kernel +acceptance, a re-audit of4807's counts, native implementation and selected +operator replay remain unclaimed. No predecessor or selected source is changed. diff --git a/research/common-covector-all-field-positive/RESULT.json b/research/common-covector-all-field-positive/RESULT.json new file mode 100644 index 0000000000..26b801a615 --- /dev/null +++ b/research/common-covector-all-field-positive/RESULT.json @@ -0,0 +1 @@ +{"case_manifest_sha256":"a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b","cases":[{"joint":[1,3],"lower_bound":[1,1],"marginal":[1,2],"n":1,"positive":true,"q":2,"ratio":[4,3]},{"joint":[4,21],"lower_bound":[35,27],"marginal":[9,28],"n":2,"positive":true,"q":2,"ratio":[448,243]},{"joint":[7,60],"lower_bound":[95,63],"marginal":[9,40],"n":3,"positive":true,"q":2,"ratio":[560,243]},{"joint":[34,465],"lower_bound":[403,243],"marginal":[81,496],"n":4,"positive":true,"q":2,"ratio":[269824,98415]},{"joint":[1441,31248],"lower_bound":[1477,837],"marginal":[27,224],"n":5,"positive":true,"q":2,"ratio":[645568,203391]},{"joint":[133,4572],"lower_bound":[12065,6561],"marginal":[729,8128],"n":6,"positive":true,"q":2,"ratio":[17296384,4782969]},{"joint":[37969,2072640],"lower_bound":[175015,92583],"marginal":[729,10880],"n":7,"positive":true,"q":2,"ratio":[826205440,202479021]},{"joint":[353,30660],"lower_bound":[644371,334611],"marginal":[6561,130816],"n":8,"positive":true,"q":2,"ratio":[2955395072,645700815]},{"joint":[138103,19117824],"lower_bound":[6537311,3352671],"marginal":[6561,174592],"n":9,"positive":true,"q":2,"ratio":[48223357952,9427231899]},{"joint":[55151,12183744],"lower_bound":[10797925,5491557],"marginal":[59049,2096128],"n":10,"positive":true,"q":2,"ratio":[1849656885248,324270949293]},{"joint":[24325489,8583644160],"lower_bound":[3463915,1751787],"marginal":[19683,931840],"n":11,"positive":true,"q":2,"ratio":[45334927339520,7137447668847]},{"joint":[83657,47180160],"lower_bound":[9493369,4782969],"marginal":[531441,33550336],"n":12,"positive":true,"q":2,"ratio":[89815054680064,12709329141645]},{"joint":[5,12],"lower_bound":[8,7],"marginal":[7,12],"n":1,"positive":true,"q":3,"ratio":[60,49]},{"joint":[10,39],"lower_bound":[65,49],"marginal":[49,117],"n":2,"positive":true,"q":3,"ratio":[3510,2401]},{"joint":[457,2808],"lower_bound":[6320,4459],"marginal":[343,1080],"n":3,"positive":true,"q":3,"ratio":[2467800,1529437]},{"joint":[338,3267],"lower_bound":[3509,2401],"marginal":[2401,9801],"n":4,"positive":true,"q":3,"ratio":[9938214,5764801]},{"joint":[63775,972972],"lower_bound":[430664,290521],"marginal":[2401,12636],"n":5,"positive":true,"q":3,"ratio":[805860900,443889677]},{"joint":[333610,8056503],"lower_bound":[15974195,10706059],"marginal":[117649,796797],"n":6,"positive":true,"q":3,"ratio":[2392375024530,1259557135291]},{"joint":[40951513,1568096496],"lower_bound":[1347023840,900132499],"marginal":[823543,7173360],"n":7,"positive":true,"q":3,"ratio":[1468799726468400,741297818623957]},{"joint":[1116986,67877919],"lower_bound":[354167749,236356841],"marginal":[5764801,64566801],"n":8,"positive":true,"q":3,"ratio":[2812688298489654,1362550153353641]},{"joint":[59273761445,5718810698172],"lower_bound":[595409386088,397119846487],"marginal":[40353607,581120892],"n":9,"positive":true,"q":3,"ratio":[34445221123113608940,16025218217036728609]},{"joint":[7635270550,1169809562889],"lower_bound":[284255114575,189540892079],"marginal":[282475249,5230147077],"n":10,"positive":true,"q":3,"ratio":[119800763847560047050,53540610685697652671]},{"joint":[148999647743,36254469946968],"lower_bound":[37526299332080,25019680229677],"marginal":[282475249,6724500120],"n":11,"positive":true,"q":3,"ratio":[5009740745638806145800,2150960122584726710957]},{"joint":[852664202,329500919223],"lower_bound":[10608952598459,7072897759711],"marginal":[13841287201,423644039001],"n":12,"positive":true,"q":3,"ratio":[3251034958021600879818,1341068619663964900807]},{"joint":[1,2],"lower_bound":[15,13],"marginal":[13,20],"n":1,"positive":true,"q":4,"ratio":[200,169]},{"joint":[1,3],"lower_bound":[1071,845],"marginal":[169,336],"n":2,"positive":true,"q":4,"ratio":[37632,28561]},{"joint":[859,3808],"lower_bound":[20145,15379],"marginal":[2197,5440],"n":3,"positive":true,"q":4,"ratio":[46729600,33787663]},{"joint":[7063,46376],"lower_bound":[37851,28561],"marginal":[28561,87296],"n":4,"positive":true,"q":4,"ratio":[19730292736,13867422257]},{"joint":[444355,4333056],"lower_bound":[12959415,9739301],"marginal":[28561,107520],"n":5,"positive":true,"q":4,"ratio":[477770496000,328739480563]},{"joint":[1253281,18174208],"lower_bound":[418045011,313742585],"marginal":[4826809,22368256],"n":6,"positive":true,"q":4,"ratio":[448539363966976,302875106592253]},{"joint":[9058528753,195453820928],"lower_bound":[456794481795,342669651337],"marginal":[62748517,357908480],"n":7,"positive":true,"q":4,"ratio":[32421242570225254400,21502012442303817229]},{"joint":[102305537,3285126144],"lower_bound":[279504468747,209642795297],"marginal":[815730721,5726601216],"n":8,"positive":true,"q":4,"ratio":[262466629639304380416,171012068560077219137]},{"joint":[25498833457,1218624225280],"lower_bound":[137275778424675,102959084412457],"marginal":[10604499373,91625881600],"n":9,"positive":true,"q":4,"ratio":[23363530952692006912000,14956569124610333286157]},{"joint":[1637223064757,116456578809856],"lower_bound":[5840564524164381,4380453578501975],"marginal":[137858491849,1466015154176],"n":10,"positive":true,"q":4,"ratio":[38403101179203785391603712,24155308957873496086716071]},{"joint":[30976398243694289,3279420191315853312],"lower_bound":[11173314706987545,8380004144025163],"marginal":[137858491849,1804326666240],"n":11,"positive":true,"q":4,"ratio":[558915413751675075730971033600,345421165162120067490432519713]},{"joint":[3964246775712049,624651604633059328],"lower_bound":[97323801851666703,72992900688732973],"marginal":[23298085122481,375299963355136],"n":12,"positive":true,"q":4,"ratio":[47609013428974337001390759477248,28910111830909347880727940522221]},{"joint":[17,30],"lower_bound":[8,7],"marginal":[7,10],"n":1,"positive":true,"q":5,"ratio":[170,147]},{"joint":[187,465],"lower_bound":[1612,1323],"marginal":[441,775],"n":2,"positive":true,"q":5,"ratio":[724625,583443]},{"joint":[13379,46500],"lower_bound":[118768,95697],"marginal":[3087,6500],"n":3,"positive":true,"q":5,"ratio":[1130525500,886249917]},{"joint":[71077,346125],"lower_bound":[727892,583443],"marginal":[194481,488125],"n":4,"positive":true,"q":5,"ratio":[1908195334375,1475091515079]},{"joint":[1394993837,9533081250],"lower_bound":[63255128,50629887],"marginal":[64827,193750],"n":5,"positive":true,"q":5,"ratio":[270280055918750,206777572126587]},{"joint":[12422388121,119200134375],"lower_bound":[209349117172,167501234313],"marginal":[85766121,305171875],"n":6,"positive":true,"q":5,"ratio":[18954817374316484375,14365931129738109873]},{"joint":[11057383451747,149009323125000],"lower_bound":[14656622765408,11725686764757],"marginal":[600362847,2543125000],"n":7,"positive":true,"q":5,"ratio":[28120308290724089375000,21119000067359195349537]},{"joint":[24603443642767,465659856796875],"lower_bound":[44394213598276,35515664939979],"marginal":[37822859361,190734765625],"n":8,"positive":true,"q":5,"ratio":[23463660283855299857421875,17462952001783914902814447]},{"joint":[4609942229308403,122542368738281250],"lower_bound":[161596275252669928,129277285141539087],"marginal":[264760015527,1589457031250],"n":9,"positive":true,"q":5,"ratio":[7327305090030540973058593750,5404335161267730800020642713]},{"joint":[14173501477311457,529160488735546875],"lower_bound":[2313769374635486612,1851016431793899573],"marginal":[16679880978201,119209287109375],"n":10,"positive":true,"q":5,"ratio":[42240325173849304749552490234375,30874733771016554206915596208173]},{"joint":[693793180872372449567,36379787176847460937500],"lower_bound":[84838249637509193488,67870608059069977077],"marginal":[5559960326067,47305273437500],"n":11,"positive":true,"q":5,"ratio":[32820076130240473516108613476562500,23773546951211752867985849540668017]},{"joint":[237490765585994835497,17490282640434228515625],"lower_bound":[10792405438379320442012,8633924608972604033673],"marginal":[7355827511386641,74505805908203125],"n":12,"positive":true,"q":5,"ratio":[88472204428703487041947629586181640625,63509660169918827440939200374086362393]},{"joint":[13,21],"lower_bound":[35,31],"marginal":[31,42],"n":1,"positive":true,"q":6,"ratio":[1092,961]},{"joint":[416,903],"lower_bound":[7955,6727],"marginal":[961,1548],"n":2,"positive":true,"q":6,"ratio":[7727616,6464647]},{"joint":[414349,1202796],"lower_bound":[1531985,1281013],"marginal":[29791,55944],"n":3,"positive":true,"q":6,"ratio":[46360680912,38162658283]},{"joint":[2795728,10874115],"lower_bound":[7751675,6464647],"marginal":[923521,2015280],"n":4,"positive":true,"q":6,"ratio":[270440386744320,220898778697219]},{"joint":[2162939753,11282746608],"lower_bound":[344601355,287215031],"marginal":[923521,2340576],"n":5,"positive":true,"q":6,"ratio":[10125049750635456,8222722491968681]},{"joint":[6047009306,42315590457],"lower_bound":[1419601613105,1183042406773],"marginal":[887503681,2612129472],"n":6,"positive":true,"q":6,"ratio":[9098249025980659064832,7349681435530957819891]},{"joint":[280399265048461,2632423105867968],"lower_bound":[1848405166613705,1540348726232557],"marginal":[27512614111,94036940928],"n":7,"positive":true,"q":6,"ratio":[52735778247233484228623616,42379020101206723585811827]},{"joint":[117564164939546,1480743139695939],"lower_bound":[9292063585844555,7743397728926839],"marginal":[852891037441,3385331553024],"n":8,"positive":true,"q":6,"ratio":[305659143993417946562678095872,244358157326679715381054822963]},{"joint":[7268298020805978637,122818830070902577920],"lower_bound":[63948088445651234825,53290089610096666669],"marginal":[26439622160671,121871945986560],"n":9,"positive":true,"q":6,"ratio":[1771603247611774359051970498237440,1408969834199255237932200648374899]},{"joint":[110814045934171463,2512203584718354408],"lower_bound":[216260877654093719585,180217408856477581477],"marginal":[819628286980801,4387390115982336],"n":10,"positive":true,"q":6,"ratio":[186694828739941034537502145258586112,147711286105153354927260926812223077]},{"joint":[14492432230046821944961,440787383133413085084672],"lower_bound":[3102873653723390655745,2585728075750690820357],"marginal":[819628286980801,5095033694779392],"n":11,"positive":true,"q":6,"ratio":[1919825193816280471443724590296787136512,1511086477681225214297430024409462727341]},{"joint":[2025418068095499331201,82647634558993781932368],"lower_bound":[122214702437006983798865,101845585606643272647061],"marginal":[787662783788549761,5686057605550583808],"n":12,"positive":true,"q":6,"ratio":[26534347339424219668620018807642085924012032,20776974166155457163102778102414944325727039]},{"joint":[37,56],"lower_bound":[48,43],"marginal":[43,56],"n":1,"positive":true,"q":7,"ratio":[2072,1849]},{"joint":[407,798],"lower_bound":[4275,3698],"marginal":[1849,2793],"n":2,"positive":true,"q":7,"ratio":[7957257,6837602]},{"joint":[1029451,2606800],"lower_bound":[1759200,1510633],"marginal":[79507,137200],"n":3,"positive":true,"q":7,"ratio":[141240677200,120105897931]},{"joint":[14667059,48037150],"lower_bound":[7974447,6837602],"marginal":[3418801,6725201],"n":4,"positive":true,"q":7,"ratio":[690472438977013,584410013880050]},{"joint":[217785651197,923074188456],"lower_bound":[11171364336,9576061601],"marginal":[3418801,7663992],"n":5,"positive":true,"q":7,"ratio":[1669107488488598424,1407761906035097243]},{"joint":[687126629519,3769439303966],"lower_bound":[12050488609275,10329107222066],"marginal":[6321363049,16148148793],"n":6,"positive":true,"q":7,"ratio":[77670761371737786143969,65294036722727049839234]},{"joint":[15295672663525753,108605989522200800],"lower_bound":[43527088381915200,37309007104713499],"marginal":[271818611107,791260114400],"n":7,"positive":true,"q":7,"ratio":[12102855701566340026126143200,10141282492984418611334233393]},{"joint":[978128212626191,8989357798426950],"lower_bound":[32754221959784247,28075057066797602],"marginal":[11688200277601,38771751370401],"n":8,"positive":true,"q":7,"ratio":[9822249661894207018387246101069,8203672245045191212412027820050]},{"joint":[3225650782105069609,38370580873993261432],"lower_bound":[23062046994953271888,19767470020087972033],"marginal":[502592611936843,1899815857503256],"n":9,"positive":true,"q":7,"ratio":[6128142506610991193266058824146904,5101748740183940334216344831889853]},{"joint":[924180428125936718537,14229381439078975154818],"lower_bound":[26977879642532262370125,23123897068532507313518],"marginal":[21611482313284249,93090977300134793],"n":10,"positive":true,"q":7,"ratio":[602230014791303007613089149187412304887,499741692510795775289470699478494177982]},{"joint":[75431607343263800558507153,1503248777963153980063141200],"lower_bound":[8309187024427921372509600,7122160318719494565847793],"marginal":[21611482313284249,106080416039161200],"n":11,"positive":true,"q":7,"ratio":[8001816289476071022478493475647458320063600,6618578995696394462361860264858613767435651]},{"joint":[9152644679646875232802031,236087147938096820963350550],"lower_bound":[13787924084027148225002619,11818220646813596020901354],"marginal":[39959630797262576401,223511436608353935601],"n":12,"positive":true,"q":7,"ratio":[14320045327795763277520026643264112548292039417,11806293343181425432969765178960883407733673850]},{"joint":[25,36],"lower_bound":[21,19],"marginal":[19,24],"n":1,"positive":true,"q":8,"ratio":[400,361]},{"joint":[725,1314],"lower_bound":[33215,29241],"marginal":[3249,4672],"n":2,"positive":true,"q":8,"ratio":[108390400,95004009]},{"joint":[960485,2186496],"lower_bound":[1714895,1502121],"marginal":[20577,33280],"n":3,"positive":true,"q":8,"ratio":[319649408000,278182294353]},{"joint":[12245105,35051328],"lower_bound":[108557071,95004009],"marginal":[10556001,19173376],"n":4,"positive":true,"q":8,"ratio":[15025920148766720,13037211382104117]},{"joint":[797665137625,2872095031296],"lower_bound":[6274446871,5490293409],"marginal":[1172889,2392064],"n":5,"positive":true,"q":8,"ratio":[3816132119535616000,3303465934794752313]},{"joint":[20291547082175,91909802041344],"lower_bound":[1467842426308895,1284367653027801],"marginal":[34296447249,78536507392],"n":6,"positive":true,"q":8,"ratio":[50996071597259293406003200,44049247460389912126969449]},{"joint":[3775411771722995,21512226446770176],"lower_bound":[10624457519238745,9296406423463023],"marginal":[217210832577,558482063360],"n":7,"positive":true,"q":8,"ratio":[21084997563054915499589632000,18173521612931166480629702439]},{"joint":[168064967376973105,1204685246482219008],"lower_bound":[4695687892401526447,4108727310190812873],"marginal":[111429157112001,321685685272576],"n":8,"positive":true,"q":8,"ratio":[6920204057724764551199711496765440,5951816272709077615673650816655349]},{"joint":[21888784136905904995225,197375642364331432083456],"lower_bound":[15464467561392367543487,13531409313946405437753],"marginal":[705717995042673,2287542665740288],"n":9,"positive":true,"q":8,"ratio":[100143055228702925996311214743460249600,85944231460260077513779614820322103921]},{"joint":[556795956406703263603625,6316020601981344807911424],"lower_bound":[5769652370599529739015325,5048445835133579943039051],"marginal":[362033331456891249,1317624576540147712],"n":10,"positive":true,"q":8,"ratio":[23476737160948765861359204223565789396992000,20104762308103852498418720504878760538811689]},{"joint":[725171055434256987801817445,10348168163773132284371140608],"lower_bound":[56414378884331780029099655,49362581539309818493814193],"marginal":[40225925717432361,164382013464248320],"n":11,"positive":true,"q":8,"ratio":[1192050781982771970121598737028710267879424000,1018641291107360036129791963118730059580732249]},{"joint":[709482258809908878607100255,12736206972257223881080700928],"lower_bound":[203029274285297943173564327503,177650615007752515608067787817],"marginal":[1176246293903439668001,5396990266126920318976],"n":12,"positive":true,"q":8,"ratio":[245060406066356395314269589487579229244352700088320,208960877512535675388191777054582145243492992543817]},{"joint":[13,18],"lower_bound":[80,73],"marginal":[73,90],"n":1,"positive":true,"q":9,"ratio":[5850,5329]},{"joint":[37,63],"lower_bound":[29848,26645],"marginal":[5329,7371],"n":2,"positive":true,"q":9,"ratio":[31909059,28398241]},{"joint":[57181,119556],"lower_bound":[39799520,35400547],"marginal":[389017,597780],"n":3,"positive":true,"q":9,"ratio":[170908290900,151334226289]},{"joint":[85853209,220610709],"lower_bound":[31944968,28398241],"marginal":[28398241,48426741],"n":4,"positive":true,"q":9,"ratio":[37418320046356821,33064863767657321]},{"joint":[12819325055,40493560338],"lower_bound":[235805176880,209607416821],"marginal":[28398241,53734590],"n":5,"positive":true,"q":9,"ratio":[44774676433964909250,39502834681247769623]},{"joint":[221223625411,859056327189],"lower_bound":[807839531004184,718080903741305],"marginal":[151334226289,317733162111],"n":6,"positive":true,"q":9,"ratio":[1897832214958402854070767,1671849507393788885941033]},{"joint":[644648054239846579,3077408354424035832],"lower_bound":[7430532263888373440,6604919200011042487],"marginal":[11047398519097,25736390913960],"n":7,"positive":true,"q":9,"ratio":[82954571629201903751799946714200,72967174588957332716930947874239]},{"joint":[11038243236902569,64779139340210169],"lower_bound":[2976744909269703208,2645995561504479761],"marginal":[806460091894081,2084647707077481],"n":8,"positive":true,"q":9,"ratio":[99613962957246746320542677276874681,87489482770971561306157405827980281]},{"joint":[131110433356717286293,945900143736289373610],"lower_bound":[168809645383868579591600,150053018762180713744747],"marginal":[58871586708267913,168856464660696450],"n":9,"positive":true,"q":9,"ratio":[110694221283735647439281713297093799250,97075376976868943679173983643784312121]},{"joint":[135784984600679586557411,1204294268798513816419089],"lower_bound":[95784128000986371040417448,85141447159360349062692475],"marginal":[4297625829703557649,13677373641003196851],"n":10,"positive":true,"q":9,"ratio":[16714637722992239750078251305663749813214849,14636243299616305265847216654972161852839651]},{"joint":[266606324298963547379282693,2906860257460762983230362092],"lower_bound":[824576406879239871865721440,732956806167433693222463813],"marginal":[4297625829703557649,15176263903460821980],"n":11,"positive":true,"q":9,"ratio":[262995715833027470712185564047878916636919489100,229948109463679644138250468499353519142115461501]},{"joint":[4809846107708056227876185659,64470007854998125660037929959],"lower_bound":[12189663739484579730059755784,10835256657419145769783834873],"marginal":[22902048046490258711521,89737248461446269904221],"n":12,"positive":true,"q":9,"ratio":[11653803591175388660420384929690895035528796081699253,10174132311134935427657040249242187358238779473545153]},{"joint":[41,55],"lower_bound":[99,91],"marginal":[91,110],"n":1,"positive":true,"q":10,"ratio":[9020,8281]},{"joint":[3772,6105],"lower_bound":[100899,91091],"marginal":[8281,11100],"n":2,"positive":true,"q":10,"ratio":[837384000,754324571]},{"joint":[10536467,20553500],"lower_bound":[30966903,27882127],"marginal":[753571,1111000],"n":3,"positive":true,"q":10,"ratio":[23412029674000,21011162325517]},{"joint":[15997006,37635125],"lower_bound":[838091619,754324571],"marginal":[68574961,111110000],"n":4,"positive":true,"q":10,"ratio":[5829961664244800000,5224505581804339831]},{"joint":[48229935811,136868550000],"lower_bound":[846590043519,761936391671],"marginal":[68574961,122100000],"n":5,"positive":true,"q":10,"ratio":[129555253575508200000,115968975835172659381]},{"joint":[4061354960419,13902776387500],"lower_bound":[23369061533093613,21032173487842517],"marginal":[567869252041,1111111000000],"n":6,"positive":true,"q":10,"ratio":[361009293714089240720000000,322797962901018387448346681]},{"joint":[14948896166751172121,61728388271605000000],"lower_bound":[63797643727123556349,57417885297912007141],"marginal":[51676101935731,111111110000000],"n":7,"positive":true,"q":10,"ratio":[3321976892724935656330728620000000,2967132493589011197831537595055071]},{"joint":[77453981505980631583,385802464891975312500],"lower_bound":[574810557566189441859,517329508154704976731],"marginal":[4702525276151521,11111111100000000],"n":8,"positive":true,"q":10,"ratio":[275391933968094755829402198816000000000,245708263907849990136368468959061042951]},{"joint":[27841453386874816518649,167285623289504500000000],"lower_bound":[5870093265939580673347341,5283083946936526060126069],"marginal":[427929800129788411,1111111111000000000],"n":9,"positive":true,"q":10,"ratio":[2536665752772705596396493893941198000000000,2260789057481441280257036717160052955186359]},{"joint":[94420492794274002807013,684350277770934275000000],"lower_bound":[4370551268397455587315588389,3933496142213796385840295501],"marginal":[38941611811810745401,111111111110000000000],"n":10,"positive":true,"q":10,"ratio":[4196466346370213239069789332085772000000000000,3736016581301092022759479068781517156315042461]},{"joint":[7060367886682680063380883246841,61728395061049382716050000000000],"lower_bound":[480760639637937070250471472279,432684575682459214254243250511],"marginal":[38941611811810745401,122100122100000000000],"n":11,"positive":true,"q":10,"ratio":[1724143562069748399388083166490261078572200000000000,1533298565269778047936377797641653057841235657641901]},{"joint":[8343375781453462376286660541,87992352408570666306250000000],"lower_bound":[131392041483344552465851664230833,118252837335270373002664978077497],"marginal":[322475487413604782665681,1111111111111000000000000],"n":12,"positive":true,"q":10,"ratio":[117178077641734687121417368957551526290084640000000000000,104094534517055041203579130721338194216864839386169954761]},{"joint":[101,132],"lower_bound":[40,37],"marginal":[37,44],"n":1,"positive":true,"q":11,"ratio":[4444,4107]},{"joint":[404,627],"lower_bound":[40565,36963],"marginal":[12321,16093],"n":2,"positive":true,"q":11,"ratio":[500621044,455421123]},{"joint":[140732693,259161672],"lower_bound":[66675440,60631641],"marginal":[455877,649528],"n":3,"positive":true,"q":11,"ratio":[91409824618904,82921711812471]},{"joint":[1794312268,3922743165],"lower_bound":[500946025,455421123],"marginal":[151807041,235793305],"n":4,"positive":true,"q":11,"ratio":[4653955018611423140,4217304118583149623]},{"joint":[35404129824961,91898837229276],"lower_bound":[179288474120,162990159687],"marginal":[50602347,85679132],"n":5,"positive":true,"q":11,"ratio":[3033395112617970413852,2746478977816306134537]},{"joint":[14983528358324,46178686791963],"lower_bound":[13017518509187465,11834112871522647],"marginal":[1870414552161,3452271037237],"n":6,"positive":true,"q":11,"ratio":[24466966066879947260816802724,22134696926811757518674290167]},{"joint":[222453502288407634037,814027448298417776016],"lower_bound":[148347774434504909920,134861619489210515169],"marginal":[69205338429957,139241604997616],"n":7,"positive":true,"q":11,"ratio":[30974782695978722708108945585455792,27999432053888695158441772777553199]},{"joint":[202411036553995537364,879440413007199382251],"lower_bound":[556760190581822625545,506145630363069481803],"marginal":[23045377697175681,50544702828493489],"n":8,"positive":true,"q":11,"ratio":[787772038270835866873204978023027170692,711523350511012464752413095396741603423]},{"joint":[279544217403282872193117989,1442099360397802262781272340],"lower_bound":[11640156103356433314186200,10581960099634831115319447],"marginal":[852678974795500197,2038636348201886620],"n":9,"positive":true,"q":11,"ratio":[569889002527982874970822763799024750060407180,514311848677760464096832043238826484966570363]},{"joint":[1424404854397462859506917388,8724701134076249116590093573],"lower_bound":[40505997251322094706606798005,36823633866911371986989455923],"marginal":[283942098606901565601,740024994423222267661],"n":10,"positive":true,"q":11,"ratio":[11595047138750824966439861564406125713916660884148,10455779878502988786990732147869941456347882504723]},{"joint":[351286725220180442370893024354261,2554766986177890565583776539377112],"lower_bound":[2970439798684204382631833432240,2700399817001481311914860622887],"marginal":[94647366202300521867,268897970947433051224],"n":11,"positive":true,"q":11,"ratio":[94460287632474977917077551071326614499824841535665464,85110048213997383994472341927690725583294725128619657]},{"joint":[49174877494381312533123508210924,424624732594229772977394098540277],"lower_bound":[27196902113957086342166338789345,24724456467248733148359182116539],"marginal":[3498450596935634189769921,10834705943388058361345353],"n":12,"positive":true,"q":11,"ratio":[5860748711991281662296619239922430262110335139334043597892,5276334658692081337198843419602430153234260356979348228559]},{"joint":[61,78],"lower_bound":[143,133],"marginal":[133,156],"n":1,"positive":true,"q":12,"ratio":[19032,17689]},{"joint":[4087,6123],"lower_bound":[250415,229957],"marginal":[17689,22608],"n":2,"positive":true,"q":12,"ratio":[4435147008,4067709373]},{"joint":[145758829,255696480],"lower_bound":[402860315,369364009],"marginal":[2352637,3257280],"n":3,"positive":true,"q":12,"ratio":[949554637050240,868979434041733]},{"joint":[4482037159,9210366360],"lower_bound":[4437403223,4067709373],"marginal":[312900721,469069056],"n":4,"positive":true,"q":12,"ratio":[201828954156388982784,184554433366372900285]},{"joint":[317347317801181,763981214750208],"lower_bound":[7721575595591,7078127209741],"marginal":[312900721,507866112],"n":5,"positive":true,"q":12,"ratio":[322339896890628366956544,294561897265271057393713]},{"joint":[6501247671115159,18335622329047296],"lower_bound":[126080986753454315,115574264727550489],"marginal":[5534900853769,9726654763008],"n":6,"positive":true,"q":12,"ratio":[9105896394107557745791858311168,8315997254685167108647994759533]},{"joint":[690432840301381965709,2281245546369819893760],"lower_bound":[2615929664001078637355,2397935580709031097049],"marginal":[736141813551277,1400638321704960],"n":7,"positive":true,"q":12,"ratio":[1934093389379432611058391130270433280,1765220647162280710381562345924881573]},{"joint":[10608213378637385688007,41062420972675394472960],"lower_bound":[28793268534693818461031,26393829549782585056621],"marginal":[97906861202319841,201691918755495936],"n":8,"positive":true,"q":12,"ratio":[410801454893778555206641062216931668393984,374699865917596472321595617636302824002845]},{"joint":[1502123020387372346763301501,6811762906047145501259071488],"lower_bound":[6663338232105959701681690163,6108060047432298373711770673],"marginal":[13021612539908538853,29043636305951195136],"n":9,"positive":true,"q":12,"ratio":[87254229381855509529347540256333503072105398272,79536791308158761126263766927035126226846458069]},{"joint":[92317977327737190683762107667,490446929329786294084994531328],"lower_bound":[10634687822432314809700982376575,9748463837433822672251821661557],"marginal":[1731874467807835667449,4182283628118889463808],"n":10,"positive":true,"q":12,"ratio":[18532798327624611729971815854182405075940364599164928,16883115620399633078994431299694142888889015279558093]},{"joint":[12917218962480398785539354099313,80394525903126937989273385697280],"lower_bound":[504412070646229481171551155755,462377731426631409228575871961],"marginal":[1731874467807835667449,4528186785337316474880],"n":11,"positive":true,"q":12,"ratio":[116983160418424686735772662858758944445994677179514880,106503764942911988750923533593629025279674762733166037]},{"joint":[2574991018342774313221673844434371,18775213895555353989109821139845120],"lower_bound":[14370741102016733822095184720927123,13173179343517818943722165852543313],"marginal":[30635127461052805121505361,86723833312789201227350016],"n":12,"positive":true,"q":12,"ratio":[64314170454726167066370174309468912386670171486673946246381568,58516494097116563326216819478002521293171031797426387059143985]},{"joint":[145,182],"lower_bound":[168,157],"marginal":[157,182],"n":1,"positive":true,"q":13,"ratio":[26390,24649]},{"joint":[11455,16653],"lower_bound":[186660,172543],"marginal":[24649,30927],"n":2,"positive":true,"q":13,"ratio":[4605494205,4253012407]},{"joint":[37903841,63792092],"lower_bound":[255697680,236063473],"marginal":[3869893,5228860],"n":3,"positive":true,"q":13,"ratio":[990969390256300,913540381718389]},{"joint":[4150442039,8089307863],"lower_bound":[4607362428,4253012407],"marginal":[607573201,883705901],"n":4,"positive":true,"q":13,"ratio":[47681011581096037807,43928278154232981719]},{"joint":[2047169120589725,4620935271976842],"lower_bound":[20365470639864,18798922412141],"marginal":[607573201,951252666],"n":5,"positive":true,"q":13,"ratio":[1947375083713851398456850,1793210270051338335434537]},{"joint":[49788380168751655,130156691969574361],"lower_bound":[155377972893142380,143425839929787073],"marginal":[14976071831449,25239591813787],"n":6,"positive":true,"q":13,"ratio":[16336299102876210707093104877305,15035689768920781827382005411439]},{"joint":[1473397926315984588767,4460887253932758011272],"lower_bound":[13319314725659208614880,12294752201704485009199],"marginal":[2351243277537493,4265491079278520],"n":7,"positive":true,"q":13,"ratio":[31423828554641511944623250686281924200,28907953463246961563777180666172398107]},{"joint":[26875345523148825129599,94236244732251390735603],"lower_bound":[39977532428307577397388,36902337665917718348767],"marginal":[369145194573386401,720867993213800601],"n":8,"positive":true,"q":13,"ratio":[251856493124597317273380365249469198156987,231579450504266032480884330952795939598639]},{"joint":[2945657321264553363775851745,11962139507012361510766000078],"lower_bound":[6164890869320508565306427592,5690668495303297609989823213],"marginal":[57955795548021664957,121826690863736800942],"n":9,"positive":true,"q":13,"ratio":[358859683868199781977604392512273422177568343790,329807219845366002623019237137971088014347246841]},{"joint":[175843382707529055714014889025,827018826903244342271245515083],"lower_bound":[5147403654468710936481750210300,4751449527242060622679202908993],"marginal":[9099059901039401398249,20588710756109377851047],"n":10,"positive":true,"q":13,"ratio":[47065051084235096157479602345048187189607516905769275,43233723865140854687514313581078342784880112496553257]},{"joint":[829586265584587762007337209775197,4518701423806830451034877010497156],"lower_bound":[1472157445199267155296571509825360,1358914564800328397987291433370247],"marginal":[9099059901039401398249,22162370176969917307140],"n":11,"positive":true,"q":13,"ratio":[91927989558078565493610641455550186823758761795015032900,84403507348067527872989221944380528044508577460842439477]},{"joint":[232023579190785747845330526886332359,1463682702862241045091863576287555343],"lower_bound":[66069147796621717148380049979109764,60986905658423965489265325663855361],"marginal":[224282727500720205065439601,588034167905566113995468101],"n":12,"positive":true,"q":13,"ratio":[1773691300211023989546667644957375223322231499274024682491543367,1627718835605151575751799002661437443133356700236764433520564359]},{"joint":[17,21],"lower_bound":[65,61],"marginal":[61,70],"n":1,"positive":true,"q":14,"ratio":[11900,11163]},{"joint":[3128,4431],"lower_bound":[540371,502335],"marginal":[33489,41356],"n":2,"positive":true,"q":14,"ratio":[3622123904,3364539363]},{"joint":[105363569,171089772],"lower_bound":[464142835,431036919],"marginal":[2042829,2702840],"n":3,"positive":true,"q":14,"ratio":[2847808688359600,2641604154611553]},{"joint":[4504271516,8386439523],"lower_bound":[3623313551,3364539363],"marginal":[1121513121,1589308336],"n":4,"positive":true,"q":14,"ratio":[801771742014449626112,743354883219919938831]},{"joint":[54875225730835,117157019848848],"lower_bound":[16655720253965,15466039776297],"marginal":[373837707,567404320],"n":5,"positive":true,"q":14,"ratio":[311364401406509362072000,288563825149233929418861]},{"joint":[12897179070893653,31573875256446726],"lower_bound":[23426963037579759671,21753610213226138955],"marginal":[37558352909169,61054981978816],"n":6,"positive":true,"q":14,"ratio":[176385896008218370071681407485952,163405953887370085284279537515679]},{"joint":[3456650984356632758321,9703537216967880963264],"lower_bound":[20006630314330700370395,18577585413154650126879],"marginal":[2291059527459309,3988925524420480],"n":7,"positive":true,"q":14,"ratio":[137883233405133497342634372274228140800,127687062173991133428205622764078999833]},{"joint":[18463763219663968953319,59434166014870922771622],"lower_bound":[156112652660560716208127,144961748977967839035891],"marginal":[1257791680575160641,2345488209835031296],"n":8,"positive":true,"q":14,"ratio":[38802658891053152482244410645357196351995904,35919341327624210510785683677737134244527807]},{"joint":[19794335873708291781748711313,73063133541328256220763841280],"lower_bound":[131320402439731965841326592075,121940373699502059033685949391],"marginal":[76725292515084799101,153238563049442393600],"n":9,"positive":true,"q":14,"ratio":[30332555858050874591383674025628283000301187968000,28067732524479145869809023573270999816769064892473]},{"joint":[7689585348976774699999024501,32546304942704344893164099232],"lower_bound":[91757146658062573909434299557861,85203064754226819211244705611425],"marginal":[42122185590781554706449,90104275073361382091776],"n":10,"positive":true,"q":14,"ratio":[155201651020481606261361192440469971244362111431245824,143557572259236826881358871387598624959191707557423193]},{"joint":[113351254879740835794764906716310513,550131494300621439679489084906392576],"lower_bound":[4710200195144829484053592349277085,4373757324064350781374155406288633],"marginal":[14040728530260518235483,32168375071735665674240],"n":11,"positive":true,"q":14,"ratio":[36463256818234108324680745296000204268461667009513452851200,33714495845189999782742729904583715827399611067397130441711]},{"joint":[32727986598377275841728443917570321,182138129869845089246708505003945408],"lower_bound":[6725965037646640489880649067311671903,6245538963529172029650448203386767059],"marginal":[1410629873249683485564270561,3461445831219101263123296256],"n":12,"positive":true,"q":14,"ratio":[50752196443266140941742270588037053093655877982918701655816142848,46908063129468263659340829674679635624804873462371900307610142419]},{"joint":[197,240],"lower_bound":[224,211],"marginal":[211,240],"n":1,"positive":true,"q":15,"ratio":[47280,44521]},{"joint":[10441,14460],"lower_bound":[190631,178084],"marginal":[44521,54225],"n":2,"positive":true,"q":15,"ratio":[8492448375,7928477764]},{"joint":[1868730377,2941164000],"lower_bound":[2425446464,2263937371],"marginal":[9393931,12204000],"n":3,"positive":true,"q":15,"ratio":[22805985520908000,21267271451495401]},{"joint":[46250925781,82744645500],"lower_bound":[8494737251,7928477764],"marginal":[1982119441,2745950625],"n":4,"positive":true,"q":15,"ratio":[1905041378327483446875,1775816460232348921412]},{"joint":[1498060937707687,3046567314150000],"lower_bound":[115191511639904,107512140599281],"marginal":[1982119441,2928150000],"n":5,"positive":true,"q":15,"ratio":[4386547134748763689050000,4087681977213728637484121]},{"joint":[271806969751967521,628355332329637500],"lower_bound":[19231688848852394621,17949577105062118444],"marginal":[88245939632761,139013932640625],"n":6,"positive":true,"q":15,"ratio":[1700323010295858442253554431328125,1583977297646900653996210044743884]},{"joint":[20751299737042370032391,54532271107656945000000],"lower_bound":[34781887335627076303232,32463094967139954573373],"marginal":[18619893262512571,31278135015000000],"n":7,"positive":true,"q":15,"ratio":[649061954911945246648715621270865000000,604459363258954992622135900968354371983]},{"joint":[105704476986046703210333,315765909908124443437500],"lower_bound":[426212788036424015364283,397798602281959719006212],"marginal":[3928797478390152481,7037580380937890625],"n":8,"positive":true,"q":15,"ratio":[11158556301214545753936959892295030857421875,10388489791025378033053244330385940510703108]},{"joint":[1280453296833989563515293040917,4348096581123892877559468750000],"lower_bound":[2438925962773694342160720843104,2276330898639080007203949225331],"marginal":[828976267940322173491,1583455585749468750000],"n":9,"positive":true,"q":15,"ratio":[2027540925163103323991552114232509452704762843750000,1887024292951064342879283862799095692659051633900521]},{"joint":[37161933904823297545074765461,143448934131702520062004687500],"lower_bound":[175436378920994593694447743524601,163740620326536413984906983563164],"marginal":[174913992535407978606601,356277506794207119140625],"n":10,"positive":true,"q":15,"ratio":[992997086944616871622439124352454894974324181396484375,923887923920608459622144949336731781870304311573898244]},{"joint":[11287145874432361949608225288059931097,49527537620732447934538503126562500000],"lower_bound":[115788010088223514682749840910394944,108068809415688947222574017130294841],"marginal":[174913992535407978606601,379916772647892187500000],"n":11,"positive":true,"q":15,"ratio":[4288176033020313915448366920411937014788625273534604687500000,3988479600847157481605943870934317483001871929796946036388051]},{"joint":[135105370509582943389431302143592469,673905174447634457202202617773437500],"lower_bound":[6579728553189616814929095669518371037,6141079982977033835543306343472038268],"marginal":[7787345861668898615544483121,18036548781458811347900390625],"n":12,"positive":true,"q":15,"ratio":[5811850534912085320593277392938616787089905269481400452091064453125,5403966658452372371929512888677885431330232225392679597740304410364]},{"joint":[113,136],"lower_bound":[255,241],"marginal":[241,272],"n":1,"positive":true,"q":16,"ratio":[61472,58081]},{"joint":[13673,18564],"lower_bound":[1052415,987377],"marginal":[58081,69888],"n":2,"positive":true,"q":16,"ratio":[61157031936,57347843537]},{"joint":[75964589,116320256],"lower_bound":[1358606085,1273774411],"marginal":[13997521,17895424],"n":3,"positive":true,"q":16,"ratio":[2718837058281472,2547097723890733]},{"joint":[8230053403,14215677440],"lower_bound":[61170719775,57347843537],"marginal":[3373402561,4581294080],"n":4,"positive":true,"q":16,"ratio":[53087647266012837969920,49718542099674576252049]},{"joint":[4207648244903933,8198544614227968],"lower_bound":[50307757378515,47163541205341],"marginal":[3373402561,4866441216],"n":5,"positive":true,"q":16,"ratio":[40952545682861123023405056,38343488175790251863070541]},{"joint":[1005978004557823,2211156147306496],"lower_bound":[11131156335291466755,10435459374780333101],"marginal":[195930594145441,300239974039552],"n":6,"positive":true,"q":16,"ratio":[2184315745723297562814377646620672,2044625755481322930924218420542541]},{"joint":[666472635989092619,1652520822885056512],"lower_bound":[901356590612107109486415,845021805551485442237857],"marginal":[47219273189051281,76861433622560768],"n":7,"positive":true,"q":16,"ratio":[102452084544657494356833935015542784,95875369701597056711165952452861323]},{"joint":[35602991704257875768893,99582909118482493734912],"lower_bound":[13523856157998775898360415,12678615150141528030469009],"marginal":[11379844838561358721,19676527011670523904],"n":8,"positive":true,"q":16,"ratio":[2331407862667891648634985845907882437001609216,2181184294490946227959225328968905023414765569]},{"joint":[82569396626325325935137393,260526032722173170580193280],"lower_bound":[1489114807403636175733764590775,1396045131956843972451536846521],"marginal":[2742542606093287451761,5037190915056373596160],"n":9,"positive":true,"q":16,"ratio":[831835629095624630910950571290864809494194421760,778035613578697468125631585729852007763897957361]},{"joint":[7544467058177585684595341918683,26853090823911745236777102737408],"lower_bound":[939604368679795985093622815859705,880879095638023017964120309046167],"marginal":[660952768068482275874401,1289520874255531152244736],"n":10,"positive":true,"q":16,"ratio":[622639856425805791978102132980636484695173306408115372032,582219476595612645010574997826611310508285358540202470967]},{"joint":[2096233452320958245014754206479679991,8416645983744443033957191947242176512],"lower_bound":[826851844439548700565493029210864255,775173604162121208576494354236501361],"marginal":[660952768068482275874401,1369781509582711896932352],"n":11,"positive":true,"q":16,"ratio":[5742763645515963817194600750887127338393664691897231069937664,5368569852021861420312718968245893617872527885583964333734887]},{"joint":[10019616775623751467642512421220032203,45382061861071507858390408764361539584],"lower_bound":[10951812426139545283795928694652260015,10267324149505864788743377131649047617],"marginal":[38388797722185519065061084481,84510040015215274668115099648],"n":12,"positive":true,"q":16,"ratio":[108385051474570941797234763569474547196626913049851927941262587461632,101296609090337216299194327749967958772503492621292334795176984066689]},{"joint":[577,650],"lower_bound":[624,601],"marginal":[601,650],"n":1,"positive":true,"q":25,"ratio":[375050,361201]},{"joint":[24811,30225],"lower_bound":[4890312,4695613],"marginal":[361201,406875],"n":2,"positive":true,"q":25,"ratio":[1766620734375,1696060111213]},{"joint":[41893787209,55185812500],"lower_bound":[49069015008,47106750817],"marginal":[217081801,254312500],"n":3,"positive":true,"q":25,"ratio":[10654113759588812500,10226018306612581417]},{"joint":[56540943484290813130615229011,110141173077141819891357421875],"lower_bound":[45019331946538067989599719256,43218558668792068792629590269],"marginal":[17021419531644106084801,24253192047271728515625],"n":8,"positive":true,"q":25,"ratio":[239977213150227385892434165459283161914356231689453125,230255701438853497176913227745814209294879542699659797]},{"joint":[22114875701280231642523063770180277955675909529522377087797781,80561775451492218689919661837436729041983373463153839111328125],"lower_bound":[3439030080025360232849701317894092387477968282546815732735384,3301468876824345823535842451378587398722397316604076853227341],"marginal":[289728722872235459745150239945139673003209601,564688631502866892712214030325412750244140625],"n":16,"positive":true,"q":25,"ratio":[312200472390298444504971638169469008978356389445452733713014656983619341709307379893143661320209503173828125,299394003082127174913233014528209888820366690538770321484177767043060306390444742070213597499438446319994533]},{"joint":[677,756],"lower_bound":[728,703],"marginal":[703,756],"n":1,"positive":true,"q":27,"ratio":[511812,494209]},{"joint":[119152,143073],"lower_bound":[3591965,3459463],"marginal":[494209,551853],"n":2,"positive":true,"q":27,"ratio":[1775368493712,1709697749767]},{"joint":[235890934373,304556633640],"lower_bound":[273117113360,263003697739],"marginal":[347428927,402320520],"n":3,"positive":true,"q":27,"ratio":[94903763380231233960,91375092502493096053]},{"joint":[1122278830594728533886239427952,2082877176854331883880985113865],"lower_bound":[115227710954475256713738782737,110960017956308364703027746767],"marginal":[59654416235884558133761,82834383195202897568241],"n":8,"positive":true,"q":27,"ratio":[2510008417044394400750831718942940610721401404517555664,2416028110297997993720423269549711206082667723774750755]},{"joint":[416082758153562693896981617988191585806426192073780033084765808,1380114389511224114383232796187670995578849080605322494899465945],"lower_bound":[57099293006916074180231472454456306136029229478875183223949441,54984504377030293655038282894099265172513217099091447792887151],"marginal":[3558649376444167173416649443111672743168005121,6607404111948863218416165262388359513904845281],"n":16,"positive":true,"q":27,"ratio":[74229127032641612525465815241226827761064757006562204015623102450424621790024052930212406891433054395691705296,71419758858624808825902783007928612186515409421488952074634691263869736979095571845424889022119049336231598915]},{"joint":[481,528],"lower_bound":[341,331],"marginal":[331,352],"n":1,"positive":true,"q":32,"ratio":[338624,328683]},{"joint":[34151,39864],"lower_bound":[33586175,32539617],"marginal":[986049,1082368],"n":2,"positive":true,"q":32,"ratio":[33119698812928,32085656803233]},{"joint":[471932942689,585777561600],"lower_bound":[356113196725,344986005483],"marginal":[326382219,369459200],"n":3,"positive":true,"q":32,"ratio":[348719934919047577600,337791893980463120331]},{"joint":[430446083176874097414780257143,726455720463446891014442188800],"lower_bound":[33767315823803874464278818498751,32712087204319228096647143255841],"marginal":[945352959132095589420801,1247923426698936583192576],"n":8,"positive":true,"q":32,"ratio":[1925194884039957204830962948604176482854896330844156198912,1864563538172947109397383428470349647314588637789053079825]},{"joint":[1224853595030732870931056374951712770303634345638738897481214555713,3379688484686570992194282903779295116785994788145147897385163161600],"lower_bound":[2064626193875869258522831475361864615332734205023522630618555649231,2000106625317248344193994094616623595999220692619112981609600847121],"marginal":[893692217339809593677055887744746833070651481601,1508646851438351399436061723806297968205182795776],"n":16,"positive":true,"q":32,"ratio":[1892220436086846137792860784846575944863787902167939070185484445012712227610503588205902486956533901481266230341926912,1832166718018210806240205065086933523534962244582392380844898468785017703248281924497173143484003205493531428953739025]},{"joint":[461,490],"lower_bound":[2400,2353],"marginal":[2353,2450],"n":1,"positive":true,"q":49,"ratio":[5647250,5536609]},{"joint":[542597,600495],"lower_bound":[141295248,138415225],"marginal":[5536609,5884851],"n":2,"positive":true,"q":49,"ratio":[156462022404303,153270196094405]},{"joint":[2003633111069,2308783976660],"lower_bound":[10865316331200,10643582678209],"marginal":[13027640977,14129644900],"n":3,"positive":true,"q":49,"ratio":[141553121846436146990500,138660773840722973370193]},{"joint":[16613689347274415147433714438803749,23426884329869407727108657845567485],"lower_bound":[13824666525568734143263037604649968,13542530474026594845323112958792805],"marginal":[939670120432694468626892161,1127436584124001634083939401],"n":8,"positive":true,"q":49,"ratio":[917813177202030666630628884079937332601613941367681088533103101,899019941237170491286536325661162690306768369113685061101154565]},{"joint":[220723414286614240730871613142111523644173515352153025692400851596800711269,429922780871590503673919579273009641801741654033679723710903808613473304485],"lower_bound":[12697546290446375314622597776018512870779890117632301535618337150555149424,12438412692682163573507850887155823303424688784798140824943226790659988565],"marginal":[882979935233994526703160487488167204587524477523249921,1245172164461582277224794151343358157141275599294278801],"n":16,"positive":true,"q":49,"ratio":[13467093924216085341798847217188497012065847046328305462641609113808552073341033013986659677921537616003807765401534220080236914981,13190425469391628902768450194684981632591841048953674289634018349639790412767522559018433277064607122055527867784809199456081191365]},{"joint":[397,416],"lower_bound":[4095,4033],"marginal":[4033,4160],"n":1,"positive":true,"q":64,"ratio":[16515200,16265089]},{"joint":[800749,865488],"lower_bound":[1073999871,1057230785],"marginal":[16265089,17043456],"n":2,"positive":true,"q":64,"ratio":[3493767769227264,3439190562312973]},{"joint":[8685021879343,9682682773504],"lower_bound":[92427338379285,90983183160619],"marginal":[65597103937,69810257920],"n":3,"positive":true,"q":64,"ratio":[6063036174377779501465600,5968233322306232708257003]},{"joint":[53952889301288300095367486586310242541,70234143356420202429557712027383758848],"lower_bound":[15507024559886557920602856848097576627,15264727301138338460018473493728142861],"marginal":[69988353395873511358695882241,80485752395443132135108509696],"n":8,"positive":true,"q":64,"ratio":[4446657422665976765457976694996413769317992706275661575387965621796864,4377042768872673849900289665332760499044562479780979860157000766659597]},{"joint":[27616014852411761613585075012173399712563034415124536835762079116265526800501533,46066874565547204266464201249059406971163840827680793966431010240146505606365184],"lower_bound":[305487920822898179950240798065714560105830913216614206689442804114126932051353779,300714672060040395888518285597065400580595514985687925210614340128651540048006157],"marginal":[4898369611065679269359671047322595842637172238649339182081,6376738270869009029928421001352562261397404509652454998016],"n":16,"positive":true,"q":64,"ratio":[360653002338838627034824931658938844563327594426395177593813031158848513304164856071791989299630767449342302715651737595008449620623275065344,354995798304136490386446688414908413807216804791338030409564456569459165812037303412789806988924397514444416917444289669030350570156929524797]}],"identities":{"A2_minus_q3_t":[1,6,9,5,1],"A_minus_q_t":[1,2,1],"qD_minus_A2_q":[-1,1],"twoA_minus_q_qplus1_t":[0,1,1]},"schema_version":1,"source_manifest_sha256":"2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59"} diff --git a/research/common-covector-all-field-positive/RUN-RECORDS.json b/research/common-covector-all-field-positive/RUN-RECORDS.json new file mode 100644 index 0000000000..3ea2f07a59 --- /dev/null +++ b/research/common-covector-all-field-positive/RUN-RECORDS.json @@ -0,0 +1,521 @@ +{ + "schema_version": 1, + "environment": { + "python_executable": "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "python_version": "3.12.14", + "platform": "macOS26.5.2arm64", + "dependencies": "stdlib only", + "concurrency": "One scientific child at a time; other work static review/metadata only." + }, + "advance_claim": { + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19385726", + "status": "Rendered before candidate execution." + }, + "immutable_inputs": { + "SOURCE-PINS.json": "2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59", + "CASES.json": "a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b", + "SCHEMA.json": "70db0325541f073c41886cf9fb43289723a6394d4c1e82d999dd49cda50507f5" + }, + "primary_first": { + "utc_after_first": "2026-11-03T23:39:03.159918+00:00", + "elapsed_seconds": 0.039713, + "returncode": 0, + "child_maxrss_bytes_darwin": 28934144, + "command": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/verify.py", + "--emit", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/RESULT.json" + ], + "code_unchanged": true, + "result_sha256": "93cbb1412fb004795565d4e3ee622f56c6165f1a0e79ab20aa91749f6027efa8", + "result_bytes": 48577, + "utc_before_first": "2026-11-03T23:39:03.101951+00:00", + "presealed_code_sha256": "5a6ac2615a6b7c39d8bbae0296975b0e9d75981f2be2d0d9efe0467ce1643d5f" + }, + "primary_strict_modes": [ + { + "label": "RETAINED", + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/verify.py" + ], + "returncode": 0, + "elapsed_seconds": 0.037322, + "utc_finished": "2026-11-03T23:40:51.814307+00:00", + "cumulative_child_maxrss_bytes_darwin": 28868608 + }, + { + "label": "OPTIMIZED-RETAINED", + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "-O", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/verify.py" + ], + "returncode": 0, + "elapsed_seconds": 0.085078, + "utc_finished": "2026-11-03T23:40:51.900037+00:00", + "cumulative_child_maxrss_bytes_darwin": 30326784 + }, + { + "label": "EMIT", + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/verify.py", + "--emit", + "/private/tmp/contribution-batch-b10-20261103T1814Z/session-08/EMIT.json" + ], + "returncode": 0, + "elapsed_seconds": 0.032374, + "utc_finished": "2026-11-03T23:40:51.932552+00:00", + "cumulative_child_maxrss_bytes_darwin": 30326784 + }, + { + "label": "OPTIMIZED-EMIT", + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "-O", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/verify.py", + "--emit", + "/private/tmp/contribution-batch-b10-20261103T1814Z/session-08/OPTIMIZED-EMIT.json" + ], + "returncode": 0, + "elapsed_seconds": 0.078679, + "utc_finished": "2026-11-03T23:40:52.011434+00:00", + "cumulative_child_maxrss_bytes_darwin": 30326784 + } + ], + "primary_emission_summary": { + "code_unchanged_since_first": true, + "receipt_unchanged_since_first": true, + "canonical_emissions_equal": true, + "result_sha256": "93cbb1412fb004795565d4e3ee622f56c6165f1a0e79ab20aa91749f6027efa8", + "utc": "2026-11-03T23:40:52.011708+00:00" + }, + "oracle_blind_first": { + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/oracle.py", + "--emit", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/ORACLE.json" + ], + "canonical_receipt_sha256": "93cbb1412fb004795565d4e3ee622f56c6165f1a0e79ab20aa91749f6027efa8", + "code_after_sha256": "ba3c2f8ac2b31af4f2a314a985dbd381ef684d96627e935d6aecbb5974b0ae6d", + "code_before_sha256": "ba3c2f8ac2b31af4f2a314a985dbd381ef684d96627e935d6aecbb5974b0ae6d", + "elapsed_seconds": 0.03890341706573963, + "exit_code": 0, + "peak_rss_bytes_macos": 28884992, + "primary_data_read": false, + "python": "3.12.14 (main, Aug 25 2026, 13:50:33) [Clang 22.1.3 ]", + "receipt_sha256": "aaa117b9104ed2e3bab87b3e046fbafc18719ed755fca14ea5d4e5e6a44a3206", + "stderr_sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855", + "stdout_sha256": "4aa7ea62fac22deb46462cb4b31b1597e76fdfc76b78ca46aae331ed8d622e48", + "utc_finished": "2026-11-03T23:39:36.736277+00:00", + "utc_started": "2026-11-03T23:39:36.697550+00:00" + }, + "oracle_actual_modes": [ + { + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-W", + "error", + "-B", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/oracle.py", + "--check-primary", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/RESULT.json" + ], + "code_sha256": "ba3c2f8ac2b31af4f2a314a985dbd381ef684d96627e935d6aecbb5974b0ae6d", + "elapsed_seconds": 0.03904387541115284, + "exit_code": 0, + "peak_rss_bytes_macos": 29048832, + "python": "3.12.14 (main, Aug 25 2026, 13:50:33) [Clang 22.1.3 ]", + "source_cases_schema": { + "CASES.json": "a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b", + "SCHEMA.json": "70db0325541f073c41886cf9fb43289723a6394d4c1e82d999dd49cda50507f5", + "SOURCE-PINS.json": "2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59" + }, + "stderr_sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855", + "stdout_sha256": "2dc1d601b21d3a7ed35fec7398163e1e1560e93a055e7832f6a4f7952455fd3c", + "utc_finished": "2026-11-03T23:41:16.824831+00:00", + "utc_started": "2026-11-03T23:41:16.785746+00:00" + }, + { + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "-I", + "-O", + "-W", + "error", + "-B", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/oracle.py", + "--check-primary", + "/private/tmp/crocswap-b9/research/common-covector-all-field-positive/RESULT.json" + ], + "code_sha256": "ba3c2f8ac2b31af4f2a314a985dbd381ef684d96627e935d6aecbb5974b0ae6d", + "elapsed_seconds": 0.08216083329170942, + "exit_code": 0, + "peak_rss_bytes_macos": 29884416, + "python": "3.12.14 (main, Aug 25 2026, 13:50:33) [Clang 22.1.3 ]", + "source_cases_schema": { + "CASES.json": "a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b", + "SCHEMA.json": "70db0325541f073c41886cf9fb43289723a6394d4c1e82d999dd49cda50507f5", + "SOURCE-PINS.json": "2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59" + }, + "stderr_sha256": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855", + "stdout_sha256": "2dc1d601b21d3a7ed35fec7398163e1e1560e93a055e7832f6a4f7952455fd3c", + "utc_finished": "2026-11-03T23:41:16.907163+00:00", + "utc_started": "2026-11-03T23:41:16.825418+00:00" + } + ], + "independence": "Neither engine read peer code or scientific results before its blind first. No predecessor executable/peer code imported or executed. After both first seals, complete peer scientific data is compared explicitly.", + "common_canonical_sha256": "93cbb1412fb004795565d4e3ee622f56c6165f1a0e79ab20aa91749f6027efa8", + "scientific_failures": [], + "corrections": [ + { + "scope": "root external-harness log filename only", + "change": "Flatten slash to underscore in output log names; expected negative-control scope and scientific package unchanged.", + "first_attempt": "Retained original sealed code and MUTANT-FIRST-UNLOGGED; first subprocess outcome UNKNOWN.", + "later_full_attempt": "26 intended rejections exit1 with diagnostics retained; mutant restored." + } + ], + "static_review": "pending final proof/metadata evidence", + "root_external_rejections": { + "first_harness_preseal": { + "at": "2026-11-03T23:40:12.326058+00:00", + "harness_sha256": "d4a2c169608e2282518fe8bcc75b73b7f0be3ba35ad52b61ec5f6cb9c91fa584", + "scope": "External actual-CLI intended rejection tests after both blind firsts; not yet executed" + }, + "first_subprocess_outcome": null, + "first_subprocess_outcome_status": "UNKNOWN: reporting exception prevented persistence of status/stdout/stderr; no outcome claimed.", + "first_failure_note": "The first external harness attempt stopped while saving the first source-control diagnostics: a slash in inputs/4807-PROOF.md-verify.py.stdout was treated as a nonexistent output subdirectory. The subprocess had returned, but its status/stdout/stderr were not persisted before this reporting exception; no first rejection outcome is claimed. The original sealed harness and altered mutant package are retained as ROOT-REJECTIONS-FIRST-CODE.py and MUTANT-FIRST-UNLOGGED. Only the log filename is corrected by replacing slash with underscore. The real scientific package, code, sources, cases, schema and first receipts were never changed. The corrected full suite will be a later run, not a replacement first.", + "corrected_harness_preseal": { + "at": "2026-11-03T23:41:53.627261+00:00", + "harness_sha256": "7671e1180e2b1f2bf46ad85ac015aea2710bb0fb378afd88383dac8afdf97110", + "change": "Output log filename slash flattened; no scientific code or expected control scope changed" + }, + "full_later_run": { + "runs": [ + { + "name": "inputs/4807-PROOF.md-verify.py", + "engine": "verify.py", + "exit": 1, + "seconds": 0.0787792494520545, + "expected_fragment": "source", + "diagnostic": "FAIL: source bytes/SHA256", + "intended": true + }, + { + "name": "inputs/4807-PROOF.md-oracle.py", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.0693961251527071, + "expected_fragment": "source", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: pinned source bytes changed", + "intended": true + }, + { + "name": "CASES.json-verify.py", + "engine": "verify.py", + "exit": 1, + "seconds": 0.07304404117166996, + "expected_fragment": "cases", + "diagnostic": "FAIL: immutable CASES.json", + "intended": true + }, + { + "name": "CASES.json-oracle.py", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.06675958354026079, + "expected_fragment": "cases", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: source/cases/schema digest changed", + "intended": true + }, + { + "name": "SCHEMA.json-verify.py", + "engine": "verify.py", + "exit": 1, + "seconds": 0.07032762467861176, + "expected_fragment": "schema", + "diagnostic": "FAIL: immutable SCHEMA.json", + "intended": true + }, + { + "name": "SCHEMA.json-oracle.py", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.06711637508124113, + "expected_fragment": "schema", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: source/cases/schema digest changed", + "intended": true + }, + { + "name": "missing-RESULT.json", + "engine": "verify.py", + "exit": 1, + "seconds": 0.07431358378380537, + "expected_fragment": "no such file", + "diagnostic": "FAIL: [Errno 2] No such file or directory: '/private/tmp/contribution-batch-b10-20261103T1814Z/session-08/MUTANT/RESULT.json'", + "intended": true + }, + { + "name": "missing-ORACLE.json", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.06716649979352951, + "expected_fragment": "no such file", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: [Errno 2] No such file or directory: '/private/tmp/contribution-batch-b10-20261103T1814Z/session-08/MUTANT/ORACLE.json'", + "intended": true + }, + { + "name": "bool-primary-version", + "engine": "verify.py", + "exit": 1, + "seconds": 0.0758636249229312, + "expected_fragment": "version", + "diagnostic": "FAIL: integer receipt version", + "intended": true + }, + { + "name": "bool-peer-version", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.08022741694003344, + "expected_fragment": "version", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: receipt schema version must be integer1", + "intended": true + }, + { + "name": "bool-peer-q", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07597837503999472, + "expected_fragment": "domain", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: algebra case order/domain invalid", + "intended": true + }, + { + "name": "wrong-peer-q", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07663604151457548, + "expected_fragment": "domain", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: algebra case order/domain invalid", + "intended": true + }, + { + "name": "int-peer-positive", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07713837455958128, + "expected_fragment": "bool", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: algebra positivity flag must be bool", + "intended": true + }, + { + "name": "unreduced-peer-rational", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07605379167944193, + "expected_fragment": "reduced", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: rational must be reduced with positive denominator", + "intended": true + }, + { + "name": "zero-peer-denominator", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07955770846456289, + "expected_fragment": "positive denominator", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: rational must be reduced with positive denominator", + "intended": true + }, + { + "name": "negative-peer-denominator", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07721558306366205, + "expected_fragment": "positive denominator", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: rational must be reduced with positive denominator", + "intended": true + }, + { + "name": "bool-peer-rational", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07637466676533222, + "expected_fragment": "not bool", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: rational entries must be integers, not bool", + "intended": true + }, + { + "name": "changed-joint-to-product", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07949808333069086, + "expected_fragment": "differs", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: actual complete primary receipt differs", + "intended": true + }, + { + "name": "lost-strict-ratio", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.0800424162298441, + "expected_fragment": "differs", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: actual complete primary receipt differs", + "intended": true + }, + { + "name": "changed-polynomial-coefficient", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07843854185193777, + "expected_fragment": "differs", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: actual complete primary receipt differs", + "intended": true + }, + { + "name": "bool-polynomial-coefficient", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.07787000015377998, + "expected_fragment": "coefficient", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: identity coefficient types/length invalid", + "intended": true + }, + { + "name": "swapped-case-order", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.09673537500202656, + "expected_fragment": "domain", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: algebra case order/domain invalid", + "intended": true + }, + { + "name": "missing-case", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.08947554230690002, + "expected_fragment": "count", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: algebra case count invalid", + "intended": true + }, + { + "name": "extra-key", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.08901162445545197, + "expected_fragment": "schema", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: receipt schema keys invalid", + "intended": true + }, + { + "name": "duplicate-peer-json", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.08753870893269777, + "expected_fragment": "duplicate", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: duplicate JSON key: schema_version", + "intended": true + }, + { + "name": "nonfinite-peer-json", + "engine": "oracle.py", + "exit": 1, + "seconds": 0.08955979254096746, + "expected_fragment": "noninteger", + "diagnostic": "FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: noninteger JSON number forbidden: NaN", + "intended": true + } + ], + "all_intended": true, + "mutant_restored": true + }, + "evidence_sha256": "1d993258bbf3c1b977af18f2a45a6b333c6bf74366adda79da156db52ef7d8b2", + "scientific_files_changed": false + }, + "registered_committed_export_cold": "pending root evidence", + "publication_ci": "pending", + "root_registered_commit_export": [ + { + "name": "REGISTERED", + "exit": 0, + "seconds": 0.6268831249326468, + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "scripts/research_package.py", + "--package", + "research/common-covector-all-field-positive" + ] + }, + { + "name": "COMMIT-CHECK", + "exit": 0, + "seconds": 0.12818054016679525, + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "scripts/check_research_commit.py", + "--package", + "research/common-covector-all-field-positive", + "--check-source-history", + "--check-modes" + ] + }, + { + "name": "INITIAL-EXPORT", + "exit": 0, + "seconds": 0.08462879247963428, + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "scripts/export_research_package.py", + "export", + "--package", + "research/common-covector-all-field-positive", + "--ref", + "HEAD", + "--output", + "/private/tmp/contribution-batch-b10-20261103T1814Z/session-08/INITIAL-PACKAGE.tar" + ] + }, + { + "name": "INITIAL-EXPORT-CHECK", + "exit": 0, + "seconds": 0.044402084313333035, + "argv": [ + "/Users/evaayala/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3", + "scripts/export_research_package.py", + "check", + "/private/tmp/contribution-batch-b10-20261103T1814Z/session-08/INITIAL-PACKAGE.tar", + "--check-inputs" + ] + } + ], + "science_freeze_utc": "2026-11-03T23:42:46.895822+00:00" +} diff --git a/research/common-covector-all-field-positive/SCHEMA.json b/research/common-covector-all-field-positive/SCHEMA.json new file mode 100644 index 0000000000..3a316ec26a --- /dev/null +++ b/research/common-covector-all-field-positive/SCHEMA.json @@ -0,0 +1,50 @@ +{ + "schema_version": 1, + "common_keys": [ + "schema_version", + "source_manifest_sha256", + "case_manifest_sha256", + "identities", + "cases" + ], + "identities": { + "qD_minus_A2_q": { + "variable": "q", + "increasing_coefficients": [ + -1, + 1 + ] + }, + "A_minus_q_t": { + "variable": "t=q-2", + "increasing_coefficients": [ + 1, + 2, + 1 + ] + }, + "twoA_minus_q_qplus1_t": { + "variable": "t=q-2", + "increasing_coefficients": [ + 0, + 1, + 1 + ] + }, + "A2_minus_q3_t": { + "variable": "t=q-2", + "increasing_coefficients": [ + 1, + 6, + 9, + 5, + 1 + ] + } + }, + "case_order": "Exact CASES.json order,205 rows; each exact keys q,n,marginal,joint,ratio,lower_bound,positive.", + "case_semantics": "A=q^2-q+1,D=q^2+(q-1)^3,x=q^(n+1); p=(q-1)A^n/((x-1)q^n),J=(q-1)(D^n-A^n)/((x-1)(x-q)q^(n-1)),ratio=J/p^2,L=q(x-1)/((q-1)(x-q))*(1-(q/A)^n). Require ratio>L>=1; positive is strict boolean ratio>1.", + "rationals": "Exact reduced integer pairs[numerator,denominator] with positive denominator. No float/bool-as-int aliases; duplicate/nonfinite JSON rejected.", + "receipt": "Own primary receipt is common5-only; oracle may retain own metadata separately but peer comparison uses exact common5. Runtime source/cases/schema byte binding specified by each engine.", + "canonical": "json.dumps(sort_keys=True,separators=(comma,colon)),UTF8+LF. No matrix/field census; nonprimepowers are parameter-algebra fixtures only." +} diff --git a/research/common-covector-all-field-positive/SOURCE-PINS.json b/research/common-covector-all-field-positive/SOURCE-PINS.json new file mode 100644 index 0000000000..f677fa8f64 --- /dev/null +++ b/research/common-covector-all-field-positive/SOURCE-PINS.json @@ -0,0 +1,26 @@ +{ + "schema_version": 1, + "scope": "Two inert prose inputs: credited4807 pair count/marginal/binary sign and explicit odd-field sign question; no predecessor executable.", + "files": [ + { + "pr": 4807, + "repository": "petalas/integer-mult-bounds", + "commit": "bd8ea82bb0a7e40427d6d4fc1477fda0ab40388b", + "source_path": "research/common-covector-header-law/README.md", + "local_path": "inputs/4807-README.md", + "bytes": 5970, + "git_blob": "08535a3694325873810a42d7022a85fb714e0555", + "sha256": "53607e82913b1f0124aa46719f97f782c0e8db7f29de4c23fb9833776f6996e7" + }, + { + "pr": 4807, + "repository": "petalas/integer-mult-bounds", + "commit": "bd8ea82bb0a7e40427d6d4fc1477fda0ab40388b", + "source_path": "research/common-covector-header-law/PROOF.md", + "local_path": "inputs/4807-PROOF.md", + "bytes": 5856, + "git_blob": "8c0baf75700a470a009dbd67cdb6b4a33efbd9d7", + "sha256": "9c9bfc2cab96c5451f819292de156ae36b04447db7ca1a0fd33cd71682f24044" + } + ] +} diff --git a/research/common-covector-all-field-positive/SOURCES.json b/research/common-covector-all-field-positive/SOURCES.json new file mode 100644 index 0000000000..75ea7c3d55 --- /dev/null +++ b/research/common-covector-all-field-positive/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + } + ] +} diff --git a/research/common-covector-all-field-positive/SOURCES.md b/research/common-covector-all-field-positive/SOURCES.md new file mode 100644 index 0000000000..83961bc48e --- /dev/null +++ b/research/common-covector-all-field-positive/SOURCES.md @@ -0,0 +1,25 @@ +# Source binding and prior coverage + +SOURCES.json binds the exact canonical catalogue and selected record as historical +provenance at7c49fe32c55de02c2c873655c804b16e4c3fef0a. This does not transfer supplier +admission. Two external prose objects are vendored exact in inputs/ and authenticate +by their immutable manifest SHA256 plus every file byte count, SHA256 and original +Gitblob in both engines. No pending external Git-object or source-checker dependency +is needed for direct replay. Package-local source changes already trigger replay. + +Both objects are Nick Petalas, PR4807, repository petalas/integer-mult-bounds, +headbd8ea82bb0a7e40427d6d4fc1477fda0ab40388b: + +- research/common-covector-header-law/README.md -> inputs/4807-README.md; + Gitblob08535a3694325873810a42d7022a85fb714e0555; + SHA25653607e82913b1f0124aa46719f97f782c0e8db7f29de4c23fb9833776f6996e7. +- research/common-covector-header-law/PROOF.md -> inputs/4807-PROOF.md; + Gitblob8c0baf75700a470a009dbd67cdb6b4a33efbd9d7; + SHA2569c9bfc2cab96c5451f819292de156ae36b04447db7ca1a0fd33cd71682f24044. + +These are inert readme/proof text only; original notices and credit remain intact. +The all-field count, common-covector orbit, dependent-pair subtraction, binary sign, +marginal4227 and partial-sum4261method are credited cited premises. SourceREADME +Open next question2 explicitly leaves odd-field signs open and suggests the identity +q*delta-alpha^2=q-1. Only the resulting universal sign proof is added here. +No predecessor executable, GLcensus, spectrum or native caller is run or audited. diff --git a/research/common-covector-all-field-positive/TASK.json b/research/common-covector-all-field-positive/TASK.json new file mode 100644 index 0000000000..c299e1b5c2 --- /dev/null +++ b/research/common-covector-all-field-positive/TASK.json @@ -0,0 +1,111 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 8, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "original_card": { + "id": "independent-moment", + "question": "Does a changed construction's serialized target/paid invoice independently support its claimed improvement?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "docs/research/recursive-invoice-preflight.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Independently recount one changed emitted word and its complete caller, importing no constructor or pricing engine. Include target losses, owned lifetimes, native orientation and extra charges. Check existing #5633/#5708/#5717/#5719 coverage to avoid duplicate audits and preserve its exact head. Stop after the chosen missing implication; a correct root alone is not supplier admission.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "invoice", + "signed moment", + "productive target", + "independent recount" + ], + "existing_checks": [ + { + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Close the credited PR4807 odd-field sign question: prove J>p^2 for the common-covector full-guard pair over every finite field and dimension, using its existing all-field count formula.", + "scope_change_reason": "Take4807READMEquestion2 as a modest algebraic sign-corollary side task. Count, marginal, binary sign and suggested identity are prior coverage; the original changed paid/target invoice acceptance gate remains unmet.", + "bottleneck_link": "Names the precise dependence law available before applying a shared-header model; it does not provide header production or a supplier/caller price.", + "budget_minutes": 60, + "stop_rule": "One existing pair formula and its sign only; freeze205algebra fixtures and4identities; no count census or physical extension. Science cutoff00:18:19UTC, final15minutes verification/handoff. Preserve first outputs/failures.", + "outcome": "completed", + "evidence": "Universal strict-ratio lower-bound proof; two blind-first engines agree on205exact parameter rows and4coefficient arrays. Primary four strict modes and independent normal/O actual peer-data comparisons pass; code/inputs/first receipts unchanged. Root rejection/registered/export/cold stages tracked separately.", + "author": "ToikY", + "ai_assistance": "Substantial OpenAI Codex assistance with separate AI primary, independent oracle and static reviewer; no independent human or formal-kernel acceptance.", + "open_questions": [ + { + "question": "What is the law for two-way pairs with independent covectors?", + "why_it_matters": "PR4807 question1 names a different partial-Gram orbit; its common-covector formula is not an arbitrary-pair law.", + "first_step": "Pin one normalized independent-covector pair and its exact full-proper-minor predicate.", + "blocked_by": "No count/overlap/physical applicability proof for that changed orbit is supplied here." + }, + { + "question": "Can an actual producer and consumer use these headers at a favorable full price?", + "why_it_matters": "Strict positive correlation is not a physical supplier or a paid/target invoice.", + "first_step": "Name the producer, complete header domain and caller, then charge selection, emission, dispatch, restoration, stock and precision.", + "blocked_by": "Those operations, compatibility and the complete physical caller bill remain unknown." + }, + { + "question": "Which restricted header catalogues preserve this sign?", + "why_it_matters": "Complete uniform GL conjugation is essential to the cited source probabilities.", + "first_step": "Choose one actual legal catalogue with its exact distribution and derive its probabilities independently.", + "blocked_by": "No restricted-header count or sign law is established." + } + ] +} diff --git a/research/common-covector-all-field-positive/VALIDATION.md b/research/common-covector-all-field-positive/VALIDATION.md new file mode 100644 index 0000000000..5ed5e4e421 --- /dev/null +++ b/research/common-covector-all-field-positive/VALIDATION.md @@ -0,0 +1,69 @@ +# Validation and scope + +The rendered advance CLAIM19385726 preceded candidate execution. Exact source2 +prose/source manifest, CASES and SCHEMA plus first code copies were retained +before the first run. Primary FIRST began2026-11-03T23:39:03.101951+00:00 and finished +23:39:03.159918UTC, exit0,0.039713s and28,934,144B direct child peakRSS onmacOS. +Independent oracle FIRST23:39:36.697550→23:39:36.736277UTC passed in0.038903s, +28,884,992B peakRSS. Neither engine read peer code/data before its blind seal. +No scientific first failure or code/input/output correction occurred. + +Primary sourceSHA2565a6ac2615a6b7c39d8bbae0296975b0e9d75981f2be2d0d9efe0467ce1643d5f +and oracleba3c2f8ac2b31af4f2a314a985dbd381ef684d96627e935d6aecbb5974b0ae6d +remain unchanged. All205exact parameter rows and4coefficient arrays agree under +whole typed common comparison. Canonical common SHA256 is +93cbb1412fb004795565d4e3ee622f56c6165f1a0e79ab20aa91749f6027efa8. +The primary compact receipt and oracle own formatted receipt have different raw +bytes; equality concerns every canonical proof-relevant field, not formatting. + +Primary later normal/optimized default/emission modes passed by23:40:52.011434UTC; +separate emissions equal the original canonical receipt,0.032–0.085s each. +Independent normal/optimized --check-primary runs passed by23:41:16.907163UTC, +comparing all actual submitted rows/coefficients as data. RUN-RECORDS.json retains +exact argv/status/UTC/resources. Primary laterRSS is explicitly a cumulative +child maximum, not a per-run aggregate sampled-memory measurement. + +Primary controls comprise14 intended rejections and one strict-replacement boundary +fixture atq2,n1. Oracle reports16 controls. Source/case/schema authentication, +strict receipt keys/number/boolean guards and actual retained typed comparisons +remain active under-O. The independent engine uses integer recurrences and +Euclidean rational normalization plus polynomial convolution; the primary uses +Fraction closed formulas and exact bounded-degree interpolation. This corroborates +a short written all-dimension sign proof, not a newly verified counting law. + +Nonprimepowers6,10,12,14,15 are parameter-algebra fixtures only. No GL/header +census, predecessor scientific checker, native implementation or selected cold +replay ran. PR4807's all-field count, dependent-pair subtraction, binary theorem +and suggested identity retain credit; PR4227 supplies the marginal. The new scope +is a modest closure of its remaining sign question. Arbitrary pairs/families, +restricted headers and full physical selection/emission/dispatch/restoration/ +stock/precision/producer/caller costs remain outside the result. + +The static AI reviewer passed the scientific code, proof and stated modest scope +without requesting a mathematical or code correction. Final metadata review is +tracked separately. Root's corrected full external suite passes all 26 intended +rejections, each exit 1 with its expected diagnostic; the temporary mutant copy is +restored. Cases include source/case/schema drift, missing receipts, strict schema, +integer/boolean/rational aliases, changed joint/strict ratio/identity coefficient, +row order/count and duplicate/nonfinite JSON. The real scientific files remain +unchanged. + +The original external harness stopped while saving the first source-control log: +its control name contained a slash, interpreted as a nonexistent subdirectory. +The subprocess had returned, but its status/stdout/stderr were not persisted. +That first subprocess outcome is UNKNOWN and no rejection outcome is claimed. +The sealed original harness and MUTANT-FIRST-UNLOGGED are preserved. Only the +log filename was corrected by replacing slash with underscore; the full 26-case +suite is a later run, not a replacement first. Original/corrected harness SHA256s +are d4a2c169608e2282518fe8bcc75b73b7f0be3ba35ad52b61ec5f6cb9c91fa584 and +7671e1180e2b1f2bf46ad85ac015aea2710bb0fb378afd88383dac8afdf97110, +sealed at 23:40:12.326058 and 23:41:53.627261 UTC. RUN-RECORDS.json retains +the exact failure note, seals and every later intended rejection diagnostic. +This was a validation-harness correction, not a scientific-engine defect. + +Metadata/committed byte-mode-history, registered commands, official export, +read-only Git-free/empty-PATH cold replay, public PR and hosted CI remain pending +evidence. Those transport gates will not establish human/formal-kernel acceptance, +supplier admission, a complete multiplication theorem or any selected-frontier change. + +At the root verification checkpoint, all four registered commands, committed-byte/source-history/mode checks, initial official export and its input check passed on local commit6a3025d4. Scientific code, written proof, inputs and first receipts remain unchanged after the23:42:46.895822UTC science freeze. Final archive and read-only empty-PATH Git-free replay follow this documentation commit and are not yet claimed here. Hosted CI/publication remain pending. diff --git a/research/common-covector-all-field-positive/VERIFY.json b/research/common-covector-all-field-positive/VERIFY.json new file mode 100644 index 0000000000..587fa763b5 --- /dev/null +++ b/research/common-covector-all-field-positive/VERIFY.json @@ -0,0 +1,63 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Exact205parameter rows and4identity coefficient arrays; strict ratio lower bounds, retained whole typed profile and14rejections/one boundary fixture" + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "-O", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Exact205parameter rows and4identity coefficient arrays; strict ratio lower bounds, retained whole typed profile and14rejections/one boundary fixture" + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/oracle.py", + "--check-primary", + "{package}/RESULT.json" + ], + "timeout_seconds": 180, + "checks": "Independent integer-recurrence/rational and polynomial-convolution profile; actual205submitted rows and4identity arrays plus16controls" + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "-O", + "{package}/oracle.py", + "--check-primary", + "{package}/RESULT.json" + ], + "timeout_seconds": 180, + "checks": "Independent integer-recurrence/rational and polynomial-convolution profile; actual205submitted rows and4identity arrays plus16controls" + } + ] +} diff --git a/research/common-covector-all-field-positive/inputs/4807-PROOF.md b/research/common-covector-all-field-positive/inputs/4807-PROOF.md new file mode 100644 index 0000000000..8c0baf7570 --- /dev/null +++ b/research/common-covector-all-field-positive/inputs/4807-PROOF.md @@ -0,0 +1,139 @@ +# A common-covector pair has a different dependence law + +This contribution was produced by Nick Petalas. Apache-2.0. + +## Statement + +Let K=F_q be any finite field, m>=2, and let a,c be independent columns +in K^m. Let b be a row with ba=bc=1. Put U=ab, V=cb, P=I-U, Q=I-V. +Thus U,V are distinct rank-one idempotents with UV=U and VU=V. Both +products are nonzero. Their complementary projectors P,Q have a common +image ker(b). This is outside the orthogonal and one-way coupling hypotheses. + +For a complete header G chosen uniformly from GL_m(K), let E_P mean that +every leading principal minor of GPG^-1 of orders 1 through m-1 is +nonzero. Define E_Q in the same way. Write n=m-1 and + +```text +alpha = q^2-q+1, +delta = q^2+(q-1)^3. +``` + +Then the exact joint passing probability is + +```text + (q-1)(delta^n-alpha^n) +J(q,m) = ----------------------------------------- . (1) + (q^m-1)(q^m-q) q^(m-2) +``` + +In particular, over F_2 the events are strictly positively correlated for +every m>=2. At m=2 the joint probability is 1/3 and each marginal is 1/2. +This refutes extension of the known negative-correlation statements to +arbitrary two-way coupled rank-one kernels. It does not contradict their +stated hypotheses. + +Claim type: scoped counting proof with finite corroboration. + +## Header orbit and the guard + +Conjugation takes the triple to (Ga,Gc,bG^-1). GL_m(K) acts transitively +on all triples (a,c,b) satisfying independence and ba=bc=1. To see this, +take a,c-a as the first two basis vectors. The second lies in ker(b). +Extend it to a basis of ker(b), and b has coordinates (1,0,...,0). +The same construction for any other triple gives the required change of +basis. Every triple therefore has the same number of complete-header +preimages, by the stabilizer coset bijection. + +There are (q^m-1)(q^m-q) ordered independent pairs a,c. For each pair, +the two independent linear equations ba=bc=1 have q^(m-2) solutions b. +Consequently the denominator in (1) is the number of triples in this orbit. + +The rank-one determinant identity gives + +```text +det(P[1:k,1:k]) = 1 - sum_(i=1)^k b_i a_i, +det(Q[1:k,1:k]) = 1 - sum_(i=1)^k b_i c_i. +``` + +This is the marginal guard identity of Nick Petalas #4227. We use its +partial-sum method, also used in #4261, and count the new common-covector +orbit directly. For every proper prefix, both partial sums must avoid 1; +at the final coordinate both sums equal 1. + +## Count first, subtract dependent pairs + +Temporarily allow all a,c, retaining ba=bc=1. At one coordinate the +increment is (b_i a_i,b_i c_i). A zero increment has q^2+q-1 preimages: +q^2 choices with b_i=0, and q-1 with b_i nonzero and a_i=c_i=0. +Every nonzero increment has q-1 preimages, one for each nonzero b_i. +Thus the increment weight is q^2 times the zero indicator plus the +constant q-1 on K^2. + +The safe state set S=(K minus {1})^2 has N=(q-1)^2 elements. Its weighted +transition matrix is q^2 I+(q-1)11^T. Every row sum is +q^2+(q-1)N=delta. Start at (0,0) in S. After n safe transitions the +total path weight is delta^n. The terminal state (1,1) is outside S, +so the last increment is nonzero from every safe state and has weight +q-1. The number of all passing triples before enforcing independence is +(q-1)delta^n. + +If a,c are dependent, the endpoint conditions force c=a. Indeed a is +nonzero, write c=t a, and 1=bc=t ba=t. Conversely every diagonal pair +c=a with ba=1 is a dependent triple. There are no other dependent cases. + +For these diagonal triples the scalar increment b_i a_i has 2q-1 +preimages at zero and q-1 at every nonzero element. On K minus {1}, +the safe transition matrix is q I+(q-1)11^T, with row sum +q+(q-1)^2=alpha. The last step again has weight q-1. Therefore exactly +(q-1)alpha^n of the passing triples have dependent columns. Subtracting +them gives the numerator of (1). Dividing by the independent-triple orbit +count proves (1), in every characteristic and every finite field. + +## Binary positive correlation in every dimension + +The cited single-request law #4227 gives + +```text +p(q,m) = (q-1)alpha^n / ((q^m-1)q^(m-1)). +``` + +At q=2, alpha=3 and delta=5, and direct cancellation yields + +```text +J(2,m) / p(2,m)^2 + = [2^(n+1)(2^(n+1)-1)/(2^(n+1)-2)] (5^n-3^n)/9^n. (2) +``` + +Since 5>9/2, replacing 5^n by (9/2)^n strictly decreases (2). The +resulting lower bound is + +```text +2(2^(n+1)-1)/(2^(n+1)-2) * (1-(2/3)^n). +``` + +This is at least 1 exactly when 3^n>=2^(n+1)-1. The latter inequality +holds for every n>=1. It is equality at n=1; if it holds at n then +3^(n+1)>=3*2^(n+1)-3>=2^(n+2)-1, since 2^(n+1)>=2. +The replacement of 5^n was strict even at n=1, so J(2,m)>p(2,m)^2 +for every m>=2. This is a written dimension-uniform proof, rather than +an inference from a finite census. + +## Credit and limits + +The two-way-coupling question is Open next question 1 of Nick Petalas +[#4778](https://github.com/CrocSwap/integer-mult-bounds/pull/4778), following +#4769/#4274's one-way law. The marginal identity and probability are from +#4227; #4261 supplies the predecessor partial-sum/header counting method. +The common-covector orbit, its dependent-pair subtraction, formula (1), +and the binary positive-correlation proof are the new contribution here. +Cinna Davis supplied the BIT request context. source527, commdata2338 and +Jose Manuel retain the normalizer and recursive-closure lineage credit. + +Only this common-covector pair and complete uniformly weighted headers are +covered. The proof does not classify arbitrary two-way pairs, larger +families, restricted header catalogues, or odd-field correlation signs. +Selection, emission, dispatch, dirty restoration, stock, precision and the +physical caller bill remain unknown. No supplier admission, new kappa, +selected-frontier change or complete multiplication theorem follows. +Independent human and formal proof-kernel review are unclaimed. diff --git a/research/common-covector-all-field-positive/inputs/4807-README.md b/research/common-covector-all-field-positive/inputs/4807-README.md new file mode 100644 index 0000000000..08535a3694 --- /dev/null +++ b/research/common-covector-all-field-positive/inputs/4807-README.md @@ -0,0 +1,104 @@ +# Positive correlation for a common-covector full-guard pair + +This contribution was produced by Nick Petalas. Apache-2.0. + +Claim type: scoped counting proof with finite corroboration. Over any finite +field F_q, let a,c be independent columns, b a row with ba=bc=1, and +P=I-ab, Q=I-cb on F_q^m, m>=2. For complete uniformly weighted GL_m(F_q) +headers, the joint full-guard passing fraction is exactly + +```text + (q-1)[(q^2+(q-1)^3)^(m-1) - (q^2-q+1)^(m-1)] +J(q,m) = ------------------------------------------------- . + (q^m-1)(q^m-q)q^(m-2) +``` + +Over F_2 these two guard events are strictly positively correlated in every +dimension m>=2. At m=2, J=1/3 exceeds the marginal product 1/4; at m=3, +J=4/21 and each marginal is 9/28. Thus negative correlation for the known +orthogonal and one-way cases does not extend to every two-way pair. + +[PROOF.md](PROOF.md) counts the common-covector header orbit by two partial +sums, subtracts exactly the equal-column paths, and proves the binary +comparison for all dimensions. This answers one case of Open next question 1 +in [#4778](https://github.com/CrocSwap/integer-mult-bounds/pull/4778). That +question and #4769/#4274's contrasting one-way law retain Nick Petalas's +credit, as do #4227's marginal law and #4261's partial-sum/header method. +Cinna Davis supplied the BIT request context; source527, commdata2338 and +Jose Manuel retain the normalizer and recursive-closure lineage credit. +No predecessor implementation is imported or replayed. + +## Reproduction and evidence + +From the repository root, using CPython 3.12 and the standard library: + +```sh +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/common-covector-header-law/verify.py +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/common-covector-header-law/verify.py +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/common-covector-header-law +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/common-covector-header-law --check-source-history +``` + +Another CPython 3.12 installation may replace the local interpreter path. +The direct marker is `PASS_COMMON_COVECTOR_HEADER_LAW`. The verifier writes +no files. It prints a generated receipt with every domain's counts and +SHA256 hashes of all six package files. Both registered modes keep explicit +checks active, including optimized Python. + +The verifier enumerates all 34,290 complete headers in eight domains: +GL_2 over F_2,F_3,F_4,F_5,F_7, GL_3 over F_2,F_3, and GL_4 over F_2. +It inverts each header, conjugates both literal projectors and tests every +leading minor through rank m-1. Both marginals and the joint count agree. +F_4 is F_2[x]/(x^2+x+1), rather than integers modulo four. + +A separate vector enumeration counts all 26,070 independent orbit triples +in nine domains: q=2,m=2..5; q=3 or 4,m=2..3; q=5,m=2. Ten coordinate +transfers enumerate the actual increment factorizations for widths one and +two over F_2,F_3,F_4,F_5,F_7, at path lengths zero through eight. Their +difference agrees with the joint formula at m=2..9. Exact rational checks +corroborate binary positive correlation in all 255 dimensions m=2..256. +Fourteen fixture, mutation and invalid-input controls distinguish the +field arithmetic, independence, orthogonal substitution, omitted diagonal +subtraction, omitted row fiber and invalid finite-check parameters. + +## Scope and implementation limits + +The all-field and all-dimension claims rest on the written proof. Finite +execution corroborates the explicitly enumerated domains. Only two distinct +rank-one kernels with a common right covector and complete equally weighted +headers are covered. Other two-way pairs, larger families, restricted +headers and odd-field correlation signs are outside the proved claims. + +Header selection, emission, dispatch, dirty restoration, stock, precision, +producer compatibility and the complete paid physical caller remain unknown. +No new kappa, supplier admission, selected-frontier change or complete +multiplication theorem is claimed. Independent human and formal proof-kernel +review are unclaimed. Lean, Docker and the selected operator replay are unrun. + +[TASK.json](TASK.json) records the change from the formal-interface card to +this algebraic side question. [SOURCES.json](SOURCES.json) binds predecessor +text, the catalogue and selected record as historical provenance on canonical +main. There are no runtime dependencies outside this package and no pending +Git-object dependency. Provenance/history checks require full Git history; +the direct verifier also runs from a standalone exported package. + +Power of Ten inspection finds no recursion or subprocesses in the verifier. +Every loop is bounded by fixed domains: at most 65,536 candidate matrices +of size four, 64 vectors per triple coordinate, 49 transfer states, nine +transfer rounds and 255 correlation dimensions. Functions fit within 60 +lines. Explicit require checks enforce input and mathematical contracts. +CPython allocates dynamically, a managed-runtime deviation from fixed +allocation; the stated domains bound live collections. Diagnostics use +warnings as errors. No shared implementation is changed. + +## Open next questions + +1. Determine the law for two-way pairs with independent covectors. Start + with one normalized pair whose two cross products are nonzero; its + partial-Gram orbit differs from the shared-covector model here. +2. Determine the correlation signs for this common-covector family over + odd fields. Compare the new joint formula with #4227's marginal squared, + starting with q*delta-alpha^2=q-1; a quantified sign proof is unclaimed. +3. Find a named physical producer and fully charged shared-header caller. + Pin its header domain before charging selection, emission, dispatch, + dirty restoration, precision and stock. Those costs are unknown. diff --git a/research/common-covector-all-field-positive/oracle.py b/research/common-covector-all-field-positive/oracle.py new file mode 100644 index 0000000000..7d9b0ca7d9 --- /dev/null +++ b/research/common-covector-all-field-positive/oracle.py @@ -0,0 +1,284 @@ +#!/usr/bin/env python3 +"""Independent integer/polynomial oracle for the credited pair-law sign. + +Nick Petalas4807 supplies the joint law, binary sign and released odd-field +question;4227/4261 supply the marginal/header lineage. This program supports +only the new inequality corollary. No predecessor or primary implementation +is read/imported/executed. Substantial OpenAI Codex assistance. Apache-2.0. +""" + +import argparse +import hashlib +import json +from pathlib import Path +import sys + + +ROOT = Path(__file__).resolve().parent +PIN_SHA = "2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59" +CASE_SHA = "a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b" +SCHEMA_SHA = "70db0325541f073c41886cf9fb43289723a6394d4c1e82d999dd49cda50507f5" +COMMON = {"schema_version", "source_manifest_sha256", "case_manifest_sha256", "identities", "cases"} +IDENTITIES = {"qD_minus_A2_q": 2, "A_minus_q_t": 3, + "twoA_minus_q_qplus1_t": 3, "A2_minus_q3_t": 5} +CASE_KEYS = {"q", "n", "marginal", "joint", "ratio", "lower_bound", "positive"} +ORDER = [(q, n) for q in range(2, 17) for n in range(1, 13)] +ORDER += [(q, n) for q in (25, 27, 32, 49, 64) for n in (1, 2, 3, 8, 16)] + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def sha(raw): + return hashlib.sha256(raw).hexdigest() + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":"), allow_nan=False) + + +def unique(pairs): + value = {} + for key, item in pairs: + require(key not in value, "duplicate JSON key: " + key) + value[key] = item + return value + + +def reject_number(value): + raise ValueError("noninteger JSON number forbidden: " + value) + + +def parse(raw): + return json.loads(raw, object_pairs_hook=unique, + parse_float=reject_number, parse_constant=reject_number) + + +def trim(coefficients): + result = list(coefficients) + while len(result) > 1 and result[-1] == 0: + result.pop() + return result + + +def add(left, right): + result = [0] * max(len(left), len(right)) + for index, coefficient in enumerate(left): + result[index] += coefficient + for index, coefficient in enumerate(right): + result[index] += coefficient + return trim(result) + + +def scale(poly, factor): + return trim([factor * coefficient for coefficient in poly]) + + +def multiply(left, right): + result = [0] * (len(left) + len(right) - 1) + for i, a in enumerate(left): + for j, b in enumerate(right): + result[i + j] += a * b + return trim(result) + + +def shift(poly, constant): + result = [0] + for coefficient in reversed(poly): + result = add(multiply(result, [constant, 1]), [coefficient]) + return result + + +def evaluate(poly, value): + result = 0 + for coefficient in reversed(poly): + result = result * value + coefficient + return result + + +def source_polynomials(): + q, qm1 = [0, 1], [-1, 1] + a = add(add(multiply(q, q), scale(q, -1)), [1]) + d = add(multiply(q, q), multiply(multiply(qm1, qm1), qm1)) + return q, a, d + + +def polynomial_identities(): + q, a, d = source_polynomials() + return {"qD_minus_A2_q": add(multiply(q, d), scale(multiply(a, a), -1)), + "A_minus_q_t": shift(add(a, scale(q, -1)), 2), + "twoA_minus_q_qplus1_t": shift(add(scale(a, 2), scale(multiply(q, add(q, [1])), -1)), 2), + "A2_minus_q3_t": shift(add(multiply(a, a), scale(multiply(multiply(q, q), q), -1)), 2)} + + +def gcd(left, right): + left, right = abs(left), abs(right) + while right: + left, right = right, left % right + return left + + +def reduced(numerator, denominator): + require(type(numerator) is int and type(denominator) is int, "ratio entries must be integers, not bool") + require(denominator > 0, "ratio denominator must be positive") + divisor = gcd(numerator, denominator) + return [numerator // divisor, denominator // divisor] + + +def compare(left, right): + difference = left[0] * right[1] - right[0] * left[1] + return (difference > 0) - (difference < 0) + + +def domain(q, n): + require(type(q) is int and type(n) is int, "q,n must be integers, not bool") + require((q, n) in ORDER, "unsupported frozen algebra probe") + + +def proper_path_counts(q, n): + unused, alpha, delta = source_polynomials() + a, d = evaluate(alpha, q), evaluate(delta, q) + single, distinct_pair, qpower = 1, 0, 1 + for unused in range(n): + distinct_pair, single = d * distinct_pair + (d - a) * single, a * single + qpower *= q + return single, distinct_pair, qpower + + +def algebra_case(q, n): + domain(q, n) + single, distinct_pair, qpower = proper_path_counts(q, n) + x = q * qpower + pnum, pden = (q - 1) * single, (x - 1) * qpower + jnum, jden = (q - 1) * distinct_pair, (x - 1) * (x - q) * (qpower // q) + p, joint = reduced(pnum, pden), reduced(jnum, jden) + ratio = reduced(jnum * pden * pden, jden * pnum * pnum) + lower = reduced(q * (x - 1) * (single - qpower), (q - 1) * (x - q) * single) + require(compare(ratio, lower) > 0 and compare(lower, [1, 1]) >= 0, "strict ratio/lower-bound chain failed") + require(compare(ratio, [1, 1]) > 0, "positive common-covector correlation failed") + if n >= 2: + require(single > x and compare(lower, [1, 1]) > 0, "large-n strict lower bound failed") + return {"q": q, "n": n, "marginal": p, "joint": joint, + "ratio": ratio, "lower_bound": lower, "positive": True} + + +def authenticate(): + for name, expected in (("SOURCE-PINS.json", PIN_SHA), ("CASES.json", CASE_SHA), ("SCHEMA.json", SCHEMA_SHA)): + require(sha((ROOT / name).read_bytes()) == expected, "source/cases/schema digest changed") + source = parse((ROOT / "SOURCE-PINS.json").read_bytes()) + require(len(source["files"]) == 2, "two inert4807 source documents required") + for entry in source["files"]: + raw = (ROOT / entry["local_path"]).read_bytes() + require(len(raw) == entry["bytes"] and sha(raw) == entry["sha256"], "pinned source bytes changed") + blob = b"blob " + str(len(raw)).encode() + b"\0" + raw + require(hashlib.sha1(blob).hexdigest() == entry["git_blob"], "pinned source Git blob changed") + parse((ROOT / "SCHEMA.json").read_bytes()) + return parse((ROOT / "CASES.json").read_bytes()) + + +def rational(value): + require(type(value) is list and len(value) == 2, "rational must be a two-entry list") + require(all(type(item) is int for item in value), "rational entries must be integers, not bool") + require(value[1] > 0 and value == reduced(*value), "rational must be reduced with positive denominator") + + +def validate_receipt(value): + require(type(value) is dict and set(value) == COMMON, "receipt schema keys invalid") + require(type(value["schema_version"]) is int and value["schema_version"] == 1, "receipt schema version must be integer1") + require(value["source_manifest_sha256"] == PIN_SHA and value["case_manifest_sha256"] == CASE_SHA, "receipt source/case binding differs") + identities = value["identities"] + require(type(identities) is dict and set(identities) == set(IDENTITIES), "identity keys invalid") + for name, size in IDENTITIES.items(): + poly = identities[name] + require(type(poly) is list and len(poly) == size and all(type(c) is int for c in poly), "identity coefficient types/length invalid") + rows = value["cases"] + require(type(rows) is list and len(rows) == len(ORDER), "algebra case count invalid") + for row, (q, n) in zip(rows, ORDER): + require(type(row) is dict and set(row) == CASE_KEYS, "algebra case keys invalid") + require(type(row["q"]) is int and type(row["n"]) is int and (row["q"], row["n"]) == (q, n), "algebra case order/domain invalid") + for key in ("marginal", "joint", "ratio", "lower_bound"): + rational(row[key]) + require(type(row["positive"]) is bool, "algebra positivity flag must be bool") + + +def rejected(function, value): + try: + function(value) + except ValueError: + return True + return False + + +def controls(receipt): + result = {"boolean_q_rejected": rejected(lambda q: domain(q, 1), True), + "boolean_n_rejected": rejected(lambda n: domain(2, n), True), + "unsupported_case_rejected": rejected(lambda q: domain(q, 1), 17), + "zero_n_rejected": rejected(lambda n: domain(2, n), 0), + "zero_denominator_rejected": rejected(lambda d: reduced(1, d), 0), + "negative_denominator_rejected": rejected(lambda d: rational([1, d]), -2), + "unreduced_rational_rejected": rejected(rational, [2, 4]), + "boolean_rational_rejected": rejected(rational, [True, 1]), + "duplicate_json_rejected": rejected(parse, '{"x":1,"x":2}'), + "nonfinite_json_rejected": rejected(parse, '{"x":NaN}'), + "float_json_rejected": rejected(parse, '{"x":1.0}')} + for name in ("boolean_version", "missing_key", "extra_key", "boolean_coefficient", "boolean_positive"): + bad = parse(canonical(receipt)) + if name == "boolean_version": + bad["schema_version"] = True + elif name == "missing_key": + del bad["identities"] + elif name == "extra_key": + bad["extra"] = 1 + elif name == "boolean_coefficient": + bad["identities"]["qD_minus_A2_q"][0] = False + else: + bad["cases"][0]["positive"] = 1 + result[name + "_rejected"] = rejected(validate_receipt, bad) + require(all(type(v) is bool and v for v in result.values()), "oracle control failed") + return result + + +def generate(cases): + require(cases["cases"] == [{"q": q, "n": n} for q, n in ORDER], "frozen case schedule differs") + value = {"schema_version": 1, "source_manifest_sha256": PIN_SHA, "case_manifest_sha256": CASE_SHA, + "identities": polynomial_identities(), "cases": [algebra_case(q, n) for q, n in ORDER]} + validate_receipt(value) + diagnostic = {"algebra_cases": len(ORDER), "identities": len(IDENTITIES), "controls": controls(value), + "code_sha256": sha(Path(__file__).read_bytes()), + "scope": "New sign corollary only; source4807 counts and binary sign are prior; nonprimepowers are algebra probes"} + return value, diagnostic + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", type=Path) + parser.add_argument("--check-primary", type=Path) + args = parser.parse_args() + require(not (args.emit and args.check_primary), "blind first emission cannot read primary data") + cases = authenticate() + frozen = None if args.emit else parse((ROOT / "ORACLE.json").read_bytes()) + if frozen is not None: + validate_receipt(frozen) + value, diagnostic = generate(cases) + if args.emit: + with args.emit.open("x") as stream: + json.dump(value, stream, indent=2, sort_keys=True) + stream.write("\n") + else: + require(canonical(value) == canonical(frozen), "retained oracle receipt differs") + if args.check_primary: + primary = parse(args.check_primary.read_bytes()) + validate_receipt(primary) + require(canonical(value) == canonical(primary), "actual complete primary receipt differs") + diagnostic["actual_primary_rows_compared"] = len(primary["cases"]) + print("PASS_COMMON_COVECTOR_ALL_FIELD_ORACLE " + canonical(diagnostic)) + + +if __name__ == "__main__": + try: + main() + except (ValueError, KeyError, TypeError, OSError) as error: + print("FAIL_COMMON_COVECTOR_ALL_FIELD_ORACLE: " + str(error), file=sys.stderr) + sys.exit(1) diff --git a/research/common-covector-all-field-positive/verify.py b/research/common-covector-all-field-positive/verify.py new file mode 100644 index 0000000000..833fb32185 --- /dev/null +++ b/research/common-covector-all-field-positive/verify.py @@ -0,0 +1,223 @@ +#!/usr/bin/env python3 +"""Exact sign corollary of the credited common-covector pair formulas.""" +from fractions import Fraction +import argparse +import hashlib +import json +import math +from pathlib import Path +import sys + +ROOT = Path(__file__).resolve().parent +SOURCE_HASH = '2b8bb283881df3bcad005e11fbe3aeaddc61b563babe9dd95c2dd18ae4fdbc59' +CASE_HASH = 'a8b26ebc34dbeb7f47b91f88eb0863bb4d6e914a6c26630e8cdd64dfe9ddf61b' +SCHEMA_HASH = '70db0325541f073c41886cf9fb43289723a6394d4c1e82d999dd49cda50507f5' +ROW_KEYS = {'q', 'n', 'marginal', 'joint', 'ratio', 'lower_bound', 'positive'} +TOP_KEYS = {'schema_version', 'source_manifest_sha256', 'case_manifest_sha256', + 'identities', 'cases'} + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def sha(raw): + return hashlib.sha256(raw).hexdigest() + + +def canonical(value): + return (json.dumps(value, sort_keys=True, separators=(',', ':')) + '\n').encode() + + +def unique(pairs): + result = {} + for key, value in pairs: + require(key not in result, 'duplicate JSON key') + result[key] = value + return result + + +def bad_number(value): + raise ValueError('noninteger JSON number: ' + value) + + +def parse(raw): + return json.loads(raw, object_pairs_hook=unique, parse_float=bad_number, + parse_constant=bad_number) + + +def typed_equal(left, right): + if type(left) is not type(right): + return False + if isinstance(left, dict): + return left.keys() == right.keys() and all(typed_equal(left[k], right[k]) for k in left) + if isinstance(left, list): + return len(left) == len(right) and all(typed_equal(a, b) for a, b in zip(left, right)) + return left == right + + +def authenticate(): + for name, expected in [('SOURCE-PINS.json', SOURCE_HASH), ('CASES.json', CASE_HASH), + ('SCHEMA.json', SCHEMA_HASH)]: + require(sha((ROOT / name).read_bytes()) == expected, 'immutable ' + name) + manifest = parse((ROOT / 'SOURCE-PINS.json').read_bytes()) + require(type(manifest) is dict and len(manifest['files']) == 2, 'two inert source documents') + for row in manifest['files']: + path = (ROOT / row['local_path']).resolve() + require(path.parent == (ROOT / 'inputs').resolve(), 'source containment') + raw = path.read_bytes() + require(len(raw) == row['bytes'] and sha(raw) == row['sha256'], 'source bytes/SHA256') + blob = b'blob ' + str(len(raw)).encode() + b'\0' + raw + require(hashlib.sha1(blob).hexdigest() == row['git_blob'], 'source Git blob') + return parse((ROOT / 'CASES.json').read_bytes()), parse((ROOT / 'SCHEMA.json').read_bytes()) + + +def alpha(q): + return q * q - q + 1 + + +def delta(q): + return q * q + (q - 1) ** 3 + + +def coefficients(evaluate, degree): + """Exact Vandermonde interpolation, independent of a convolution expansion.""" + work = [[Fraction(x ** power) for power in range(degree + 1)] + + [Fraction(evaluate(x))] for x in range(degree + 1)] + for column in range(degree + 1): + pivot = next(row for row in range(column, degree + 1) if work[row][column]) + work[column], work[pivot] = work[pivot], work[column] + scale = work[column][column] + work[column] = [entry / scale for entry in work[column]] + for row in range(degree + 1): + if row != column: + scale = work[row][column] + work[row] = [a - scale * b for a, b in zip(work[row], work[column])] + answer = [row[-1] for row in work] + require(all(x.denominator == 1 for x in answer), 'integer polynomial coefficients') + result = [x.numerator for x in answer] + while len(result) > 1 and result[-1] == 0: + result.pop() + return result + + +def identities(): + return { + 'qD_minus_A2_q': coefficients(lambda q: q * delta(q) - alpha(q) ** 2, 4), + 'A_minus_q_t': coefficients(lambda t: alpha(t + 2) - (t + 2), 2), + 'twoA_minus_q_qplus1_t': coefficients(lambda t: 2 * alpha(t + 2) - (t + 2) * (t + 3), 2), + 'A2_minus_q3_t': coefficients(lambda t: alpha(t + 2) ** 2 - (t + 2) ** 3, 4), + } + + +def pair(value): + return [value.numerator, value.denominator] + + +def case(q, n): + require(type(q) is int and type(n) is int, 'integer parameter domain') + require(2 <= q <= 64 and 1 <= n <= 16, 'finite parameter domain') + a, d, x = alpha(q), delta(q), q ** (n + 1) + marginal = Fraction((q - 1) * a ** n, (x - 1) * q ** n) + joint = Fraction((q - 1) * (d ** n - a ** n), (x - 1) * (x - q) * q ** (n - 1)) + ratio = joint / marginal ** 2 + lower = Fraction(q * (x - 1), (q - 1) * (x - q)) * (1 - Fraction(q, a) ** n) + require(0 < marginal < 1 and 0 < joint < 1, 'source probability algebra range') + require(ratio > lower >= 1, 'strict sign certificate ratio > L >= 1') + if n == 1: + require(lower == Fraction(q * q - 1, a), 'n1 exact lower bound') + else: + require(a ** n > x and lower > 1, 'n>=2 strict lower bound') + return {'q': q, 'n': n, 'marginal': pair(marginal), 'joint': pair(joint), + 'ratio': pair(ratio), 'lower_bound': pair(lower), 'positive': ratio > 1} + + +def profile(cases, schema): + result = identities() + expected = {key: row['increasing_coefficients'] for key, row in schema['identities'].items()} + require(typed_equal(result, expected), 'actual polynomial identity coefficients') + require(len(cases['cases']) == cases['case_count'] == 205, '205 frozen parameter rows') + return {'schema_version': 1, 'source_manifest_sha256': SOURCE_HASH, + 'case_manifest_sha256': CASE_HASH, 'identities': result, + 'cases': [case(row['q'], row['n']) for row in cases['cases']]} + + +def rational(value): + require(type(value) is list and len(value) == 2, 'rational pair shape') + require(all(type(x) is int for x in value), 'rational integers') + require(value[1] > 0 and math.gcd(*value) == 1, 'reduced rational positive denominator') + + +def admit(value): + require(type(value) is dict and value.keys() == TOP_KEYS, 'exact receipt keys') + require(type(value['schema_version']) is int and value['schema_version'] == 1, 'integer receipt version') + require(value['source_manifest_sha256'] == SOURCE_HASH and value['case_manifest_sha256'] == CASE_HASH, + 'receipt source/case binding') + require(type(value['identities']) is dict and type(value['cases']) is list, 'receipt containers') + for coeffs in value['identities'].values(): + require(type(coeffs) is list and all(type(x) is int for x in coeffs), 'identity integer coefficients') + require(len(value['cases']) == 205, 'receipt case count') + for row in value['cases']: + require(type(row) is dict and row.keys() == ROW_KEYS, 'exact case keys') + require(type(row['q']) is int and type(row['n']) is int, 'case integer parameters') + require(type(row['positive']) is bool, 'strict positive boolean') + for key in ['marginal', 'joint', 'ratio', 'lower_bound']: + rational(row[key]) + + +def check_receipt(value, expected): + admit(value) + require(typed_equal(value, expected), 'actual complete retained receipt differs') + + +def rejected(call, fragment): + try: + call() + except ValueError as error: + require(fragment in str(error), 'intended rejection: ' + fragment) + return + raise ValueError('negative control accepted: ' + fragment) + + +def controls(expected): + for q, n in [(1, 1), (2, 0), (65, 1), (2, 17)]: + rejected(lambda: case(q, n), 'finite parameter domain') + rejected(lambda: case(True, 1), 'integer parameter domain') + rejected(lambda: case(2, 1.0), 'integer parameter domain') + rejected(lambda: parse(b'{"q":2,"q":3}'), 'duplicate') + rejected(lambda: parse(b'{"q":NaN}'), 'noninteger') + rejected(lambda: parse(b'{"q":2.0}'), 'noninteger') + changes = [('schema_version', True), ('extra', 0)] + for key, value in changes: + bad = parse(canonical(expected)); bad[key] = value + rejected(lambda: check_receipt(bad, expected), 'version' if key == 'schema_version' else 'keys') + for key, value, fragment in [('ratio', [1, 1], 'differs'), ('positive', 1, 'boolean'), + ('marginal', [True, 2], 'integers')]: + bad = parse(canonical(expected)); bad['cases'][0][key] = value + rejected(lambda: check_receipt(bad, expected), fragment) + first = expected['cases'][0] + require(first['lower_bound'] == [1, 1] and first['ratio'] == [4, 3], 'strict replacement at boundary') + return 15 + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--emit', type=Path) + args = parser.parse_args() + frozen_cases, schema = authenticate() + value = profile(frozen_cases, schema) + count = controls(value) + if args.emit: + args.emit.write_bytes(canonical(value)) + else: + check_receipt(parse((ROOT / 'RESULT.json').read_bytes()), value) + print('PASS_COMMON_COVECTOR_ALL_FIELD_POSITIVE cases=205 identities=4 controls=' + str(count)) + + +if __name__ == '__main__': + try: + main() + except (OSError, ValueError, KeyError, TypeError) as error: + print('FAIL: ' + str(error), file=sys.stderr) + sys.exit(1)