From 161e482bc2d8c78ecef96135430c60d49b8fc345 Mon Sep 17 00:00:00 2001 From: Dillon Amburgey Date: Tue, 10 Nov 2026 16:58:40 -0500 Subject: [PATCH] Conditional kappa .003642219284637 from a nonunit-pivot helper split Package-only publication of canonical-based scientific commit ccf43d83249c3affc69814effd8f9dcec0e500f9. Complete frozen source closure and predecessor credit retained. Substantial OpenAI Codex assistance; no subagents. --- .../p104-nonunit-pivot-split/APPLICATION.md | 31 + .../p104-nonunit-pivot-split/DISCOVERY.json | 246 ++ .../p104-nonunit-pivot-split/ENVIRONMENT.json | 14 + research/p104-nonunit-pivot-split/INPUTS.json | 189 + .../NATIVE-RESULT.json | 3072 +++++++++++++++++ research/p104-nonunit-pivot-split/PROOF.md | 114 + research/p104-nonunit-pivot-split/README.md | 51 + research/p104-nonunit-pivot-split/REPLAY.txt | 73 + research/p104-nonunit-pivot-split/RESULT.json | 1561 +++++++++ .../p104-nonunit-pivot-split/SOURCES.json | 24 + research/p104-nonunit-pivot-split/TASK.json | 145 + .../p104-nonunit-pivot-split/VALIDATION.md | 22 + research/p104-nonunit-pivot-split/VERIFY.json | 29 + .../p104-nonunit-pivot-split/WITNESS.json | 483 +++ .../p104-nonunit-pivot-split/WORD.json.gz | Bin 0 -> 371002 bytes research/p104-nonunit-pivot-split/adapt.py | 38 + .../p104-nonunit-pivot-split/construct.py | 46 + .../p104-nonunit-pivot-split/derive_grid.py | 36 + .../inputs/pr7123.tar | Bin 0 -> 9799680 bytes research/p104-nonunit-pivot-split/price.py | 53 + research/p104-nonunit-pivot-split/source.py | 57 + research/p104-nonunit-pivot-split/split.py | 155 + research/p104-nonunit-pivot-split/support.py | 18 + research/p104-nonunit-pivot-split/verify.py | 51 + .../p104-nonunit-pivot-split/verify_native.py | 211 ++ 25 files changed, 6719 insertions(+) create mode 100644 research/p104-nonunit-pivot-split/APPLICATION.md create mode 100644 research/p104-nonunit-pivot-split/DISCOVERY.json create mode 100644 research/p104-nonunit-pivot-split/ENVIRONMENT.json create mode 100644 research/p104-nonunit-pivot-split/INPUTS.json create mode 100644 research/p104-nonunit-pivot-split/NATIVE-RESULT.json create mode 100644 research/p104-nonunit-pivot-split/PROOF.md create mode 100644 research/p104-nonunit-pivot-split/README.md create mode 100644 research/p104-nonunit-pivot-split/REPLAY.txt create mode 100644 research/p104-nonunit-pivot-split/RESULT.json create mode 100644 research/p104-nonunit-pivot-split/SOURCES.json create mode 100644 research/p104-nonunit-pivot-split/TASK.json create mode 100644 research/p104-nonunit-pivot-split/VALIDATION.md create mode 100644 research/p104-nonunit-pivot-split/VERIFY.json create mode 100644 research/p104-nonunit-pivot-split/WITNESS.json create mode 100644 research/p104-nonunit-pivot-split/WORD.json.gz create mode 100644 research/p104-nonunit-pivot-split/adapt.py create mode 100644 research/p104-nonunit-pivot-split/construct.py create mode 100644 research/p104-nonunit-pivot-split/derive_grid.py create mode 100644 research/p104-nonunit-pivot-split/inputs/pr7123.tar create mode 100644 research/p104-nonunit-pivot-split/price.py create mode 100644 research/p104-nonunit-pivot-split/source.py create mode 100644 research/p104-nonunit-pivot-split/split.py create mode 100644 research/p104-nonunit-pivot-split/support.py create mode 100644 research/p104-nonunit-pivot-split/verify.py create mode 100644 research/p104-nonunit-pivot-split/verify_native.py diff --git a/research/p104-nonunit-pivot-split/APPLICATION.md b/research/p104-nonunit-pivot-split/APPLICATION.md new file mode 100644 index 0000000000..392f7aeb3c --- /dev/null +++ b/research/p104-nonunit-pivot-split/APPLICATION.md @@ -0,0 +1,31 @@ +# Conditional application of the nonunit-pivot helper split + +This applies Rohan Arun's #7113 component proof and the retained changed-native adapters to the exact #7123 word plus one rank-nine split. The complete frozen source closure remains intact. PROOF.md supplies the source-specific cut, legal unit basis and arbitrary-input replacement. Both native and application invoices are recounted. The five assumptions and selected completed BIT predecessor remain. The template is the [#7000 application review](https://github.com/CrocSwap/integer-mult-bounds/blob/e54523517d0f03e58352e647c403a5af3e525a57/docs/research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md), including its BIT ambient 134 / log-power 617 repair. Current substitutions follow. + +## Native and caller operator substitution + +The new basis swaps cocharted boundary coordinates 639 and 802 using four charged scalar instructions, replacing a forbidden nonunit normalization by the legal unit 3. Complete boundary/cut bases 426/17 are applied in both directions. The cut after event 37583 is at chart 1027; the declared neutral placement leaves the source program byte-identical. One independent helper target 3→127 is split into 3→1027 (rank 5) and 1027→127 (rank 4). All 880 ADDs, 6 SCALEs and the fresh input are charged. Owned transitions and lifetimes are retained. The complete forward and adjoint replays include every owned row. + +All 3,048 current paid/helper chart pairs and 104 main boundary pairs are rebuilt with the pinned compiler and distinct signed-Pauli/absolute-phase interpreter. For these Clifford maps, the signed Pauli action determines the operator up to global phase, which the exact Gaussian check fixes. Thus every column of each map is determined. The native check additionally replays all 512 columns of the three target boundary pairs and rejects a deliberately wrong absolute phase. No new pair is introduced, but changed multiplicities and the entire catalogue are recounted. + +The unchanged 17-stage caller has five noncommuting quarter turns and twelve padding turns in inverse pairs. Its grouped idle bases lie over Z[1/30]. Its exact rational and integer Laurent engines agree on all 72 output fields for every formal central/body variable. In the physical substitution, seventeen disjoint eight-axis stage blocks and nine central axes use ambient 145. For each invocation, exchange the eight native complement axes with the fresh stage block while fixing the routed central axis and spectator axes. The phase-polynomial checks verify both directions. Literal A and B routes then apply commuting body operators on disjoint stage blocks. + +A signed rank-nine idle uses one positive rank-nine recursive request plus the charged ordinary conjugation/phase implementing the inverse on the protected central axis. Current finite signed-child checks cover widths 1,2,3; the symbolic phase geometry supplies the disjoint-axis substitution. The ordered occurrence digest is recomputed from the literal caller and current native geometry. It binds 13,600 native contact boundaries, 110,655 paid positions and 22,308 productive fields. Main-owner aliasing is rejected. Allocate 18,564 distinct (stage,helper) public inputs and 867 reserved native owned banks, plus the retained serial query/LAMBDA bank. The surplus is 1,424. The ownership discipline and owned-erasure hypothesis remain explicit. + +## Common-grid and fixed-root induction + +Scale each of the 3,744 raw caller main input fields by 675 and divide each completed caller main output by 675. The independent integer Laurent replay checks the necessary valuations 3³ and 5², rejects a lower exponent of either prime, and uses safe binary valuation 381. Every normalized main coefficient and pre-ADD product is integral on that odd grid. Substituting actual binary Clifford address operators introduces only powers of two, so the odd-divisibility invariant transfers to whole arrays and all spectators. + +Within each native invocation, scale all 1,492 public fields by 1125 and unscale the completed returns. The separate exact prefix/pre-product derivation and integer replay establish the native grid at fractional height 25. Fresh helpers receive their own independent inputs. The previous F24 grid is rejected on the new word. The forward integer replay changes both its scale to 2^25 and its measured trailing-bit offset to 26. Both native and caller precision adapters explicitly request frac=25 from the unchanged authenticated grid engine. The exact native endpoint ensures these helper inputs do not perturb the normalized main caller invariant. Both odd scales are included simultaneously in the unfinished-context mass allowance. + +The fresh forward/adjoint envelope has height 406 and context mass exponent 1181, giving c=2362. This is recomputed from the current word and caller; #7123's allowance was 2344. It remains below 4096. The same conservative ambient 153 compiler threshold funds it: Kstar has 14,093 bits and c·Kstar has 14,104 bits, below H=16495300000000000000000. The regenerated compiler gap is 1/100000000000000000. Every rounded caller bound, outer and fixed-tape gate is checked with these current values. Apply the retained full-root common-format induction with fixed padding, signed width p+h+2D+3, fractional width p+D, and 26 temporary bits. Completed child returns preserve this format. Exact finite-state odd division retains the reviewed carry/remainder invariant. + +## Physical upper-cost substitution + +The source-unit ordinary bound 779,122,208 includes the caller and native conversion services. It is distinct from the physical-machine bound. The fresh raw-occurrence counts give 1,161,423 native scalar macro inputs, 117,856 caller macro inputs and 58,216 conversions. The retained conservative factor 32 gives 42,799,840 scalar services; with the reviewed 2²⁰ service constant this is 44,878,885,027,840 times the root scalar-width envelope. Numerators of all actual native/caller instructions and both conversion scales fit 24 bits. + +The current occurrence count gives 298,774 monomial map slots. At actual ambient 145, the retained elementary bound 4(145+1)² is 85,264 records per map, hence at most 25,474,666,336 elementary records per raw occurrence. Use actual owner widths and these finite coefficients in the same fixed-tape stock and movement envelopes from the selected review. The positive compiler/outer slack permits enlarging the eventual cutoffs. This is a conditional asymptotic substitution, not an enumerated machine trace. + +The recomputed complete recurrence has the bracket and claim in README.md; both exact price engines, the compiler and 54 strict plus 4 functional outer inequalities pass. These checks establish the stated conditional component application under the five assumptions. Independent mathematical review, formal-kernel validation and maintainer admission are separate obligations. + +Credit Rohan Arun for the #7113 proof and implementation, Douglas Colkitt and the #7000 application reviewers, the retained compiler/precision/source authors, and the complete lineage in README.md. Adapted for this exact nonunit-pivot helper split, retaining all peer and predecessor credit, by dillona with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/p104-nonunit-pivot-split/DISCOVERY.json b/research/p104-nonunit-pivot-split/DISCOVERY.json new file mode 100644 index 0000000000..6c461a696c --- /dev/null +++ b/research/p104-nonunit-pivot-split/DISCOVERY.json @@ -0,0 +1,246 @@ +{ + "source_head": "020d581d9856b6db83e448c3f20418bc63b72c34", + "screen_kappa": ".003641239650184", + "scope": "Complete rational kernels followed by basis nominations in group 3\u2192127; no exhaustive rational support/cost optimization.", + "counts": { + "systems": 38473, + "saved": 10293, + "pairs": 44172, + "hits": 0, + "classes": { + "F1zero": 8286, + "witness": 1756, + "F2zero": 251 + }, + "rescued": 0, + "budget_reject": { + "8": 3240, + "10": 2865, + "6": 4231, + "13": 1545, + "12": 1926, + "4": 2297, + "9": 3954, + "7": 3679, + "14": 1738, + "15": 2006, + "5": 3213, + "3": 3031, + "2": 1236, + "18": 893, + "16": 1113, + "21": 466, + "24": 407, + "11": 2332, + "17": 1103, + "20": 469, + "19": 644, + "22": 322, + "25": 164, + "23": 530, + "28": 181, + "29": 109, + "27": 152, + "26": 167, + "30": 99, + "31": 34, + "33": 5, + "32": 10 + }, + "best_budget": { + "cut": 37622, + "frame": 1027, + "cost": 0.0, + "gain": 0.02236181478033039, + "paths": [ + { + "role": 1298, + "lo": 36613, + "hi": 37622, + "frame": 1027, + "old": 1027, + "new": 525, + "moves": [ + 37621 + ], + "old_paid": [ + 1 + ], + "new_paid": [ + 0, + 1 + ], + "cost": 0.0, + "private": false, + "neutral": true + } + ], + "paid_roles": 0 + } + }, + "chosen_index": 10, + "constructed_indices": [ + 10 + ], + "legal_basis_nominations": [ + { + "index": 10, + "alpha": "1", + "cut": 37583, + "paths": 1, + "G": 426, + "J": 17, + "instructions": 886, + "operations": { + "ADD": 880, + "SCALE": 6 + }, + "maximum_scalar": "1338551/256" + }, + { + "index": 8, + "alpha": "7", + "cut": 37585, + "paths": 0, + "G": 427, + "J": 17, + "instructions": 888, + "operations": { + "ADD": 882, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 9, + "alpha": "7", + "cut": 37584, + "paths": 0, + "G": 427, + "J": 17, + "instructions": 888, + "operations": { + "ADD": 882, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 7, + "alpha": "7", + "cut": 37586, + "paths": 0, + "G": 427, + "J": 18, + "instructions": 890, + "operations": { + "ADD": 884, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 5, + "alpha": "7", + "cut": 37588, + "paths": 0, + "G": 427, + "J": 19, + "instructions": 892, + "operations": { + "ADD": 886, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 6, + "alpha": "7", + "cut": 37587, + "paths": 0, + "G": 427, + "J": 19, + "instructions": 892, + "operations": { + "ADD": 886, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 0, + "alpha": "1", + "cut": 37622, + "paths": 1, + "G": 426, + "J": 20, + "instructions": 892, + "operations": { + "ADD": 890, + "SCALE": 2 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 2, + "alpha": "7", + "cut": 37591, + "paths": 0, + "G": 427, + "J": 20, + "instructions": 894, + "operations": { + "ADD": 888, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 3, + "alpha": "7", + "cut": 37590, + "paths": 0, + "G": 427, + "J": 20, + "instructions": 894, + "operations": { + "ADD": 888, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 4, + "alpha": "7", + "cut": 37589, + "paths": 0, + "G": 427, + "J": 20, + "instructions": 894, + "operations": { + "ADD": 888, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + }, + { + "index": 1, + "alpha": "7", + "cut": 37592, + "paths": 0, + "G": 427, + "J": 21, + "instructions": 896, + "operations": { + "ADD": 890, + "SCALE": 6 + }, + "maximum_scalar": "1338551/384" + } + ], + "selection": "Try alpha=1 and the common nonunit denominator-clearing gauge, then order legal candidates by total scalar instruction count, path count, largest absolute scalar, index.", + "basis_repair": "Keep pivot only if its nonzero entry is a 2,3,5 unit; otherwise choose the same smallest smooth swap entry as #7112. Original d639=-7867/16, chosen d802=3.", + "corrected_screen": "An inherited discovery script still used .003640102187396 in two preliminary group screens. Both were rerun at the actual .003641239650184 and gave identical zero-hit counts; the group 3\u2192127 nominations and this result use the corrected value. Exact certificate and prices do not trust discovery floats.", + "local_only": "Discovery scripts, rejected nominations and earlier negative rounds remain local. Public WITNESS and source-bound constructor are sufficient to reproduce this result; broader search closure is not claimed.", + "stop_reason": "One legal candidate selected; full verification takes priority." +} diff --git a/research/p104-nonunit-pivot-split/ENVIRONMENT.json b/research/p104-nonunit-pivot-split/ENVIRONMENT.json new file mode 100644 index 0000000000..0f956a75c4 --- /dev/null +++ b/research/p104-nonunit-pivot-split/ENVIRONMENT.json @@ -0,0 +1,14 @@ +{ + "initial_python": "3.14.7", + "initial_platform": "macOS-27.0.1-arm64-arm-64bit-Mach-O", + "registered_replay": { + "python": "3.12.16", + "platform": "macOS-27.0.1-arm64-arm-64bit", + "result": "PASS both complete commands; every native and composition receipt field matched" + }, + "dependencies": "Python standard library", + "interpreter_origin": "Official Astral python-build-standalone release20261026; isolated /tmp installation", + "interpreter_archive_sha256": "fbf4afef53c2a6b72bb741bc06d5671a9dfaf87bd84e5aa73ac9b3d0d589f14e", + "hosted_ci": "Not yet published; no hosted scientific pass claimed.", + "completed_utc": "2026-11-10T21:58:03.626947+00:00" +} diff --git a/research/p104-nonunit-pivot-split/INPUTS.json b/research/p104-nonunit-pivot-split/INPUTS.json new file mode 100644 index 0000000000..a63ef6b2a1 --- /dev/null +++ b/research/p104-nonunit-pivot-split/INPUTS.json @@ -0,0 +1,189 @@ +{ + "head": "020d581d9856b6db83e448c3f20418bc63b72c34", + "pr": 7123, + "prefix": "research/p104-recharted-rank8-split", + "archive": "inputs/pr7123.tar", + "archive_sha256": "834098d9b40ed09035fe6128b90805517dba7c9332ef191d55c48b40e72bb620", + "files": [ + { + "path": "research/p104-recharted-rank8-split/APPLICATION.md", + "size": 7030, + "sha256": "de7df820369111fbee559086a0ca68c6688fb5e7048c22ec3443827b070247fa", + "git_blob": "3e9fe6d9029d78b6791d7a7d72b639542558b3d2" + }, + { + "path": "research/p104-recharted-rank8-split/DISCOVERY.json", + "size": 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], + [ + "XOR", + 4, + 3 + ], + [ + "XOR", + 8, + 0 + ], + [ + "XOR", + 4, + 0 + ], + [ + "SWAP", + 0, + 3 + ] + ], + "old9_inverse": [ + 280, + 2, + 4, + 273, + 265, + 32, + 64, + 128, + 25 + ], + "old9_route": [ + 280, + 2, + 4, + 273, + 265, + 32, + 64, + 128, + 25 + ], + "ordinary_elementary_units": 37, + "ordinary_route_units": 19, + "port": 55, + "positive_child_slots": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "q": 280, + "stage": 10 + } + ], + "paid_calls": 32, + "proposed_sha": "9557f713ab4ffb91ede05e8a6d5668c694b9940fc16f2f2d657e2f2b2cac2d3f", + "status": "PASS_PHYSICAL_RANK9_ALGEBRA", + "word_sha": "a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2" + }, + "source_head": "020d581d9856b6db83e448c3f20418bc63b72c34", + "status": "PASS_P104_NONUNIT_PIVOT_NATIVE", + "word_canonical_sha256": "a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2" +} diff --git a/research/p104-nonunit-pivot-split/PROOF.md b/research/p104-nonunit-pivot-split/PROOF.md new file mode 100644 index 0000000000..bf58fa414a --- /dev/null +++ b/research/p104-nonunit-pivot-split/PROOF.md @@ -0,0 +1,114 @@ +# A nonzero unit pivot recovers an exact helper split + +The source is the complete 30-file export of #7123 at +`020d581d9856b6db83e448c3f20418bc63b72c34`, authenticated by `INPUTS.json`. +The replay reconstructs its entire nested source chain and every byte of its +native word, SHA256 +`34cc0c51ca9eaaf2bf3789b8ea2c92f0837b4be9f0fedb22a6150169038e8c38`. +This retains Rohan Arun's #7122 global input rechart, the earlier independent +helper splits, and the exact #7113 signed caller. Frozen evidence is unchanged. + +## Exact cut and constructor obstruction + +Take the source cut immediately after event 37583, at chart 1027, dimension +5, with pivot 639. The discovery witness describes a neutral placement of +role 643's MOVE from 3 to 1027, at event 37583, over interval [37583,37584). +Removing and reinserting that event at this same cut leaves the source +program byte-identical. The constructor checks the complete interval and +source-read conditions anyway. There is no added MOVE or paid-rank change. +The helper boundary group is 3→127, dimensions 0 and 9. + +`WITNESS.json` gives the complete rational vectors a, b, c, d. They have +7, 11, 76 and 347 nonzero entries. With P the prefix through event 37583 +and S the suffix, exact arithmetic checks every public input and owned row: + +``` +aP = c, Sb = d, ab = cd = 1. +``` + +Both c and d use only independent helpers with the common boundary 3→127. +All cut coordinates in a, b, and the pivot are at 1027. The cut vectors are + +``` +a = e643ᵀ + e640ᵀ/2 + e641ᵀ/3 + 2e1298ᵀ/3 + + e639ᵀ/6 − 17e1300ᵀ/6 − 14e1383ᵀ/3, +b = e643/4 + e641/8 − e1298/16 − e642/8 − e1300/4 + − 3e639/8 − 3e640/8 − 3e645/8 − e1383/16 − e644/4 − e646/8. +``` + +The original Ali Romman basis routine, including the #7112 zero-pivot +repair, would retain nonzero d639=−7867/16. Normalization then emits +SCALE −16/7867, outside the allowed ring Z[1/30]. That is a failure of this +pivot choice, not a proof that the rational split has no legal scalar basis. +The same direction has d802=3, a unit in Z[1/30]. Both coordinates are in +the same helper boundary group, so the following ordinary cocharted scalar +instructions swap their values even when both entries are nonzero: + +``` +x639 += x802 +x802 -= x639 +x639 += x802 +x802 *= −1 +``` + +They map (x639,x802) to (x802,x639). Normalization can now scale coordinate +639 by 1/3. The remainder of the attributed elimination routine is unchanged. +The emitter keeps an existing pivot only when its entry is already a unit; +otherwise it selects a unit by the same size/role ordering used in #7112. +Every resulting coefficient is checked: ADD coefficients are in Z[1/30], +SCALE coefficients and their inverses are units, and |q|+1<2^16. +This does not enlarge the instruction alphabet or grant free physical transport. + +## Independent arbitrary-input replacement + +The emitter produces a boundary basis G of length 426 and a cut basis J of +length 17. Exact row/column elimination gives + +``` +row639(G)=c, Gd=e639, row639(J)=a, Jb=e639. +``` + +G is applied at chart 3 and its output-boundary counterpart at chart 127; +J is applied at 1027. Inverses reverse the instruction order and invert each +scalar operation. The complete G/J vectors and programs are reproducible from +`WITNESS.json` and `split.py`, without the discovery search. + +Apply G⁻¹, then P and J. Coordinate 639 equals its independent input because +aPG⁻¹=cG⁻¹=e639ᵀ. Retire this field at 1027 and replace its continuation by +a fresh arbitrary input z, new public role 1491. After J⁻¹, S and G, the +output change is GSb(z−x639)=Gd(z−x639)=e639(z−x639). Every other output +is unchanged. The continuing pivot is relabelled to 1491, and owned labels +are shifted by one to keep the inventories disjoint. + +This argument uses neither P⁻¹ nor S⁻¹. It retains the source's explicit +initialization and owned-erasure assumptions, including erasure of correlated +nonzero owned content. The fresh public helper is independent, not zeroed. + +The retained target is 3→1027 of rank 5; the new target is 1027→127 of rank 4. +The two G/J traversals add 880 ADDs and 6 SCALEs. There are 74,606 events, +1,492 public fields and 1,092 helpers. All 54 owned lifetimes, peak allocation +43, and 23 rises of total mass 56 remain unchanged. The canonical word hash is +`a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2`. + +## Complete application obligation + +Relative to #7123, ΔP={} and ΔT={4:+1,5:+1,9:−1} per native invocation. +For H_r=r^(1−κ), the local difference H5+H4−H9 is positive for 0<κ<1. +The signed 17-stage application has ΔT={4:+17,5:+17,9:−17}, unchanged +paid positions and surplus, and no empty credit. + +The exact native grid derivation requires 1125/F25; F24 is rejected. +`APPLICATION.md` carries this changed binary height, all basis operations, +independent inputs, odd conversions, forward/adjoint envelopes and physical +and fixed-tape costs into the full application. A positive local difference +alone is not a complete conditional multiplication theorem. + +Credit Ali Romman for the helper identity and basis algorithm; dillona/OpenAI +Codex #7112 for the earlier zero-pivot smooth swap; Jerry Chen/CubeJerry for +causal/native/invoice/compiler tools; Matarener for complete kernels/pairing; +Rohan Arun for #7122's rechart and #7113's signed caller; 1337isnot1337/OpenAI +Codex for the alpha-expansion rechart method; ToikY for the retained signed +sources, chart-120 lead and independent chart-259 reproduction; DreamingOfClouds, +Douglas Colkitt/#7000 reviewers and all nested source notices. This nonzero +nonunit-pivot repair was prepared for dillona with substantial OpenAI Codex +assistance; no subagents. Apache-2.0. diff --git a/research/p104-nonunit-pivot-split/README.md b/research/p104-nonunit-pivot-split/README.md new file mode 100644 index 0000000000..90141cc13f --- /dev/null +++ b/research/p104-nonunit-pivot-split/README.md @@ -0,0 +1,51 @@ +# Conditional κ = 0.003642219284637 from a nonunit-pivot repair + +A rational helper split on exact #7123 was rejected because the basis emitter retained a nonzero pivot whose reciprocal was outside Z[1/30]. Choosing an available unit in the same boundary group repairs the construction without changing the operation alphabet. The complete candidate claim is **κ = 0.003642219284637**, a gain of **0.000000979634453** over #7123. + +The exact cut after event 37583 / chart 1027 / pivot 639 splits a rank-nine helper into ranks five and four. Boundary direction d639=−7867/16 cannot be normalized directly, while d802=3 can. Four ordinary scalar instructions swap those cocharted coordinates. The resulting boundary/cut bases have lengths 426/17; the construction adds **880 ADDs and 6 SCALEs**, one fresh independent helper, and **no paid-profile change**. The declared neutral placement of role 643 leaves the source word byte-identical before applying the split. [PROOF.md](PROOF.md) gives the complete arbitrary-input argument. + +The emitted word has 74,606 events, 1,492 public fields and 1,092 independent helpers. Owned lifetimes, peak allocation and rise mass are unchanged. The fresh rational grid requires **1125/F25**, with F24 explicitly rejected. The extra binary height is propagated through the precision and complete cost checks. + +| Signed 17-stage application | #7123 | This construction | +|---|---:|---:| +| Paid positions |110655|110655| +| Productive fields |22291|22308| +| Rank surplus |1424|1424| +| Empty credit |0|0| + +Relative to #7123, ΔP={}, ΔT={4:+17,5:+17,9:−17}. Both exact price engines reject the predecessor invoice at the new claim. The independent raw crossing is + +``` +(0.00364221928463783897927791107627154, + 0.00364221928463783897927791107627155). +``` + +This bounds the emitted invoice, not other constructions. The retained BIT cap .00376669 leaves .000124470715363 headroom. The historical nine-stage coverage ceiling does not apply to this signed 17-stage caller and its independent helper targets. The selected #7000 record is unchanged. + +Both complete direct CPython 3.14.7 replays passed. The complete ordinary source-unit bound is **779,122,208 < 10⁹**, distinct from physical machine steps. Fresh precision gives height 406, mass exponent 1181 and **c=2362**. [APPLICATION.md](APPLICATION.md) records every current ownership, physical, precision, ordinary and fixed-tape substitution. Final registered isolated Python 3.12.16 replay passed both complete commands and matched every frozen native and composition receipt field. [VALIDATION.md](VALIDATION.md) records exact coverage. + +## Frozen inputs and reproduction + +`INPUTS.json` authenticates the complete 30-file #7123 export at `020d581d9856b6db83e448c3f20418bc63b72c34`, including every nested source and notice. Its exact native SHA256 is `34cc0c51ca9eaaf2bf3789b8ea2c92f0837b4be9f0fedb22a6150169038e8c38`; the new word is `a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2`. The #7113 caller remains byte-identical, SHA256 `255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc`, at source head `07a76c5e2738882c0cb322278e56f6cae3c9885d`. + +```sh +python3.12 -B scripts/research_package.py --package research/p104-nonunit-pivot-split +``` + +`DISCOVERY.json` records the finite nomination scope and deterministic choice of index 10 among eleven legal repaired bases. Only the selected candidate is constructed. The recorded pre-repair screen has `counts.hits=0`; the separate eleven-entry `legal_basis_nominations` list records the successful repaired bases. The search is not exhaustive rational support/cost optimization. Discovery scripts and earlier negative rounds remain local; the public witness and source-bound replay do not depend on them. + +The refreshed overlap check found Rohan Arun's separate output rechart #7124 at `97dc14132da53562b7939776d7a83d72af72eeb1`, reporting completed local verification of κ=.003641428753638. This candidate exceeds that claim by .000000790530999, but does not incorporate or independently replay #7124. The frozen #7123 inputs are preserved. + +## Remaining obligations and credit + +The five assumptions remain: `native_all_columns`, `owned_erasure`, `compiler`, `precision_tape`, `analytic_recovery`. Independent human/formal review, maintainer admission and compiled top-level execution remain open. + +Credit **Ali Romman** for helper bases/splits; **dillona/OpenAI Codex #7112** for the zero-pivot smooth swap extended here to a nonzero nonunit pivot; **Jerry Chen/CubeJerry** for causal/native/invoice/compiler tools; **Matarener** for complete kernels/pairing; **Rohan Arun** for #7122's rechart and #7113's signed caller/application; **1337isnot1337/OpenAI Codex** for fresh-helper-boundary alpha expansion; **ToikY** for the retained signed sources and chart-120 lead, independent chart-259 reproduction and reported independent #7123 replay; **DreamingOfClouds**, **Douglas Colkitt/#7000 reviewers**, and every nested source notice. Prepared for dillona with substantial OpenAI Codex assistance; no subagents. Apache-2.0. + +## Open next questions + +- Independently reproduce the unit-pivot repair and full F25 application, including the F24 rejection and complete costs. +- After a fresh canonical/overlap checkpoint, determine whether this split composes with #7124's output rechart. Endpoint and cut compatibility must be checked; no combined gain is established here. +- Can a legal localized-ring basis recover other nominations when no individual direction entry is a unit? This package only treats the available-unit case. + +[Canonical investigation](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19520521). diff --git a/research/p104-nonunit-pivot-split/REPLAY.txt b/research/p104-nonunit-pivot-split/REPLAY.txt new file mode 100644 index 0000000000..8d218db96b --- /dev/null +++ b/research/p104-nonunit-pivot-split/REPLAY.txt @@ -0,0 +1,73 @@ +CHECK Authenticate complete 30-file #7123 export and nested closure; reconstruct every source/candidate byte; arbitrary-input forward/adjoint, exact cut and unit basis, complete paid/target invoice, freshly derived F25 grid with F24 rejection, separate 18-stage ingredient/precision, affected 512-column maps, corruption/unit controls and finite native/signed physical replay; compare every receipt field. +PASS source reconstruction, whole cut, adjoint and independent forward map +caller 0 terms 77 +caller 500 terms 621 +caller 1000 terms 2648 +caller 1500 terms 3619 +caller 2000 terms 1590 +caller 2500 terms 398 +caller 3000 terms 1918 +caller 3500 terms 1797 +caller 4000 terms 1817 +caller 4500 terms 912 +caller 5000 terms 167 +PASS full signed caller, ordinary bill, two exact price engines, precision and compiler gates +events 74606 public 1492 owned roles 51 paid {1: 4028, 2: 842, 3: 819, 4: 232, 5: 333, 6: 16, 7: 11, 8: 6} owned UP {1: 10, 2: 4, 3: 1, 4: 6, 5: 1, 6: 1} helpers {1: 18, 2: 18, 3: 47, 4: 218, 5: 75, 6: 42, 7: 18, 8: 53, 9: 603} +endpoint bad rows 0 odd certificate S 1125 +PASS_HOST3 decoupled ports 96 hosted ports 8 +gate interpreter agrees with the library on 4 exact state vectors +replayed 74606 events, 2963 chart pairs, 20s +prime 1000000009 seed 11: helper rows bad 0 (of 1092), X rows bad 0, Y rows bad 0, X2 rows bad 0, Y2 rows bad 0 (of 104 ports; 96 with second mains) +tableau on 104 ports: XX!=D 0 YY!=D 0 YX!=Q^-1D 0 XY!=QD 0 | controls matching (must be 0): 0 0 +PASS_PHYSICAL 27s +PASS chart columns and phase, rejection controls and finite physical replay +PASS_P104_NONUNIT_PIVOT_NATIVE 728324295181/200000000000000 +CHECK Reconstruct #7123 and candidate 17-stage invoices; unchanged literal caller, all 3048 paid/helper maps and 104 main boundaries, fresh F25 grid/envelopes, ordinary/physical/fixed-tape costs, two prices and 54+4 outer gates; compare every receipt field. +PASS two reconstructed invoices and both exact price engines 0.003642219284637 +RUN emit_odd_type_b.py +caller 0 terms 41 +caller 500 terms 1178 +caller 1000 terms 2699 +caller 1500 terms 1262 +caller 2000 terms 881 +caller 2500 terms 2484 +caller 3000 terms 765 +caller 3500 terms 640 +caller 0 terms 41 +caller 500 terms 1178 +caller 1000 terms 2701 +caller 1500 terms 1264 +caller 2000 terms 881 +caller 2500 terms 2485 +caller 3000 terms 765 +caller 3500 terms 641 +PASS exact short type B 3877 events Counter({8: 34, 9: 4, 56: 4, 48: 4, 40: 4, 32: 4, 24: 4, 16: 4, 64: 2}) +RUN emit_odd_type_ab.py +caller 0 terms 73 +caller 500 terms 1076 +caller 1000 terms 2476 +caller 1500 terms 1334 +caller 2000 terms 2078 +caller 2500 terms 1235 +caller 3000 terms 2978 +caller 3500 terms 2335 +caller 4000 terms 1046 +caller 4500 terms 299 +PASS exact short A+B 4783 events 3752 ['7284438569275677958555822152543/2000000000000000000000000000000000', '9105548211594597448194777690679/2500000000000000000000000000000000'] +RUN check_odd_caller_exact_grid.py +PASS odd caller grid [381, 69, 62] [381, 3, 2] scale bits 10 checked 176874 +RUN check_odd_physical_binding.py +PASS exact physical binding 110655 13600 22308 +RUN check_odd_precision.py +PASS short precision 406 1181 2362 +RUN check_odd_partial_admission.py +ordinary bill 779122208 +PASS partial signed short gates 779122208 3642219284637/1000000000000000 {'strict_count': 54, 'functional_count': 4, 'minimum_margin': '1/1000000000000000000', 'BIT_just_below_effective_rejected': True} +RUN check_odd_fixed_tape_counts.py +PASS finite tariff substitution 42799840 25474666336 precision 2362 +RUN complete catalogue 0 1000 +RUN complete catalogue 1000 2000 +RUN complete catalogue 2000 3048 +PASS complete 8+9 component application checks 3642219284637/1000000000000000 3048 110655 +PASS_P104_NONUNIT_PIVOT_SPLIT 3642219284637/1000000000000000 +PASS_REGISTERED_RESEARCH_PACKAGE research/p104-nonunit-pivot-split outcome=partial diff --git a/research/p104-nonunit-pivot-split/RESULT.json b/research/p104-nonunit-pivot-split/RESULT.json new file mode 100644 index 0000000000..9d18b2f08d --- /dev/null +++ b/research/p104-nonunit-pivot-split/RESULT.json @@ -0,0 +1,1561 @@ +{ + "adapter": { + "adapted_sha256": { + "check_odd_partial_admission.py": "cd324a6cbb150d180aecb42cab66151f3b5f7acf3022658bbfa2011aa148e5e3", + "check_odd_precision.py": "94be27f8f66981bddb750553f892976c452561df721be766d9ef90fb73e70d9d", + "emit_odd_type_ab.py": "6fd9f61f9ba6c726524d1a585d0201b0eac61829ccae6be598f0f0fc1cb64f1a" + }, + "edits": [ + { + "file": "emit_odd_type_ab.py", + "new": "invoice=json.loads((root/\"COHORT-PRICE.json\").read_text())", + "old": "invoice=next(x for x in json.loads((root/\"SHORT-CALLER-RAW-PRICE.json\").read_text())[\"rows\"] if tuple(x[\"shape\"])==shape)" + }, + { + "file": "check_odd_partial_admission.py", + "new": "actual_native=ind.native(w)\nassert actual_native==N and not N[\"bad_inputs\"], \"Fresh complete native inventory and arbitrary-input adjoint\"", + "old": "previous=json.loads((root/\"SHORT-ADMISSION-PARTIAL.json\").read_text())\nassert previous[\"native_sha256\"]==digest and not N[\"bad_inputs\"]" + }, + { + "file": "check_odd_partial_admission.py", + "new": "claim=Q(\".003642219284637\")", + "old": "claim=Q(\".00363797977\")" + }, + { + "file": "check_odd_partial_admission.py", + "new": "tested=claim+Q(7,10**17)\nwhile tested>=Q(reference[\"raw_bracket\"][0]):\n tested=claim+(tested-claim)/10", + "old": "tested=claim+Q(7,10**17)" + }, + { + "file": "check_odd_partial_admission.py", + "new": "g=gate(invoice,claim,tested,*bracket,r[\"gate\"][\"BIT_pin\"])\ntry:\n gate(invoice,claim,Q(bracket[0]),*bracket,r[\"gate\"][\"BIT_pin\"])\nexcept AssertionError:\n crossing_probe_rejected=True\nelse:\n raise AssertionError(\"Probe at lower crossing unexpectedly accepted\")", + "old": "g=gate(invoice,claim,tested,*bracket,r[\"gate\"][\"BIT_pin\"])" + }, + { + "file": "check_odd_partial_admission.py", + "new": "\"crossing_probe_rejected\":crossing_probe_rejected,\"scope\":\"Reuse exact same native word all-column adjoint;", + "old": "\"scope\":\"Reuse exact same native word all-column adjoint;" + }, + { + "file": "check_odd_precision.py", + "new": "", + "old": "previous=json.loads((root/\"SHORT-PRECISION.json\").read_text())" + }, + { + "file": "check_odd_precision.py", + "new": "assert grid_receipt[\"caller_sha256\"]==sha256(cpath.read_bytes()).hexdigest()", + "old": "assert previous[\"native_sha256\"]==sha and grid_receipt[\"caller_sha256\"]==sha256(cpath.read_bytes()).hexdigest()" + }, + { + "file": "check_odd_precision.py", + "new": "wg=grid.word_run(w, frac=25)\nwp,wr=env.native_envelope(w)\nwg=json.loads(json.dumps(wg,default=str));wr=json.loads(json.dumps(wr,default=str))\nassert wg==r[\"precision\"][\"word\"] and wr==r[\"precision\"][\"rounded_native\"], \"Fresh changed-native grid and envelope\"", + "old": "wg=previous[\"native_grid\"]\nwr=previous[\"rounded_native\"]\nwp={key:(Q(v[\"exact\"]),v[\"witness\"]) for key,v in wr[\"bounds\"].items()}" + } + ] + }, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "catalogue": [ + { + "catalogue_digest": "3466f64b2c8ac14c447dd20c7ade116c14c9ac905fc8ac264f41afe89825e0ec", + "catalogue_size": 3048, + "checked_maps": 1000, + "distinct_helper_maps": 186, + "distinct_paid_maps": 2963, + "exact_recipe_digest": "54d0d837eab62474173c517e7c33c088acaee420893adf6f55d713fef5018114", + "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945", + "main_boundary_pairs": 0, + "phase_control_rejected": true, + "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.", + "slice_start": 0, + "slice_stop": 1000, + "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE", + "word_sha256": "250ec5734ad5fa70f0178b1562d74894192f5263d96a99400e5a8b066681ada1" + }, + { + "catalogue_digest": "3466f64b2c8ac14c447dd20c7ade116c14c9ac905fc8ac264f41afe89825e0ec", + "catalogue_size": 3048, + "checked_maps": 1000, + "distinct_helper_maps": 186, + "distinct_paid_maps": 2963, + "exact_recipe_digest": "4f89979ad1c62005411ec1845c5e0a0df2662e641da6b5c4659b9967ecb7838c", + "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945", + "main_boundary_pairs": 0, + "phase_control_rejected": true, + "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. 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Fresh integrated physical native/caller and changed-word precision/occurrence application remain separate." + }, + "ODD-CALLER-EXACT-GRID.json": { + "caller_odd_scale": "675", + "caller_odd_scale_bits": 10, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "grid_exponents": [ + 381, + 3, + 2 + ], + "peak_terms": 3752, + "preproduct_exact_divisions": 176874, + "prime_order": [ + 2, + 3, + 5 + ], + "safe_valuation_bound": [ + 381, + 69, + 62 + ], + "scope": "Independent integer Laurent caller endpoint and pre-product divisibility. Valuation bound propagates complete field operators whose Gaussian coefficients have only power-of-two denominators, so odd factors are sourced only from the charged scalar operations. Fixed conversion and storage bounds still needed." + }, + "ODD-FIXED-TAPE-COUNTS.json": { + "H": 16495300000000000000000, + "Kstar_bits": 14093, + "actual_ambient": 145, + "caller_odd_scale": 675, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "common_grid": { + "fractional": "p+D", + "signed_width": "p+h+2D+3", + "temp_padding": 26 + }, + "compiler_ambient_cap": 153, + "context_bound_bits": 14104, + "context_c": 2362, + "elementary_records_per_map_upper": 85264, + "elementary_records_upper": 25474666336, + "log_power": 2235, + "max_scalar_numerator_bits": 24, + "monomial_map_slots": 298774, + "native_invocations": 17, + "native_sha256": "a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2", + "owned_banks_per_raw_occurrence": 867, + "scalar_macro_inputs": { + "caller": 117856, + "conversions": 58216, + "native": 1161423 + }, + "scalar_services_upper": 42799840, + "scalar_steps_coefficient": 44878885027840, + "scope": "Exact finite-cost and common-format substitutions in the selected #7000 conditional application proof, using the conservative primitive movement and scalar constants there. The premise is the complete signed native/physical binding and retained compiler, BIT, stock, and outer contracts. This script counts the raw occurrence, not an enumerated top-level compiled multiplier.", + "tested_claim": "3642219284637/1000000000000000" + }, + "ODD-PHYSICAL-BINDING.json": { + "aliased_main_rejected": true, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "native_sha256": "a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2", + "occurrence_and_geometry": { + "ambient": 145, + "complete_paid_position_digest": "4ae8fa27e41f8737d778d70878b730680292d74c07daaf1f100e82ab91101a21", + "fresh_helpers": 18564, + "idle_uses": 3392, + "lambda_uses": 11280, + "native_calls": 17, + "native_contact_boundaries": 13600, + "native_public": 1492, + "nonzero_boundary_translations": 13600, + "paid": { + "1": 68860, + "16": 416, + "2": 14314, + "24": 416, + "3": 13923, + "32": 416, + "4": 3944, + "40": 416, + "48": 416, + "5": 5661, + "56": 416, + "6": 272, + "64": 208, + "7": 187, + "8": 758, + "9": 32 + }, + "paid_positions": 110655, + "phase_record_digest": "586ab7499fb677afdd83c397ea0b6d3b25f73ea6cdfa1ec95dd68adccff935ad", + "productive_fields": 22308, + "query_uses": 384, + "rank_surplus": 1424, + "reserved_native_banks": 867, + "reserved_serial_query_lambda_bank": 1, + "targets": { + "1": 306, + "137": 208, + "17": 416, + "2": 306, + "25": 416, + "3": 799, + "33": 416, + "4": 3706, + "41": 416, + "49": 416, + "5": 1275, + "57": 416, + "6": 714, + "65": 416, + "7": 306, + "73": 208, + "8": 901, + "9": 10667 + } + }, + "patched_application_sha256": "733b31b1cee4567b466fdf834a34460b530f1f87ca6dca9270c0fabb2cf89849", + "scope": "Current caller port and ownership substitution, full phase-polynomial native contact identities on disjoint stage axes, whole signed idle/output geometry, and ordered paid positions. Retains the standard nested chart and local operator premises and requires separate full native replay and complete fixed-tape tariff application.", + "source_reviewer_sha256": "d98987db98553dc55bfc80e3ca47abfcd51c57af6f8cda61101391d8eae94184" + }, + "ODD-PRECISION.json": { + "caller_grid": { + "caller_odd_scale": "675", + "caller_odd_scale_bits": 10, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "grid_exponents": [ + 381, + 3, + 2 + ], + "peak_terms": 3752, + "preproduct_exact_divisions": 176874, + "prime_order": [ + 2, + 3, + 5 + ], + "safe_valuation_bound": [ + 381, + 69, + 62 + ], + "scope": "Independent integer Laurent caller endpoint and pre-product divisibility. Valuation bound propagates complete field operators whose Gaussian coefficients have only power-of-two denominators, so odd factors are sourced only from the charged scalar operations. Fixed conversion and storage bounds still needed." + }, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "context_c": 2362, + "context_height": 406, + "context_mass_bits": 1181, + "native_grid": { + "coefficient_visits": 15457099, + "dyadic_height": 25, + "mass_witness": [ + 65206, + "stored add" + ], + "maximum_scaled_mass": "814448574117075/8192", + "numerator_bits": 24, + "odd_scale_lcm": 1125 + }, + "native_sha256": "a32696e806c5cde0510cdf2f494e1f14ebb01e73d4ec577413fd7e7c0d9d68b2", + "precision_program_sha256": "7696f2e4074ccc9c970670494595e2a973742279a6109d1e60fd551a4611d236", + "rounded_caller": { + "bounds": { + "E_joint_entrance": { + "exact": 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Each LAMBDA, QUERY and signed/unsigned idle is one unitary with one child defect. The caller allocation assumes independent stage helpers. 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"38015085126560937795490109843252434211640761825966011687324191627420622198046177/100000000000000000000000000000000000000000000000000000000000000000000000000000000", + "38015085126560937795490109843252434211640761825966011687324191627420622232022239/100000000000000000000000000000000000000000000000000000000000000000000000000000000" + ], + "claim_decimal": "0.003642219284637", + "gain": "9.79634453E-7", + "gain_exact": "979634453/1000000000000000", + "independent_raw_bracket": [ + "0.00364221928463783897927791107627154", + "0.00364221928463783897927791107627155" + ], + "previous_claim": "455154956273/125000000000000", + "raw_bracket": [ + "0.0036422192846378389792779110762715", + "0.0036422192846378389792779110762716" + ] + } + }, + "status": "PASS_P104_NONUNIT_PIVOT_SPLIT" +} diff --git a/research/p104-nonunit-pivot-split/SOURCES.json b/research/p104-nonunit-pivot-split/SOURCES.json new file mode 100644 index 0000000000..c4150ae397 --- /dev/null +++ b/research/p104-nonunit-pivot-split/SOURCES.json @@ -0,0 +1,24 @@ +{ + "schema_version": 1, + "base_commit": "e54523517d0f03e58352e647c403a5af3e525a57", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "75d77b328ea02ded535e7f23aee5b1e55d0bb1a8", + "sha256": "154c3d30455d778fd3343b6b4851f0fa4665f0f7625b0adb3675e2bafbbf6bf1" + }, + { + "path": "docs/research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md", + "usage": "provenance", + "git_blob": "3dd1af2285e597676725e85ad4f65e7ad326d695", + "sha256": "4501502c2ceb9759b20372435fe4beb51082c5a5e2910c1fd5dbe6edca415055" + } + ] +} diff --git a/research/p104-nonunit-pivot-split/TASK.json b/research/p104-nonunit-pivot-split/TASK.json new file mode 100644 index 0000000000..f562a935db --- /dev/null +++ b/research/p104-nonunit-pivot-split/TASK.json @@ -0,0 +1,145 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "base_commit": "e54523517d0f03e58352e647c403a5af3e525a57", + "priority_revision": 8, + "original_card": { + "id": "p104-side-correction", + "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?", + "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", + "research/p104-helper-subspace-splits/README.md", + "research/dyadic-helper-channel-capacity/README.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": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "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": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.", + "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": [ + "P104", + "helper basis", + "helper split", + "5718", + "dyadic capacity" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "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" + } + ] + }, + "author": "Prepared for dillona with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", + "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19520521", + "scope_status": "changed", + "scope_change_reason": "Exact #7123 has eleven affordable rational rank-nine nominations rejected by the existing basis emitter because a nonzero pivot has a forbidden reciprocal. Extend the earlier zero-pivot unit-swap choice to a nonzero nonunit pivot; retain the operation alphabet, physical contract and complete bill.", + "concrete_question": "Can a legal unit pivot recover one rational helper split on exact #7123 and improve the complete signed application?", + "actual_scope": "Exact #7123 cut 37583/chart 1027/pivot 639, helper group 3\u2192127, rank 9\u21925+4. The declared neutral placement of role 643 leaves the source program byte-identical. Swap boundary coordinates 639/802 before normalizing; bases 426/17 add 880 ADDs and 6 SCALEs. No paid change. Fresh grid 1125/F25 is charged.", + "domain": "Correct-current-kappa screen of groups 3\u2192924, 3\u2192246, 3\u2192120, 3\u2192127; full-group screen yields eleven affordable rational nominations. Deterministic legal basis/gauge comparison selects index 10. Only that candidate is constructed and fully replayed.", + "success": "A complete arbitrary-input native and signed 17-stage application with \u03ba > .003641239650184.", + "bottleneck_link": "A nonzero nonsmooth pivot is a constructor obstruction, not a rational pairing or operation-alphabet obstruction when a cocharted unit entry is present. The additional basis work, changed grid and all application costs must pass.", + "predecessor_head": "020d581d9856b6db83e448c3f20418bc63b72c34", + "predecessors": [ + "dillona/OpenAI Codex #7123 exact 020d581d9856b6db83e448c3f20418bc63b72c34, retained complete 30-file export and all nested sources. #7112 zero-pivot smooth swap is extended here to a nonzero nonunit pivot.", + "Rohan Arun7122 global input rechart, exact98aad9eb0e7d7f985622a35c7981695fe680c68a, retained as complete9-fileexport with nested7121closure; draft native/price evidence at this frozen head.", + "1337isnot1337/OpenAI Codex fresh-helper-boundary/discover-cut.cpp alpha-expansion method used by Rohan Arun7122; later completed source6391d64 retains identical six construction/source files, recorded in PEER-STATUS.json.", + "ToikY Discussion7111 original chart120 pattern, retained through7120; it is retained through the exact predecessor chain.", + "Ali Romman: helper bases, independent split identity and paid meetings", + "Jerry Chen/CubeJerry: causal retiming, native/invoice/compiler engines", + "Matarener: complete kernels including zero boundary images and pairing decision", + "Rohan Arun: exact7113 signed17-stage caller and source-specific application", + "ToikY: #7108\u2013#7110 signed sources and splits, plus the credited chart-120 lead in Discussion #7111", + "DreamingOfClouds, Douglas Colkitt/#7000 reviewers and all retained nested-source notices", + "dillona/OpenAI Codex:7105,7107,7112,7115,7116,7117; exact7117 parent retains all earlier exports", + "dillona/OpenAI Codex7118: first funded residual mode and exact source-specific application", + "dillona/OpenAI Codex7119: exact reciprocal source and full application", + "ToikY original chart120 pattern and dillona/OpenAI Codex7120 exact-source composition, fully retained as the immediate source." + ], + "outcome": "completed", + "evidence_status": "Both complete direct CPython 3.14.7 commands and final registered isolated CPython 3.12.16 replay passed, matching every frozen native and composition receipt field. Coverage includes 17 native controls, F25 and F24 rejection, 3048 paid/helper maps and 104 main boundaries, complete costs and 54+4 outer conditions.", + "evidence": "WITNESS.json,WORD.json.gz,INPUTS.json,NATIVE-RESULT.json,RESULT.json,REPLAY.txt when complete.", + "overlap": "Canonical e545 / priority 8 / selected #7000 unchanged. Refreshed complete remote pagination: 428 open PRs at 21:45:01 UTC and 7031 Discussion records at 21:46:01 UTC. Local sparse coverage is 12 working-tree records, with 10167 canonical note paths unsearched. Read peer #7124 completed output rechart at 97dc14132da53562b7939776d7a83d72af72eeb1, \u03ba=.003641428753638; this candidate exceeds it but retains frozen #7123 and does not claim composition with #7124. Other new claims concern register-model/profile, graph, port and scalar-boundary scopes. No selected-frontier change. Final canonical fetch and live #7124 head check at 21:53 UTC found no guidance or source-head changes.", + "open_questions": [ + { + "question": "Does an independent reviewer reproduce the nonzero unit-pivot repair and full F25 application?", + "why_it_matters": "A rational pairing and legal scalar basis still require exact chart availability, full endpoint correctness and complete costs.", + "first_step": "Replay the registered Python 3.12 commands; inspect the 639/802 unit swap, source-identical neutral placement, F24 rejection and complete F25 precision/cost substitution.", + "blocked_by": "Independent human/formal review and maintainer admission remain separate." + }, + { + "question": "Can subsequent changed helper endpoints support another fully priced legal construction?", + "why_it_matters": "This result is one exact word, not a fixed-model or global optimum.", + "first_step": "Refresh canonical main and overlap, pin the emitted word, and name a changed source-specific contract before searching.", + "blocked_by": "No gain is established beyond this emitted instance." + } + ], + "stop_rule": "One new fully checked invoice; refresh before any further research round." +} diff --git a/research/p104-nonunit-pivot-split/VALIDATION.md b/research/p104-nonunit-pivot-split/VALIDATION.md new file mode 100644 index 0000000000..2c4edebc7f --- /dev/null +++ b/research/p104-nonunit-pivot-split/VALIDATION.md @@ -0,0 +1,22 @@ +# Validation record + +Both complete direct commands passed under CPython 3.14.7: + +```sh +python3 -I -B research/p104-nonunit-pivot-split/verify_native.py --out research/p104-nonunit-pivot-split/NATIVE-RESULT.json +python3 -I -B research/p104-nonunit-pivot-split/verify.py --out research/p104-nonunit-pivot-split/RESULT.json +``` + +The native command authenticates the entire 30-file #7123 export and nested source closure, reconstructs every source/candidate byte, and checks the exact cut, forward and adjoint endpoints, complete target/paid deltas, fresh grid and separate 18-stage ingredient invoice/precision. It replays all 512 columns of three boundary maps, finite native and signed physical routes, and 17 controls: 15 corruption/grid controls, one nonzero-pivot unit-basis identity control, and one explicit rejection of the original forbidden reciprocal. Missing boundary/cut corrections fail. The source-identical neutral placement and agreement of the independently derived rational/integer grid heights and masses were separately checked, then made explicit assertions for the registered replay. + +The application reconstructs both complete 17-stage invoices; replays the unchanged rational/integer Laurent caller, all 3,048 paid/helper maps and 104 main boundaries; and checks owner/phase bindings, fresh precision/error envelopes, ordinary/fixed-tape costs, both exact prices and 54 strict plus 4 functional outer conditions. The crossing-probe rejection remains active. + +The independent rational grid derivation found F25 before the complete verifier was run. Explicit one-occurrence source adapters change the forward integer scale from 2^24 to 2^25 and the measured trailing-bit offset from 25 to 26. Both precision paths explicitly request `frac=25` from the unchanged authenticated grid engine. The insufficient-grid control rejects F24. This is a charged precision change; no divisibility check is disabled and no frozen source is edited. + +Final registered isolated CPython 3.12.16 replay passed both complete commands and compared every frozen native and composition receipt field. REPLAY.txt preserves the actual stdout; the process exited successfully. Metadata was marked completed afterwards, explaining outcome=partial in the runner line. All 18 frozen code, source, witness, manifest and scientific receipt hashes stayed unchanged after this comparison. No hosted scientific pass is claimed. The existing canonical guide6030/selected7000 onboarding mismatch remains outside this package-only change. + +Discovery records eleven affordable rational nominations in group 3→127. All eleven obtain legal bases under the recorded unit-pivot/gauge trials; only the shortest selected candidate, index 10, is constructed. Complete kernels and a finite basis list do not establish a rational cost optimum. The public witness is replayable without local search code. Two preliminary negative group screens used an inherited older floating nomination κ; both were preserved and rerun at the actual current κ, with identical counts and zero hits. The chosen group and all exact certificate/price checks use the current source. No global barrier is claimed. + +Overlap was refreshed from canonical main and all remote pages; #7124's separate output rechart was read and left uncombined. The sparse local overlap report explicitly leaves 10,167 canonical package-note paths unsearched. Frozen sources and prior local evidence are retained. + +Five framework assumptions, independent human/formal review, maintainer admission and compiled top-level execution remain. No Lean or Docker was run. diff --git a/research/p104-nonunit-pivot-split/VERIFY.json b/research/p104-nonunit-pivot-split/VERIFY.json new file mode 100644 index 0000000000..149c761811 --- /dev/null +++ b/research/p104-nonunit-pivot-split/VERIFY.json @@ -0,0 +1,29 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify_native.py" + ], + "timeout_seconds": 600, + "checks": "Authenticate complete 30-file #7123 export and nested closure; reconstruct every source/candidate byte; arbitrary-input forward/adjoint, exact cut and unit basis, complete paid/target invoice, freshly derived F25 grid with F24 rejection, separate 18-stage ingredient/precision, affected 512-column maps, corruption/unit controls and finite native/signed physical replay; compare every receipt field." + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Reconstruct #7123 and candidate 17-stage invoices; unchanged literal caller, all 3048 paid/helper maps and 104 main boundaries, fresh F25 grid/envelopes, ordinary/physical/fixed-tape costs, two prices and 54+4 outer gates; compare every receipt field." + } + ] +} diff --git a/research/p104-nonunit-pivot-split/WITNESS.json b/research/p104-nonunit-pivot-split/WITNESS.json new file mode 100644 index 0000000000..7749c4a365 --- /dev/null +++ b/research/p104-nonunit-pivot-split/WITNESS.json @@ -0,0 +1,483 @@ +{ + "frame": 1027, + "pivot": 639, + "cut": 37583, + "ranks": [ + 5, + 4 + ], + "gain": 0.02236181478033039, + "paths": [ + { + "role": 643, + "lo": 37583, + "hi": 37584, + "frame": 1027, + "old": 3, + "new": 1027, + "moves": [ + 37583 + ], + "old_paid": [ + 5 + ], + "new_paid": [ + 5, + 0 + ], + "cost": 0.0, + "private": false, + "neutral": true + } + ], + "a": { + "643": "1", + "640": "1/2", + "641": "1/3", + "1298": "2/3", + "639": "1/6", + 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