From 18041465a778f8cad956dc1c31f1ee2420eb1b97 Mon Sep 17 00:00:00 2001 From: CubeJerry <80299683+CubeJerry@users.noreply.github.com> Date: Tue, 10 Nov 2026 03:34:26 +0800 Subject: [PATCH] Prove the pinned QSELF-pair interval needs three queries (no new kappa) --- .../p104-query-interval-optimum/CHECKPOINT.md | 21 ++ .../DEPENDENCIES.json | 29 ++ .../p104-query-interval-optimum/NOTICE.md | 25 ++ .../p104-query-interval-optimum/OVERLAP.md | 25 ++ .../PR-DESCRIPTION.md | 62 ++++ .../p104-query-interval-optimum/PR-TITLE.txt | 1 + research/p104-query-interval-optimum/PROOF.md | 186 ++++++++++ .../QUERY-ONLY-CALLER.json | 1 + .../p104-query-interval-optimum/README.md | 54 +++ .../p104-query-interval-optimum/SOURCES.json | 18 + .../p104-query-interval-optimum/TASK.json | 90 +++++ .../p104-query-interval-optimum/VERIFY.json | 57 +++ .../data/caller_efree.json | 1 + .../evidence/REPLAY.json | 113 ++++++ .../retained/ATTAINMENT-PROOF.md | 287 +++++++++++++++ .../review/RESULT.json | 335 ++++++++++++++++++ .../review/REVIEW.md | 83 +++++ .../review/check_covectors.py | 131 +++++++ .../p104-query-interval-optimum/verify.py | 166 +++++++++ 19 files changed, 1685 insertions(+) create mode 100644 research/p104-query-interval-optimum/CHECKPOINT.md create mode 100644 research/p104-query-interval-optimum/DEPENDENCIES.json create mode 100644 research/p104-query-interval-optimum/NOTICE.md create mode 100644 research/p104-query-interval-optimum/OVERLAP.md create mode 100644 research/p104-query-interval-optimum/PR-DESCRIPTION.md create mode 100644 research/p104-query-interval-optimum/PR-TITLE.txt create mode 100644 research/p104-query-interval-optimum/PROOF.md create mode 100644 research/p104-query-interval-optimum/QUERY-ONLY-CALLER.json create mode 100644 research/p104-query-interval-optimum/README.md create mode 100644 research/p104-query-interval-optimum/SOURCES.json create mode 100644 research/p104-query-interval-optimum/TASK.json create mode 100644 research/p104-query-interval-optimum/VERIFY.json create mode 100644 research/p104-query-interval-optimum/data/caller_efree.json create mode 100644 research/p104-query-interval-optimum/evidence/REPLAY.json create mode 100644 research/p104-query-interval-optimum/retained/ATTAINMENT-PROOF.md create mode 100644 research/p104-query-interval-optimum/review/RESULT.json create mode 100644 research/p104-query-interval-optimum/review/REVIEW.md create mode 100644 research/p104-query-interval-optimum/review/check_covectors.py create mode 100644 research/p104-query-interval-optimum/verify.py diff --git a/research/p104-query-interval-optimum/CHECKPOINT.md b/research/p104-query-interval-optimum/CHECKPOINT.md new file mode 100644 index 0000000000..00eaf1517b --- /dev/null +++ b/research/p104-query-interval-optimum/CHECKPOINT.md @@ -0,0 +1,21 @@ +# Wave 8 lead checkpoint + +Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`. +Branch: `research/p104-query-interval-optimum-20261109`. +Package: `research/p104-query-interval-optimum`. + +Complete: exact source rank-three certificate and universal query-count +proof in the stated fixed linear/affine model. The pinned predecessor +provides three-query attainment. No whole-caller or kappa bound is claimed. +All four direct normal/optimized forward/reverse checks passed; receipts +agree across modes. Independent reviewer artifacts are retained unchanged. + +Next: registered package and metadata checks, commit, byte/mode/export +validation, inspect additions-only diff, then lead-controlled fork branch +publication and remote ref/tree/parent verification. No upstream PR. + +Restart: read PROOF.md, DEPENDENCIES.json and review/REVIEW.md. Reproduce +with README commands. The durable session manifest records exact frozen +local and API publication commits; do not interpret this checkpoint as +proof-kernel or human admission. Remaining work includes possible changed +boundaries, actual reachable-input subspaces and full physical precision. diff --git a/research/p104-query-interval-optimum/DEPENDENCIES.json b/research/p104-query-interval-optimum/DEPENDENCIES.json new file mode 100644 index 0000000000..fe87c4911f --- /dev/null +++ b/research/p104-query-interval-optimum/DEPENDENCIES.json @@ -0,0 +1,29 @@ +{ + "schema_version": 1, + "files": [ + { + "path": "research/p104-query-interval-optimum/data/caller_efree.json", + "git_blob": "5a71ca9f80ced1aeb8a68e97516cab52eb72a52a", + "sha256": "c5b6c5236462ae84e5431a791a2f8ce795774342f13e11c4af35689092a8af30", + "repository": "DreamingOfClouds/integer-mult-bounds", + "commit": "a98df73ddae1d1ea85a62b6bdf2714b28cb7b359", + "source_path": "research/p104-two-chain-findings/data/caller_efree.json" + }, + { + "path": "research/p104-query-interval-optimum/QUERY-ONLY-CALLER.json", + "git_blob": "cf55f4271009a06ad192a070d330a4466b6d44fa", + "sha256": "3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e", + "repository": "CubeJerry/integer-mult-bounds", + "commit": "617903497387a98f7ca929ad0b6928dd32abffec", + "source_path": "research/p104-query-only-interval/QUERY-ONLY-CALLER.json" + }, + { + "path": "research/p104-query-interval-optimum/retained/ATTAINMENT-PROOF.md", + "git_blob": "2f8610ae455bb8c6b79161223cc948e136253add", + "sha256": "0cede285a98dd61b78020651202729c6d9cd16fb078ee5fe9a01aa2400df5432", + "repository": "CubeJerry/integer-mult-bounds", + "commit": "617903497387a98f7ca929ad0b6928dd32abffec", + "source_path": "research/p104-query-only-interval/PROOF.md" + } + ] +} diff --git a/research/p104-query-interval-optimum/NOTICE.md b/research/p104-query-interval-optimum/NOTICE.md new file mode 100644 index 0000000000..4234c636c8 --- /dev/null +++ b/research/p104-query-interval-optimum/NOTICE.md @@ -0,0 +1,25 @@ +# Credit and retained inputs + +Prepared for @CubeJerry with substantial OpenAI assistance in mathematical +reasoning, exact source checks, implementation, independent AI cross-review +and packaging. No independent human review or proof-kernel verification +is asserted. Apache-2.0, consistent with the repository. + +The original two-chain caller and its definitions are by the contributors +to CrocSwap/integer-mult-bounds#6937, from the pinned DreamingOfClouds fork. +They are retained byte-for-byte and are not new execution in this package. +The public QUERY-only construction by @CubeJerry with OpenAI assistance +is a separate prior contribution at `617903497387a98f7ca929ad0b6928dd32abffec`. +Its complete formal proof and candidate caller are retained unchanged and +credited as the attainment of the lower bound, not newly invented here. + +The classical rank and product-difference argument is used transparently. +The canonical query-information and affine-tag packages and #6825/#6800 +retain credit for their different query/rank investigations. This package +claims only the source-specific optimality theorem under its exact model. + +The reverse-covector evaluator and `review/REVIEW.md` were produced by a +separate shared-context AI worker without importing the lead forward +engine or predecessor arithmetic. Both approaches share the authenticated +source words and the claimed minor. This is method diversity, not a claim +of statistical, organizational or human independence. diff --git a/research/p104-query-interval-optimum/OVERLAP.md b/research/p104-query-interval-optimum/OVERLAP.md new file mode 100644 index 0000000000..7b6f6e1f53 --- /dev/null +++ b/research/p104-query-interval-optimum/OVERLAP.md @@ -0,0 +1,25 @@ +# Bounded overlap and scope record + +Canonical main was rechecked on 2026-11-09 at 19:21 UTC: +`7c49fe32c55de02c2c873655c804b16e4c3fef0a`. The latest relevant proposals +#6936 and #6937 remained open and did not replace the selected certificate. +No unclaimed global improvement is inferred from them. + +| Predecessor | Established scope | Relation to this package | +| --- | --- | --- | +| #6937, `p104-two-chain-findings` | Exact two-chain source and QSELF-pair caller; QUERY-only route discussed, complete replacement then unbuilt | Original word and question; no claim to discover that a QUERY-only route was conceivable | +| Public `p104-query-only-interval`, commit `617903497387a98f7ca929ad0b6928dd32abffec` | Full formal 223-event three-query replacement and its complete conditional invoice | Supplies the upper bound unchanged; this package supplies the matching local minimum | +| Canonical `actual-query-information-bounds` | Historical stage-cover, snapshot and residual-information bounds for another source/task model | Read as a query-information predecessor; not the same fixed order-four interval | +| Canonical `affine-tag-query-minimum` | Normalized quadratic-phase membership-query oracle model | Different query access and target; not this linear register alphabet | +| #6825 with #6800 antecedent | Characteristic-two target/rank factorization, square-zero paid calls and constant free bases | Rank/query proof perspective credited; different field, target and source boundary | + +The reconnaissance used current metadata, the named README files, relevant +PR descriptions and the exact proposed caller/proof. It was bounded, not +an exhaustive literature or archive novelty certification. The general +rank-subadditivity and telescoping method is classical and is not claimed +as new. No search over all possible replacement words is claimed. + +Concurrent precision work examines rounded scalar/native contracts for +the same public replacement. It is complementary: this package prices +only the necessary number of formal queries at fixed endpoints, and +does not establish physical execution or precision admission. diff --git a/research/p104-query-interval-optimum/PR-DESCRIPTION.md b/research/p104-query-interval-optimum/PR-DESCRIPTION.md new file mode 100644 index 0000000000..60e3c78efe --- /dev/null +++ b/research/p104-query-interval-optimum/PR-DESCRIPTION.md @@ -0,0 +1,62 @@ +## Result and why it matters + +The exact #6937 interval at zero-based events 457..575 needs **at least +three QUERY operations** in the stated fixed q-even linear/affine rewrite +model, even with arbitrary finite helpers, copies and erasures. The public +three-query replacement already attains this count. This rules out reducing +that specific interval to two queries while preserving its full independent +input/output boundary and the charged-operation contract. + +The proof evaluates the actual source at q=+1 and q=-1, D9=1. A response +minor on rows/columns 0,1,19 has determinant 8. The classical telescoping +identity bounds response rank by the number of rank-one charged operations, +without requiring invertible helpers or free maps. A forward full-state +rational engine and separately coded reverse-covector engine recover the +same exact certificate. + +## Sources, novelty and complete scope + +Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`. +Original #6937 source: `a98df73ddae1d1ea85a62b6bdf2714b28cb7b359`. +The matching construction is the [published QUERY-only package](https://github.com/CubeJerry/integer-mult-bounds/tree/617903497387a98f7ca929ad0b6928dd32abffec/research/p104-query-only-interval), +which is retained unchanged and credited. The lower bound is new for this +pinned source/model; neither the three-query construction nor the general +rank method is claimed as new. `OVERLAP.md` distinguishes earlier +query-information, affine-tag and #6825/#6800 rank-factorization scopes. + +The theorem requires lawful evaluations, regular free denominators, +independent inputs, identical free initialization/output extraction at both +signs and rank-one full-state charged queries. It excludes free odd-q side +information, nonlinear/adaptive coefficients, unpriced wider payloads and +changed endpoints. No complete-caller, native-rank or multiplication lower +bound follows. Existing helper, arithmetic, storage, source access, +precision and compiler costs are not waived or repriced. + +## Reproduction and verification + +```sh +python3 -I -B research/p104-query-interval-optimum/verify.py +python3 -I -B research/p104-query-interval-optimum/review/check_covectors.py research/p104-query-interval-optimum +python3 -B scripts/research_package.py --package research/p104-query-interval-optimum +python3 -B scripts/check_research_commit.py --package research/p104-query-interval-optimum --check-modes +``` + +The registered commands include normal and optimized Python executions. +Expected response rank is 3, determinant 8 and 55 nonzero response entries. +Each of six deleted charged-site controls loses rank three. Both complete +source words and the predecessor proof are byte authenticated. The finite +two-point attainment check is not substituted for the predecessor's full +formal identity proof. Universal candidate-rewrite exclusion is the written +telescoping argument, not a finite circuit search. + +## Status, limitations and credit + +**No new kappa.** This is a rigorous scoped negative result and verification +advance. The accepted bound remains conditional on the five framework +assumptions; no selected artifact changes. Whole-caller rearrangements, +proved reachable subspaces or additional operator relations remain open. + +Prepared for @CubeJerry with substantial OpenAI assistance in proof, source +audit, exact checks, separate AI review and packaging. The #6937 authors, +the prior public QUERY-only package and cited query/rank contributors keep +their credit. No independent human or proof-kernel acceptance is claimed. diff --git a/research/p104-query-interval-optimum/PR-TITLE.txt b/research/p104-query-interval-optimum/PR-TITLE.txt new file mode 100644 index 0000000000..c3e0b58535 --- /dev/null +++ b/research/p104-query-interval-optimum/PR-TITLE.txt @@ -0,0 +1 @@ +Prove the pinned QSELF-pair interval needs three queries (no new kappa) diff --git a/research/p104-query-interval-optimum/PROOF.md b/research/p104-query-interval-optimum/PROOF.md new file mode 100644 index 0000000000..f007319880 --- /dev/null +++ b/research/p104-query-interval-optimum/PROOF.md @@ -0,0 +1,186 @@ +# A source-specific three-query minimum + +Prepared for @CubeJerry with substantial OpenAI assistance. Apache-2.0. + +## 1. Claim, sources and exact boundary + +The original #6937 caller is pinned at +`a98df73ddae1d1ea85a62b6bdf2714b28cb7b359`, file +`research/p104-two-chain-findings/data/caller_efree.json`, Git blob +`5a71ca9f80ced1aeb8a68e97516cab52eb72a52a`. Consider exactly its zero-based +events 457 through 575, inclusive. They contain 119 operations, begin with +`QSELF(0,-1)`, end with `QSELF(19,-1)`, and contain one QUERY between them. +The complete state has 76 independent formal input registers. Only the +38 A registers are touched; the 38 B registers are unchanged. + +The public package `p104-query-only-interval`, commit +`617903497387a98f7ca929ad0b6928dd32abffec`, replaces that same interval by +223 events using exactly three QUERYs and no QSELF. It preserves the +entire boundary map, with all independent inputs and formal D variables. +We retain and authenticate its proof rather than claim its construction +again. The original and replacement words are included byte-for-byte. + +**Theorem.** In the fixed linear/affine rewrite model in Section 2, every +replacement of this exact interval's full independent-input map uses at +least three charged QUERY operations. The cited three-query construction +attains this bound in the model. Extra finite linear helpers, copies, +erasures and affine constants do not reduce the minimum. + +This is a local formal-operator result. It does not prove optimality of +the complete caller, a paid native-rank lower bound, a bit-complexity lower +bound, or a limit on multiplication kappa. + +## 2. Rewrite model and legal evaluations + +The required identity is over + + R = Q(i)[q,D1,...,D18]/(q^4-1), + +with no additional q/D relations or D idempotence. In particular q is a +formal operator parameter, not an input register. Both evaluations +`q=+1,D9=1` and `q=-1,D9=1` are lawful; other D variables may also be set +to 1, since none occurs in this interval. We take matrix ranks only over +the field Q(i) after evaluation, not over the quotient ring R. + +A candidate has a fixed finite instruction stream and finite register +state. It may add any finite number of helper registers. Free steps are +linear or affine maps whose coefficients, constants, initialization and +final output extraction evaluate identically at the two chosen points. +Arbitrary q-even coefficients are allowed when defined at both points; +any allowed rational denominator must be regular there. Free maps may be +singular or rectangular. Copying, erasure and arbitrary q-independent +initial helper values are allowed without cost for this lower bound. + +A charged query must have full-state matrix difference of rank at most +one between the two evaluations, after homogenizing affine state. The +retained instruction `dest += q^k source`, for odd k and distinct roles, +has difference `2 E_dest,source`, hence meets this condition. Surrounding +it by any permitted free maps still has difference rank at most one. +Even powers have zero response and cannot improve the bound by themselves. +The original QSELF steps also have rank-one difference, although QSELF +is not an allowed uncharged operation in the replacement alphabet. + +All query-dependent side information must be accounted for. In particular +a prequeried helper bank cannot enter this interval for free, and odd-q +linear coefficients are not free. Every independent boundary input is +preserved as specified by the source map; restricting to a reachable +subspace or discarding selected outputs changes this task. Data-dependent +branches, nonlinear coefficient synthesis and a wider payload query whose +full-state difference has rank greater than one are outside the model. + +These restrictions are essential. For example, freely applying q to three +independent registers has response 2 I_3 and would supply the rank-three +witness with no charged queries. Restricting the input to two dimensions +also makes any response rank at most two. Neither is an admissible rewrite +of the problem stated here. + +## 3. Classical product-difference bound, including helpers + +Append one constant coordinate to homogenize affine maps. At the two +evaluations let the chronological step matrices be A_j^+ and A_j^-. +Initialization E and final extraction P are the same at both evaluations. +Variable register dimensions can be kept in the following compatible +rectangular products, or padded into the finite union of all registers. + +The difference of whole maps is + + M^+ - M^- = P sum_j [ A_m^+ ... A_(j+1)^+ + (A_j^+ - A_j^-) + A_(j-1)^- ... A_1^- ] E. (1) + +This is the usual telescoping identity, with no inversion. A free step +contributes zero. A charged query contributes a term of rank at most one, +because multiplication on either side cannot increase rank. Rank +subadditivity therefore gives + + rank(M^+ - M^-) <= number of charged queries. (2) + +For affine maps, restrict the columns to independent original inputs to +obtain the same bound on the linear response. Extra initial constants do +not invalidate (2). Noninvertible helpers, copies, rectangular maps and +erasures cause no problem. Correlated q-independent initial helpers are +already part of E. The rank and telescoping facts are classical; no +novelty is claimed for this general argument. + +## 4. Exact source witness + +Evaluate the original 119-event word at the two points in Section 2. +LAMBDA_s is the actual even polynomial + + ((1+s i) + (1-s i)q^2)/2, + +so it evaluates to 1 at either sign. The single IDLE_ONE in the interval +is D9 and evaluates to 1. All ADD/SCALE coefficients remain their exact +rationals; SWAP is unchanged. Thus direct rational arithmetic suffices. + +Let Delta=M^+-M^-. Its rows and columns numbered 0,1,19 give + +| | input 0 | input 1 | input 19 | +| --- | ---: | ---: | ---: | +| output 0 | -2 | -4 | 0 | +| output 1 | 0 | -2 | 0 | +| output 19 | 0 | 0 | 2 | + +The determinant is 8. Hence rank(Delta)>=3 over Q(i). The supplied forward +evaluator also computes the complete 76 by 76 response and finds rank +exactly 3, with 55 nonzero entries. Rank at least 3 is all the lower bound +needs. Applying (2) proves that two or fewer queries are impossible in +the stated model. + +There are two independently coded source checks. `verify.py` propagates +all original input columns forward and performs exact rational elimination. +`review/check_covectors.py` propagates three output covectors backwards +through literal transposed instructions, retaining all 76 input coordinates. +The latter was written by a separate shared-context AI worker without +importing the lead evaluator or the predecessor arithmetic. It recovers +the same minor and determinant. Its proof review is retained separately; +this is not human or proof-kernel acceptance. + +Both checks authenticate source bytes and fixed interval endpoints. Each +also checks the corresponding response of the public replacement. Deleting +any one of the three charged source sites or any one of the three replacement +queries destroys this rank-three witness; all six controls are included. +These are exact certificates for a finite, explicitly given matrix. The +universal claim over all candidate straight-line rewrites comes from +Sections 2 and 3, not from enumeration of candidate circuits. + +## 5. Attainment, budget and limits + +The pinned predecessor proves the full R-valued identity for its 223-event +replacement, including the untouched independent inputs, the formal D9 +service, the correct unit-valued LAMBDA factors and their conjugations. +It uses only three odd-power QUERYs and permitted even/constant free maps. +Its entire formal proof is retained as `retained/ATTAINMENT-PROOF.md`. +The two sign checks in this package alone would not establish that full +identity at q=+i,-i or all D9; they are supplementary source checks only. + +The exact three-query minimum prevents a one-query reduction of this +particular interval while preserving the model and boundary. It does not +reprice the predecessor. That package's additional free-operation costs, +helper access, width, copying, restoration, finite compiler and physical +supplier obligations remain in force. In particular no uncharged wider +payload query or queried initialization is being hidden in this result. +We do not multiply the formal rank by the number of physical ports and +call it a new native or whole-caller lower bound. + +No runtime algorithm, selected certificate or accepted kappa changes here. +The selected kappa remains 781451/250000000, conditional on all five +retained framework assumptions. The proposed QUERY-only caller still has +its separate precision, complete native admission and compiler obligations. +Global reordering, changing the interval boundaries, exploiting a proved +reachable-input subspace, or exploiting extra relations of a particular +native operator remain possible research directions and are not excluded. + +## 6. Relation to prior work + +The #6937 two-chain source and the public three-query construction are +the indispensable predecessors. The latter supplied the upper bound; +this package supplies a matching source-specific lower bound. + +The bounded overlap review read the canonical actual-query information +and affine-tag minimum packages, and #6825's characteristic-two rank +factorization result with #6800 antecedent. Their source targets, operation +models and coefficient fields differ from this order-four characteristic-zero +interval. We credit their rank/query perspective and make no claim to +inventing the rank method or exhaustively surveying all circuit complexity. +`OVERLAP.md` records the distinctions and exact scope. diff --git a/research/p104-query-interval-optimum/QUERY-ONLY-CALLER.json b/research/p104-query-interval-optimum/QUERY-ONLY-CALLER.json new file mode 100644 index 0000000000..cf55f42710 --- /dev/null +++ b/research/p104-query-interval-optimum/QUERY-ONLY-CALLER.json @@ -0,0 +1 @@ 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k): R[x] *= q^k, one paid rank-1 job on one register (new op; not in the retained alphabet).; source interval457..575 replaced by a three-QUERY even-basis factorization; no QSELF"} diff --git a/research/p104-query-interval-optimum/README.md b/research/p104-query-interval-optimum/README.md new file mode 100644 index 0000000000..59c540126e --- /dev/null +++ b/research/p104-query-interval-optimum/README.md @@ -0,0 +1,54 @@ +# The pinned QSELF-pair interval needs exactly three queries + +The original #6937 interval at events 457..575 cannot be replaced by two +QUERYs in the stated fixed q-even linear/affine model, even with arbitrary +finite helpers. Its response between q=+1 and q=-1, D9=1 has an exact +3 by 3 minor of determinant 8. The separately published three-query +replacement attains the bound. **No new kappa.** + +This closes one local budget-reduction direction. It does not prove a +whole-caller optimum, a native complexity lower bound, or any of the five +global framework assumptions. The exact independent-input boundary, the +rank-one charged operation and the absence of free odd-q side information +are essential. See `PROOF.md` for the universal statement and exclusions. + +## Reproduce + +```sh +python3 -I -B research/p104-query-interval-optimum/verify.py +python3 -I -B research/p104-query-interval-optimum/review/check_covectors.py research/p104-query-interval-optimum +python3 -B scripts/research_package.py --package research/p104-query-interval-optimum +python3 -B scripts/check_research_commit.py --package research/p104-query-interval-optimum --check-modes +``` + +Expected lead status: `PASS_P104_QUERY_INTERVAL_OPTIMUM`, response rank 3, +minor determinant 8, and six deleted-site controls of rank 2. The independent +reverse-covector checker returns the same minor and six singular deletion +controls. Registered commands also run under `python -O`; no safety-critical +check relies on Python assertions. Both source words and the predecessor +formal attainment proof are authenticated locally, without Git or network. +Complete receipts are in `evidence/REPLAY.json` and `review/RESULT.json`. + +## Provenance and credit + +Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`. +Source: CrocSwap/integer-mult-bounds#6937 at +`a98df73ddae1d1ea85a62b6bdf2714b28cb7b359`. +Attainment: [public QUERY-only package](https://github.com/CubeJerry/integer-mult-bounds/tree/617903497387a98f7ca929ad0b6928dd32abffec/research/p104-query-only-interval). +Exact byte and commit pins are in `DEPENDENCIES.json` and `SOURCES.json`. + +Prepared for @CubeJerry with substantial OpenAI assistance. The two-chain +source and QUERY-only construction retain their predecessor credit. +The product-difference/rank argument is classical. The source-specific +matching lower bound and its independently coded certificates are this +package's contribution. Separate AI review is not human or proof-kernel +acceptance. Further scope and prior work are in `OVERLAP.md` and `NOTICE.md`. + +## Open next questions + +Can a complete-caller rearrangement, or a rigorously identified reachable +input subspace, reduce the paid budget? The present fixed-boundary minimum +does not answer that question. A next attempt must count all query-dependent +side information and prove its changed source boundary before applying a +new response bound. Literal rounded precision and native/compiler admission +of the existing three-query construction remain separate obligations. diff --git a/research/p104-query-interval-optimum/SOURCES.json b/research/p104-query-interval-optimum/SOURCES.json new file mode 100644 index 0000000000..75ea7c3d55 --- /dev/null +++ b/research/p104-query-interval-optimum/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/p104-query-interval-optimum/TASK.json b/research/p104-query-interval-optimum/TASK.json new file mode 100644 index 0000000000..b59595a865 --- /dev/null +++ b/research/p104-query-interval-optimum/TASK.json @@ -0,0 +1,90 @@ +{ + "schema_version": 1, + "task_id": "uniform-transfer-audit", + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "original_card": { + "id": "uniform-transfer-audit", + "question": "Can one of the selected record's five inherited assumptions be proved at its actual caller?", + "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" + ], + "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": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.", + "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": "Choose one assumption ID (native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery), one quantified implication and exact dependency closure. Check current handoffs, including #5625 row reentry and #5707 root-prefix lowering, without treating their partial scope as the whole theorem. Prove or falsify that implication with a caller-bound argument; stop at the chosen obligation. Finite tests or root digits do not discharge an all-size statement.", + "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": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "existing_checks": [ + { + "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "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": "refined", + "scope_change_reason": "Source-specific complementary lower bound after the public QUERY-only interval construction; a local compiler-model obstruction, not removal of a global selected assumption.", + "actual_scope": "Exactly three QUERY operations are necessary and sufficient for the pinned 119-event interval in the stated q-even linear/affine model, with arbitrary finite helpers and independent boundary inputs.", + "bottleneck_link": "Closes attempts to reduce this precise interval below the attained three-query budget; does not bound other rewrites, the whole caller or kappa.", + "stop_rule": "Stop if the response minor is singular, legal specializations fail, or prior work already proves this same source-specific claim. No unbounded circuit search.", + "evidence": "Universal product-difference proof, exact source rank/minor, independent backward covectors and all four normal/optimized source/control gates passed. Publication byte/mode/export gates follow freeze.", + "author": "@CubeJerry", + "ai_assistance": "Substantial OpenAI assistance in research, proof development, implementation, tests and documentation; no independent human or proof-kernel admission claimed.", + "outcome": "completed", + "open_questions": [ + { + "question": "Can a whole-caller or reachable-subspace rewrite improve the paid budget?", + "why_it_matters": "The fixed independent-input interval lower bound does not apply automatically to changed boundaries or correlated state.", + "first_step": "State the actual source subspace and all query-dependent helpers, then compute a new legal response certificate.", + "blocked_by": "New source/interface proof and complete cost accounting." + } + ], + "time_budget_minutes": 60, + "freshness": { + "checked_utc": "2026-11-09T19:21:00Z", + "canonical_main": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "bounded_overlap": "Actual-query information, affine-tag query-minimum and #6825/#6800 rank-factorization scopes read; none is this characteristic-zero order-four fixed interval. Classical rank method is credited, not claimed new." + }, + "wave": 8, + "worker": "lead", + "track": "60/75" +} diff --git a/research/p104-query-interval-optimum/VERIFY.json b/research/p104-query-interval-optimum/VERIFY.json new file mode 100644 index 0000000000..51df74b9d0 --- /dev/null +++ b/research/p104-query-interval-optimum/VERIFY.json @@ -0,0 +1,57 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p104-query-interval-optimum/data/caller_efree.json", + "research/p104-query-interval-optimum/QUERY-ONLY-CALLER.json", + "research/p104-query-interval-optimum/retained/ATTAINMENT-PROOF.md" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 30, + "checks": "Normal forward exact source response and charged-site controls." + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/review/check_covectors.py", + "{package}" + ], + "timeout_seconds": 30, 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k): R[x] *= q^k, one paid rank-1 job on one register (new op; not in the retained alphabet)."} \ No newline at end of file diff --git a/research/p104-query-interval-optimum/evidence/REPLAY.json b/research/p104-query-interval-optimum/evidence/REPLAY.json new file mode 100644 index 0000000000..4d00e7cc17 --- /dev/null +++ b/research/p104-query-interval-optimum/evidence/REPLAY.json @@ -0,0 +1,113 @@ +{ + "forward": { + "attainment_interval": [ + 457, + 680 + ], + "attainment_opcodes": { + "ADD": 162, + "IDLE_ONE": 1, + "LAMBDA": 32, + "QUERY": 3, + "SCALE": 5, + "SWAP": 20 + }, + "attainment_rows": 223, + "attainment_scope": "Full formal identity is the pinned predecessor theorem; two-point checking alone is insufficient.", + "complete_character_comparisons": 2, + "deleted_site_controls": [ + { + "local_index": 0, + "response_rank": 2, + "word": "source" + }, + { + "local_index": 38, + "response_rank": 2, + "word": "source" + }, + { + "local_index": 118, + "response_rank": 2, + "word": "source" + }, + { + "local_index": 75, + "response_rank": 2, + "word": "attainment" + }, + { + "local_index": 81, + "response_rank": 2, + "word": "attainment" + }, + { + "local_index": 92, + "response_rank": 2, + "word": "attainment" + } + ], + "dependencies_authenticated": 3, + "independent_inputs": 76, + "lower_bound_scope": "Written telescoping proof plus exact finite source minor; no physical or whole-caller optimality.", + "minor": [ + [ + "-2", + "-4", + "0" + ], + [ + "0", + "-2", + "0" + ], + [ + "0", + "0", + "2" + ] + ], + "minor_determinant": "8", + "minor_rows_and_columns": [ + 0, + 1, + 19 + ], + "no_new_kappa": true, + "nonzero_response_entries": 55, + "response_rank": 3, + "scope_controls": [ + "independent-input subspace restriction", + "free odd-q coefficients forbidden" + ], + "source_interval": [ + 457, + 576 + ], + "source_opcodes": { + "ADD": 88, + "IDLE_ONE": 1, + "LAMBDA": 4, + "QSELF": 2, + "QUERY": 1, + "SCALE": 5, + "SWAP": 18 + }, + "source_rows": 119, + "status": "PASS_P104_QUERY_INTERVAL_OPTIMUM" + }, + "registered_checks": [ + "forward", + "reverse", + "forward-O", + "reverse-O" + ], + "durations_seconds": { + "forward": 0.2731586750014685, + "reverse": 0.06503239599987864, + "forward-O": 0.35474096200050553, + "reverse-O": 0.11612551799771609 + }, + "reverse_receipt": "review/RESULT.json", + "physical_execution": false +} diff --git a/research/p104-query-interval-optimum/retained/ATTAINMENT-PROOF.md b/research/p104-query-interval-optimum/retained/ATTAINMENT-PROOF.md new file mode 100644 index 0000000000..2f8610ae45 --- /dev/null +++ b/research/p104-query-interval-optimum/retained/ATTAINMENT-PROOF.md @@ -0,0 +1,287 @@ +# Removing both separated QSELF sites within the existing paid budget + +Prepared for **@CubeJerry**, with substantial OpenAI assistance. Apache-2.0. +**No new kappa. Exact formal caller identity; physical and rounded interfaces remain conditional.** + +## 1. Exact claim, sources and novelty + +Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`. +The source is DreamingOfClouds' [#6937](https://github.com/CrocSwap/integer-mult-bounds/pull/6937), +head `a98df73ddae1d1ea85a62b6bdf2714b28cb7b359`, +`research/p104-two-chain-findings/data/caller_efree.json` (Git blob +`5a71ca9f80ced1aeb8a68e97516cab52eb72a52a`). The unchanged local native word +is from [#6936](https://github.com/CrocSwap/integer-mult-bounds/pull/6936), +head `03626137d0bd57f09b0bf9597376183ce6fa9683`. + +The E-free root and caller are entirely DreamingOfClouds' work. Its README +reports a QUERY-only gadget with a projected cost loss, while saying the +whole QUERY-only caller was not built. The preceding public package +`CubeJerry/integer-mult-bounds@4e2fd1b6abed49c202a057fd5c73ead0a460f976`, +`research/p104-qself-owned-lowering`, supplies the reproducible formal caller +certificate and an owned QSELF expansion with an explicitly uninstalled new +token registry. Its single-QSELF determinant obstruction expressly leaves +paired source synthesis open. This package supplies a different result: a +whole actual separated interval replacement with the same paid profile and +only existing caller operations. It does not rerun or extend that obstruction. + +**Theorem.** Let Q,D_1,...,D_18 be commuting operators on any complex vector +space V, with Q^4=I. Interpret the exact pinned caller with its stated scalar, +QUERY, LAMBDA, IDLE_ONE and joint-contact semantics. Replace zero-based events +457 through 575 inclusive by the 223 events emitted by `replacement.py`. +The resulting 3,095-event caller has exactly the same operator on all 76 +independent inputs. It has no QSELF event. The replaced interval uses exactly +three QUERY(-1) events, the same number of rank-one jobs as its former two +QSELF(-1) events and one QUERY(-1). It uses the same public roles and no new +owned role, arbitrary helper, productive credit, or operation type. + +This theorem includes all input columns and absolute coefficients in the +commutative operator model. It does not assert success on the same finite +signed or rounded inputs, install a physical compiler/service binding, or +prove the retained scalar and routing rates. Those are separate obligations. + +## 2. A three-query identity on four arbitrary fields + +Work first in R=Q(i)[q]/(q^4-1). Put x=q^-1 and t=x^2=q^2, so t^2=1 and +x^-1=t*x. The source's actual phase units are + + lambda_s = ((1+s*i)+(1-s*i)*q^2)/2, s in {+1,-1}. + +They satisfy lambda_+*lambda_-=1 and lambda_+^2=lambda_-^2=t. They are +**units, not the projection (1+q^2)/2**. No inverse of a projection or of any +D variable is used anywhere below. + +For four arbitrary independent fields (a,b,c,d), perform the invertible +q-even preprocessing + + (w1,w2,w3,w4) = (c, a+d, b+t*c, t*d). + +Then perform exactly three generalized query shears in this order: + + w1 <- w1 + x*w2; + w2 <- w2 + x*(w3-t*w1); + w3 <- w3 + x*(w4-t*w2). + +Each query is one literal QUERY(-1). Its indicated source is made by an even +ADD into the other existing public field, then restored after the query. +The query destination differs from that source, so restoring the source +does not undo the update. Multiplication by t uses two source LAMBDA(+1) +events. A temporary t scaling is undone by two LAMBDA(-1) events. These +scans and field transformations are charged; they are not a free oracle. + +After these three steps direct substitution gives + + w1 = c+x*(a+d), + w2 = x*b, + w3 = t*c+t*x*d, + w4 = t*d. + +The even postprocessing + + (w1-t*w3, w2, t*w3, t*w4) + +therefore returns exactly + + (x*a, x*b, c+x*d, d). + +The gadget is a genuine four-input map. In particular d is arbitrary and +restored, and c is arbitrary and receives the prescribed shear. No field is +assumed zero. The emitted word uses 38 existing events: three QUERYs, +26 LAMBDAs, seven ADDs and two SWAPs. The inverse even basis exists over the +entire quotient ring, including q=+/-i. The exact local matrix certificate +checks every coefficient, and a separate unit-basis round trip detects loss +of either q^2 sector. + +## 3. Why that gadget replaces the actual separated sites + +Use column-vector convention: later operations multiply on the left. Let +S_0 multiply role0 by x, S_19 multiply role19 by x, and let +U=I+x*e0*e1^T be the actual QUERY at event495. Partition the intervening +even source events exactly as follows: + +| Block | Zero-based source events | Roles | Content | +| --- | --- | --- | --- | +| E1 | 458..494 | 0..18 | Invertible ADD/SCALE/LAMBDA prefix | +| E2 | 496..544 | 0..18 | Invertible ADD/SCALE/SWAP/LAMBDA suffix | +| B | 545..574 | 19..37 | Other chain prefix, including IDLE_ONE(28,[9]) | + +The original complete interval is the matrix S_19 B E2 U E1 S_0. +Every operation in B has support disjoint from every first-chain operation. +Thus B may move to the right of all first-chain factors, and S_19 may move +leftward across first-chain factors. We obtain + + E2 E1 (E1^-1 U E1) S_0 S_19 B. + +**B is never inverted.** Its IDLE_ONE multiplies by the unrestricted formal +D9 and may be noninvertible. It moves only across disjoint role supports. +E1 alone is conjugated, and its scalar factors are units. + +Let + + s = e1+...+e18, + w = sum_{k=1}^{18} (-1)^k e_k^T, + lambda = lambda_+. + +Then w*s=0 and w*e0=w*e19=0. Reading the actual E1 events gives + + E1^-1 e0 = lambda*(-e0+s), e1^T E1 = w. + +For example, E1 sends role0 to -lambda_- times its old value, sends each +rolek for 2<=k<=18 to old rolek+old role0, and sends role1 to w applied to +the old roles. Solving E1 v=e0 gives the displayed inverse column; this does +not infer a source relation from a finite input probe. Hence + + E1^-1 U E1 = I + x*lambda*(s-e0)*w. + +Writing S=S_0 S_19, the three paid source operations reduce to + + (E1^-1 U E1) S + = S (I+x*lambda*s*w) (I-lambda*e0*w). + +All cross terms vanish because w kills s,e0,e19. This is the source-specific +correction missed by treating the two QSELF sites as an adjacent pair. +The original QUERY contributes the nontrivial independent shear along s. + +Now change the first-chain coordinates using only existing even events. +Subtract role1 from each role2..18. Into role2 add (-1)^k times rolek for +k=3..18, then apply LAMBDA(+1) to role2. The new coordinates include + + c = old role1, + d = lambda*w(old roles). + +The other residual roles retain all remaining independent input information. +The inverse first applies LAMBDA(-1) to role2, undoes its signed sum, and +adds the new role1 into roles2..18. Increasing c in these coordinates +increases every original role1..18 by the same amount: its direction is s. + +Call this invertible coordinate map P^-1. Its two emitted directions each +cost 34 events. In coordinates (a,b,c,d)=(role0,role19,role1,role2), the +factor I-lambda*e0*w is simply ADD(0,2,-1). The factor +S(I+x*lambda*s*w) is exactly the four-field map in section2. + +The complete replacement is therefore, chronologically: + + B; P^-1; ADD(0,2,-1); THREE_QUERIES; P; E1; E2. + +Its event count is 30+34+1+38+34+37+49=223. All source events before457 and +after575 remain byte-for-byte equal as parsed records. This construction +replaces the whole separated interval, not merely a same-cut subexpression. + +## 4. Formal certificates and failure detection + +`interval_certificate.py` is a separate exact sparse-matrix implementation. +It starts with 38 independent interval input generators. Coefficients are +Gaussian rationals, q exponents are reduced only modulo4, and D monomials +are sorted tuples with repetitions retained. The complete two interval +matrices agree in all 180 nonzero endpoint entries. The interval uses D9, +but never specializes it or assumes its inverse or idempotence. + +The full generated caller is also replayed by the unchanged public forward +certificate over Q(i)[q,D1,...,D18]/(q^4-1). All 18 D variables remain +formal and all 76 input generators remain independent. It returns the same +76 diagonal monomials as the source. A different unchanged backward-covector +checker uses integer dyadics at q=1,i,-1,-i, with D variables still formal. +Evaluation at all four distinct fourth roots is injective coefficientwise +on this quotient, so these checks are faithful operator certificates, not +sampled D or sampled field-value experiments. + +The newly supplied interval arithmetic imports none of those predecessor +arithmetic routines. The reused forward and backward engines are credited; +replaying either alone would be regression evidence, not a new independent +implementation. The proof above derives the identity without their code. + +Controls change a query orientation, delete one query, omit the source +conjugation correction, break a t scaling/restoration, repeat D9, contaminate +another independent input, replace lambda with a projection, and remove the +q^4 relation by working modulo q^8-1. Each changes the exact interval matrix. +These controls do not prove minimality of three queries or a general lower +bound for another word. + +Induction over the exact source semantics proves that each matrix entry is +the indicated formal coefficient. A homomorphism into the commuting operator +algebra generated by Q,D maps the identity to every V and every collection +of input fields. No dimension bound, sampled numerical values, or rounded +input assumptions enter that exact theorem. + +## 5. Complete recursive profile and positive ordinary invoice + +Each A event occurs at 96 actual ports. The replacement deletes 192 QSELF +instances, adds 192 QUERY instances, and leaves the former QUERY instances +in the total paid count. Across the full caller, the source has 224 QUERYs +plus 192 QSELFs; the new caller has 416 QUERYs and zero QSELFs. All queries +here have exponent -1, so both complete frame conversions and the return +translation have the same inherited charge per job. + +The 18 local native words, their 400 actual main fields per call, and their +1,061 fresh arbitrary helper fields per call are unchanged. The caller still +has 3,952 actual A/B main inputs and 19,098 fresh local helpers. The root +targets are unchanged, with no empty-mask E input restored or credited. +For every rank r, T_new(r)=T_source(r) and P_new(r)=P_source(r). Thus every +signed target/paid moment agrees identically as a function of kappa. The +complete totals remain T=23,050, P=117,846; surplus=1,520; paid rank mass=317,324. + +No public role is newly allocated. The temporary linear sources in section2 +use already live roles and are restored by ordinary invertible operations. +The existing QUERY contract still needs its copied owned bank and completed +query lifecycle. Three serial query jobs can reuse its fixed inventory; there +are 416 outer query lifetimes overall, the same total as QUERY plus owned +QSELF lifetimes in the baseline. No uninitialized or arbitrary helper is +treated as zero, and no productive target is claimed for query scratch. +All private native workspace, historical backing and parked ancestors remain +charged by the inherited QUERY/LAMBDA/scalar interfaces. + +Under the **inherited scalar/routing convention**, the extra 104 A events +cost 104*32*38*96=12,140,544 units. The extra 28 A LAMBDAs receive the +separate conservative charge 28*1,000*96=2,688,000. The eliminated owned +QSELF-specific macro surcharge is 192*128=24,576. Every other term remains. + +| Complete conditional invoice | QSELF baseline | QUERY-only caller | +| --- | ---: | ---: | +| Reviewed raw ordinary upper | 796,934,944 | 809,050,912 | +| Separate LAMBDA reading | 11,792,000 | 14,480,000 | +| Per-call 1125 conversion reading | 2,734,992 | 2,734,992 | +| All displayed readings included | 811,461,936 | 826,265,904 | +| Margin below inherited 10^9 cap | 188,538,064 | 173,734,096 | + +`complete_invoice.py` reconstructs the unchanged local word and both caller +profiles and checks each changed term. These are conditional scalar/pass +counts, not a new proof of the complete bit-tape tariff. Increased arithmetic +length, temporary coefficients and cross-chain intermediate values require +fresh rounding, signed-width, common-grid and source-placement bounds. There +is no claimed improvement to the accepted kappa or unconditional theorem. + +## 6. Remaining obligations and credit + +The substitution removes the need for a new abstract QSELF operation in this +exact proposed caller. It does not prove arbitrary-Q synthesis: the gadget +and actual source phase algebra use Q^4=I. It neither changes the selected +certificate nor discharges all native_all_columns, owned_erasure, compiler, +precision_tape or analytic_recovery premises. + +Before physical supplier use, regenerate the actual compiler records and +bind the new source occurrences to the existing QUERY, LAMBDA and scalar +providers; prove matching formats and all intermediate signed admission; +reprice complete bit-tape work and historical backing; and propagate errors +through the changed order and additional even operations. Existing opcode +semantics alone do not install an exact source-specific service registry. + +DreamingOfClouds receives credit for #6936/#6937, the E-free construction and +prior QUERY-only feasibility suggestion. The public owned-lowering package +receives credit for the prior formal engines, exact semantics/source pins and +full invoice baseline. Its underlying native, caller, compiler and physical +predecessors retain their attribution. The three-query four-input identity, +its exact separated-source reduction, emitted whole caller and new interval +certificate were prepared for @CubeJerry with substantial OpenAI assistance. + +## Open next questions + +1. Can the regenerated caller satisfy the actual common-format and rounded + QUERY/LAMBDA contracts at this interval? Start with its 223 new intermediate + coefficient rows and the actual source compiler; exact operator equality + does not establish headroom or an error budget. +2. Can the 28 added LAMBDA occurrences be reduced without increasing the paid + profile or changing arbitrary-input restoration? Preserve this complete + verified source as the baseline; an isolated two-register identity is + insufficient. This optimization is outside the present bounded task. +3. Can the resulting existing-op caller be admitted with all native/owned + dependencies and a complete bit-tape certificate? The inherited tariff, + literal source registry and universal proof assumptions remain blockers. diff --git a/research/p104-query-interval-optimum/review/RESULT.json b/research/p104-query-interval-optimum/review/RESULT.json new file mode 100644 index 0000000000..68af5de565 --- /dev/null +++ b/research/p104-query-interval-optimum/review/RESULT.json @@ -0,0 +1,335 @@ +{ + "all_six_attainment_covectors_match": true, + "attainment_git_blob": "cf55f4271009a06ad192a070d330a4466b6d44fa", + "attainment_opcodes": { + "ADD": 162, + "IDLE_ONE": 1, + "LAMBDA": 32, + "QUERY": 3, + "SCALE": 5, + "SWAP": 20 + }, + "credit": "Separate shared-context AI review for @CubeJerry; no human or proof-kernel independence claimed.", + "deleted_query_controls": [ + { + "determinant": "0", + "local_index": 0, + "minor": [ + [ + "0", + "-4", + "0" + ], + [ + "0", + "-2", + "0" + ], + [ + "0", + "0", + "2" + ] + ], + "operation": [ + "A", + "QSELF", + 0, + -1 + ], + "word": "original" + }, + { + "determinant": "0", + "local_index": 38, + "minor": [ + [ + "-2", + "0", + "0" + ], + [ + "0", + "0", + "0" + ], + [ + "0", + "0", + "2" + ] + ], + "operation": [ + "A", + "QUERY", + 0, + 1, + -1 + ], + "word": "original" + }, + { + "determinant": "0", + "local_index": 118, + "minor": [ + [ + "-2", + "-4", + "0" + ], + [ + "0", + "-2", + "0" + ], + [ + "0", + "0", + "0" + ] + ], + "operation": [ + "A", + "QSELF", + 19, + -1 + ], + "word": "original" + }, + { + "determinant": "0", + "local_index": 75, + "minor": [ + [ + "-4", + "-4", + "0" + ], + [ + "-2", + "-2", + "0" + ], + [ + "0", + "0", + "2" + ] + ], + "operation": [ + "A", + "QUERY", + 0, + 19, + -1 + ], + "word": "attainment" + }, + { + "determinant": "0", + "local_index": 81, + "minor": [ + [ + "-6", + "-4", + "0" + ], + [ + "-2", + "-2", + "0" + ], + [ + "0", + "0", + "0" + ] + ], + "operation": [ + "A", + "QUERY", + 19, + 1, + -1 + ], + "word": "attainment" + }, + { + "determinant": "0", + "local_index": 92, + "minor": [ + [ + "-2", + "0", + "0" + ], + [ + "0", + "0", + "0" + ], + [ + "0", + "0", + "2" + ] + ], + "operation": [ + "A", + "QUERY", + 1, + 2, + -1 + ], + "word": "attainment" + } + ], + "determinant": "8", + "full_response_covectors": [ + { + "0": "-2", + "1": "-4", + "10": "4", + "11": "-4", + "12": "4", + "13": "-4", + "14": "4", + "15": "-4", + "16": "4", + "17": "-4", + "18": "4", + "2": "4", + "3": "-4", + "4": "4", + "5": "-4", + "6": "4", + "7": "-4", + "8": "4", + "9": "-4" + }, + { + "1": "-2", + "10": "2", + "11": "-2", + "12": "2", + "13": "-2", + "14": "2", + "15": "-2", + "16": "2", + "17": "-2", + "18": "2", + "2": "2", + "3": "-2", + "4": "2", + "5": "-2", + "6": "2", + "7": "-2", + "8": "2", + "9": "-2" + }, + { + "19": "2" + } + ], + "inputs": [ + 0, + 1, + 19 + ], + "interval_start": 457, + "interval_stop_exclusive": 576, + "minor": [ + [ + "-2", + "-4", + "0" + ], + [ + "0", + "-2", + "0" + ], + [ + "0", + "0", + "2" + ] + ], + "minus_covectors": [ + { + "0": "1", + "1": "4", + "10": "-3", + "11": "4", + "12": "-4", + "13": "4", + "14": "-4", + "15": "4", + "16": "-4", + "17": "4", + "18": "-4", + "2": "-4", + "3": "4", + "4": "-4", + "5": "4", + "6": "-4", + "7": "4", + "8": "-4", + "9": "4" + }, + { + "1": "2", + "10": "-1", + "11": "2", + "12": "-2", + "13": "2", + "14": "-2", + "15": "2", + "16": "-2", + "17": "2", + "18": "-2", + "2": "-2", + "3": "2", + "4": "-2", + "5": "2", + "6": "-2", + "7": "2", + "8": "-2", + "9": "2" + }, + { + "19": "-1" + } + ], + "original_opcodes": { + "ADD": 88, + "IDLE_ONE": 1, + "LAMBDA": 4, + "QSELF": 2, + "QUERY": 1, + "SCALE": 5, + "SWAP": 18 + }, + "outputs": [ + 0, + 1, + 19 + ], + "plus_covectors": [ + { + "0": "-1", + "10": "1" + }, + { + "10": "1" + }, + { + "19": "1" + } + ], + "replacement_stop_exclusive": 680, + "scope": "Exact reverse-covector source check, not a full formal replacement identity or physical admission.", + "source_git_blob": "5a71ca9f80ced1aeb8a68e97516cab52eb72a52a", + "source_sha256": "c5b6c5236462ae84e5431a791a2f8ce795774342f13e11c4af35689092a8af30", + "specialization": "q=+1 and q=-1, D9=1; all other D_j absent from interval" +} diff --git a/research/p104-query-interval-optimum/review/REVIEW.md b/research/p104-query-interval-optimum/review/REVIEW.md new file mode 100644 index 0000000000..d646173bc6 --- /dev/null +++ b/research/p104-query-interval-optimum/review/REVIEW.md @@ -0,0 +1,83 @@ +# Independent fixed-interval response-rank audit + +Prepared for @CubeJerry with substantial OpenAI assistance. This is a separate +shared-context AI check, not human review or proof-kernel admission. + +## Actual source check + +`check_covectors.py` imports no predecessor evaluator or matrix routine. It +authenticates the original #6937 source blob +`5a71ca9f80ced1aeb8a68e97516cab52eb72a52a` at commit +`a98df73ddae1d1ea85a62b6bdf2714b28cb7b359`, and the attainment blob +`cf55f4271009a06ad192a070d330a4466b6d44fa` at public commit +`617903497387a98f7ca929ad0b6928dd32abffec`. It applies literal transposed +operations in reverse order to output covectors 0, 1 and 19, keeping all 76 +input coordinates and using exact rational arithmetic. + +For the exact original events `[457:576]`, its response at q=+1 minus q=-1, +with D9=1, has the claimed rows/columns 0,1,19 minor + +``` +[-2 -4 0] +[ 0 -2 0] +[ 0 0 2] +``` + +with determinant 8. LAMBDA specializes to 1 at both signs directly from +its even polynomial; the interval's only IDLE_ONE contains D9. No other +D_j is specialized or occurs in this interval. The replacement has exactly +223 rows, leaves both external event segments unchanged, contains exactly +three QUERY operations, and has no QSELF. All six complete reverse covectors +agree at these two specializations. This finite two-point comparison is not +a substitute for the predecessor's formal replacement-identity proof. + +Deleting each of the three charged original sites or each of the three +attainment queries makes this response minor singular: six negative controls. +Normal and optimized Python runs both passed and produced identical receipts. + +## Mathematical scope review + +Let the chosen full finite state include every auxiliary register and one +homogeneous constant coordinate. Every fixed affine instruction is then a +linear map on that state. The initial embedding and output extraction are +the same at both evaluations by premise; they may have arbitrary rank. +If a fixed finite instruction stream changes register dimensions, padding +all registers to their finite union gives the same conclusion without any +invertibility assumption. + +At the two legal evaluations, a charged rank-one QUERY has matrix difference +of rank at most one. The same holds for an even-conjugated version because +its two surrounding free matrices agree at the evaluations. The telescoping +identity for the difference of the two whole matrix products is a sum of +one term per charged site; each term has rank at most one after all prefix, +suffix, initialization and extraction maps. Therefore the response rank is +at most the number of queries. Copy, erase, auxiliary initialization and +noninvertible maps do not invalidate this argument. The exhibited determinant +8 proves at least three queries in this model over characteristic zero. + +The declared coefficient ring Q(i)[q,D1,...,D18]/(q^4-1), with no additional +q/D relations and all free denominators regular at both signs, makes both +evaluations legitimate. The claim must retain the following restrictions: +independent inputs at the fixed interval boundary; fixed, data-independent +linear/affine control; identical free initialization and extraction at both +signs; no free odd-q side information; and rank-one charged operations on +the entire chosen state, rather than an unpriced wider payload operation. +A reachable-input subspace, nonlinear or adaptive coefficient generation, +changed endpoints, or extra relations excluding a sign could defeat this +particular lower bound and are outside the statement. There is no issue +with q^4-1 having multiple components: the proof uses two lawful evaluations +into Q(i), not a rank calculation over the quotient ring itself. + +The rank argument is classical. The new source-specific fact is the exact +minor, and hence three-query optimality for this interval in the stated +model together with the separately proved three-query attainment. + +## Reproduction + +```sh +python3 -I -B check_covectors.py /path/to/research/p104-query-only-interval +python3 -I -O -B check_covectors.py /path/to/research/p104-query-only-interval +``` + +Expected: the exact JSON receipt in `RESULT.json`; determinant `8`, all six +attainment covectors equal, and all six deleted-site determinants `0`. diff --git a/research/p104-query-interval-optimum/review/check_covectors.py b/research/p104-query-interval-optimum/review/check_covectors.py new file mode 100644 index 0000000000..cb156f6c66 --- /dev/null +++ b/research/p104-query-interval-optimum/review/check_covectors.py @@ -0,0 +1,131 @@ +"""Independent exact reverse-covector check of the fixed 457..575 interval. + +Prepared for @CubeJerry with substantial OpenAI assistance. Apache-2.0. +No source evaluator or matrix arithmetic is imported from either predecessor. +""" +from collections import Counter +from fractions import Fraction +from hashlib import sha1, sha256 +import json +from pathlib import Path +import sys + + +SOURCE_SHA = "c5b6c5236462ae84e5431a791a2f8ce795774342f13e11c4af35689092a8af30" +ORIGINAL_BLOB = "5a71ca9f80ced1aeb8a68e97516cab52eb72a52a" +NEW_BLOB = "cf55f4271009a06ad192a070d330a4466b6d44fa" +ROWS = (0, 1, 19) + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def git_blob(data): + return sha1(b"blob " + str(len(data)).encode() + b"\0" + data).hexdigest() + + +def pullback(events, output, q, roles): + """Apply the transpose of each literal map in reverse chronological order. + + LAMBDA_s=(1+s*i)/2 + (1-s*i)*q^2/2 specializes to 1 at either sign. + The only IDLE_ONE in the interval is D9, specialized to 1. There is + no assumption on the other D_j and none occurs in this interval. + """ + require(q in (-1, 1), "two legal sign specializations") + cov = [Fraction(0) for _ in range(roles)] + cov[output] = Fraction(1) + for row in reversed(events): + require(row[0] == "A", "fixed interval has only A operations") + op, d = row[1:3] + if op in ("ADD", "QUERY"): + s, c = row[3:5] + c = Fraction(c) if op == "ADD" else Fraction(q if c % 2 else 1) + old_dest = cov[d] + cov[s] += c * old_dest + elif op == "SCALE": + cov[d] *= Fraction(row[3]) + elif op == "QSELF": + cov[d] *= q if row[3] % 2 else 1 + elif op == "SWAP": + s = row[3] + cov[d], cov[s] = cov[s], cov[d] + elif op == "LAMBDA": + require(row[3] in (-1, 1), "literal lambda sign") + elif op == "IDLE_ONE": + require(row[3] == [9], "only D9 is specialized") + else: + raise ValueError("unexpected interval operation " + op) + return cov + + +def determinant3(m): + a, b, c = m + return (a[0]*(b[1]*c[2]-b[2]*c[1]) + - a[1]*(b[0]*c[2]-b[2]*c[0]) + + a[2]*(b[0]*c[1]-b[1]*c[0])) + + +def response(events, roles): + plus = [pullback(events, row, 1, roles) for row in ROWS] + minus = [pullback(events, row, -1, roles) for row in ROWS] + delta = [[a-b for a,b in zip(p,m)] for p,m in zip(plus,minus)] + minor = [[row[col] for col in ROWS] for row in delta] + return plus, minus, delta, minor + + +def sparse(cov): + return {str(i): str(x) for i,x in enumerate(cov) if x} + + +def main(folder): + old_bytes = (folder/"data/caller_efree.json").read_bytes() + new_bytes = (folder/"QUERY-ONLY-CALLER.json").read_bytes() + require(sha256(old_bytes).hexdigest() == SOURCE_SHA, "exact original SHA256") + require(git_blob(old_bytes) == ORIGINAL_BLOB, "exact original Git blob") + require(git_blob(new_bytes) == NEW_BLOB, "exact public attainment Git blob") + old = json.loads(old_bytes); new = json.loads(new_bytes) + require(old["roles"] == new["roles"] == 76, "complete public role inventory") + before = old["events"][457:576] + require(len(before) == 119 and before[0] == ["A", "QSELF", 0, -1] + and before[-1] == ["A", "QSELF", 19, -1], "original exact endpoints") + after = new["events"][457:680] + require(len(after) == 223 and old["events"][:457] == new["events"][:457] + and old["events"][576:] == new["events"][680:], "same replacement boundaries") + require(Counter(e[1] for e in after)["QUERY"] == 3 + and not any(e[1] == "QSELF" for e in after), "attainment uses three literal queries") + plus, minus, delta, minor = response(before, 76) + require(minor == [[-2,-4,0],[0,-2,0],[0,0,2]] and determinant3(minor) == 8, + "nonzero actual response minor") + new_plus, new_minus, _, new_minor = response(after, 76) + require((plus, minus, minor) == (new_plus, new_minus, new_minor), + "all six complete covectors agree with the public attainment") + controls = [] + for label, word, charged in (("original", before, ("QSELF","QUERY")), + ("attainment", after, ("QUERY",))): + for index,row in enumerate(word): + if row[1] in charged: + changed = word[:index]+word[index+1:] + mutated_minor = response(changed, 76)[3] + require(determinant3(mutated_minor) == 0, "deleted charged site loses rank-three witness") + controls.append(dict(word=label, local_index=index, operation=row, + minor=[[str(x) for x in r] for r in mutated_minor], determinant="0")) + result = dict( + source_sha256=SOURCE_SHA, source_git_blob=ORIGINAL_BLOB, + attainment_git_blob=NEW_BLOB, interval_start=457, interval_stop_exclusive=576, + replacement_stop_exclusive=680, outputs=list(ROWS), inputs=list(ROWS), + specialization="q=+1 and q=-1, D9=1; all other D_j absent from interval", + plus_covectors=[sparse(v) for v in plus], minus_covectors=[sparse(v) for v in minus], + full_response_covectors=[sparse(v) for v in delta], + minor=[[str(x) for x in row] for row in minor], determinant="8", + original_opcodes=dict(Counter(e[1] for e in before)), + attainment_opcodes=dict(Counter(e[1] for e in after)), + all_six_attainment_covectors_match=True, deleted_query_controls=controls, + scope="Exact reverse-covector source check, not a full formal replacement identity or physical admission.", + credit="Separate shared-context AI review for @CubeJerry; no human or proof-kernel independence claimed.") + print(json.dumps(result, indent=2, sort_keys=True)) + + +if __name__ == "__main__": + main(Path(sys.argv[1])) diff --git a/research/p104-query-interval-optimum/verify.py b/research/p104-query-interval-optimum/verify.py new file mode 100644 index 0000000000..9c065921c1 --- /dev/null +++ b/research/p104-query-interval-optimum/verify.py @@ -0,0 +1,166 @@ +"""Exact forward response certificate for one pinned source interval. + +Prepared for @CubeJerry with substantial OpenAI assistance. Apache-2.0. +No predecessor emitter, evaluator or matrix routine is imported. +""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha1, sha256 +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +PIVOTS = (0, 1, 19) + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def authenticate(): + entries = json.loads((HERE / "DEPENDENCIES.json").read_text())["files"] + for entry in entries: + data = (ROOT / entry["path"]).read_bytes() + require(sha256(data).hexdigest() == entry["sha256"], "dependency SHA256") + blob = sha1(b"blob " + str(len(data)).encode() + b"\0" + data).hexdigest() + require(blob == entry["git_blob"], "dependency Git blob") + return len(entries) + + +def identity(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def evaluate(events, sign, roles=76): + """Propagate every independent input column, at q=sign and D9=1.""" + require(sign in (-1, 1), "legal sign") + rows = identity(roles) + for event in events: + require(event[0] == "A", "only A-chain operations in this interval") + op, dest = event[1:3] + require(0 <= dest < 38, "original A role range") + if op in ("ADD", "QUERY"): + source, coefficient = event[3:5] + require(0 <= source < 38 and source != dest, "distinct original roles") + c = F(coefficient) if op == "ADD" else F(sign if coefficient % 2 else 1) + rows[dest] = [a + c*b for a, b in zip(rows[dest], rows[source])] + elif op == "SWAP": + source = event[3] + require(0 <= source < 38, "swap source") + rows[dest], rows[source] = rows[source], rows[dest] + elif op == "SCALE": + rows[dest] = [F(event[3])*a for a in rows[dest]] + elif op == "QSELF": + c = sign if event[3] % 2 else 1 + rows[dest] = [c*a for a in rows[dest]] + elif op == "LAMBDA": + require(event[3] in (-1, 1), "literal lambda sign") + # ((1+s*i)+(1-s*i)*q^2)/2 = 1 at either q sign. + elif op == "IDLE_ONE": + require(event[3] == [9], "only the unconstrained formal D9 occurs") + else: + raise ValueError("unhandled source operation " + op) + return rows + + +def difference(a, b): + return [[x-y for x, y in zip(r, s)] for r, s in zip(a, b)] + + +def rank(matrix): + rows = [row[:] for row in matrix] + pivot = 0 + for col in range(len(rows[0])): + chosen = next((i for i in range(pivot, len(rows)) if rows[i][col]), None) + if chosen is None: + continue + rows[pivot], rows[chosen] = rows[chosen], rows[pivot] + d = rows[pivot][col] + rows[pivot] = [x/d for x in rows[pivot]] + for i in range(pivot+1, len(rows)): + c = rows[i][col] + if c: + rows[i] = [a-c*b for a, b in zip(rows[i], rows[pivot])] + pivot += 1 + if pivot == len(rows): + break + return pivot + + +def determinant3(m): + a, b, c = m + return (a[0]*(b[1]*c[2]-b[2]*c[1]) + - a[1]*(b[0]*c[2]-b[2]*c[0]) + + a[2]*(b[0]*c[1]-b[1]*c[0])) + + +def response(word): + return difference(evaluate(word, 1), evaluate(word, -1)) + + +def main(): + authenticated = authenticate() + old = json.loads((HERE / "data/caller_efree.json").read_text()) + new = json.loads((HERE / "QUERY-ONLY-CALLER.json").read_text()) + require(old["roles"] == new["roles"] == 76, "independent complete role inventory") + before, after = old["events"][457:576], new["events"][457:680] + require(len(old["events"]) == 2991 and len(new["events"]) == 3095, "whole source sizes") + require(len(before) == 119 and len(after) == 223, "fixed interval sizes") + require(before[0] == ["A", "QSELF", 0, -1] + and before[-1] == ["A", "QSELF", 19, -1], "exact source endpoints") + require(old["events"][:457] == new["events"][:457] + and old["events"][576:] == new["events"][680:], "unchanged enclosing event segments") + for word in (before, after): + require(sum(e[1] == "IDLE_ONE" for e in word) == 1, "one formal D9 operation") + counts = [Counter(e[1] for e in word) for word in (before, after)] + require(counts[0]["QSELF"] == 2 and counts[0]["QUERY"] == 1, "old charged sites") + require(counts[1]["QUERY"] == 3 and counts[1]["QSELF"] == 0, "prior three-query attainment") + delta = response(before) + minor = [[delta[i][j] for j in PIVOTS] for i in PIVOTS] + require(minor == [[-2, -4, 0], [0, -2, 0], [0, 0, 2]], "actual source minor") + require(determinant3(minor) == 8 and rank(delta) == 3, "exact response rank") + for sign in (-1, 1): + require(evaluate(before, sign) == evaluate(after, sign), "complete two-point attainment check") + controls = [] + for name, word, charged in (("source", before, {"QUERY", "QSELF"}), + ("attainment", after, {"QUERY"})): + for index, event in enumerate(word): + if event[1] in charged: + r = rank(response(word[:index]+word[index+1:])) + require(r <= 2, "deleted paid site must lose response rank three") + controls.append({"word": name, "local_index": index, "response_rank": r}) + require(len(controls) == 6, "all charged-site controls executed") + # These boundary examples explain why the theorem retains its premises. + require(rank([[delta[i][j] for j in (2, 3)] for i in range(76)]) <= 2, + "two-input restriction cannot prove a three-query bound") + require(rank([[F(2 if i == j else 0) for j in range(3)] for i in range(3)]) == 3, + "free odd-q diagonal would defeat the even-map premise") + result = { + "status": "PASS_P104_QUERY_INTERVAL_OPTIMUM", + "dependencies_authenticated": authenticated, + "independent_inputs": 76, + "source_interval": [457, 576], + "attainment_interval": [457, 680], + "source_rows": 119, + "attainment_rows": 223, + "source_opcodes": dict(counts[0]), + "attainment_opcodes": dict(counts[1]), + "response_rank": 3, + "minor_rows_and_columns": list(PIVOTS), + "minor": [[str(x) for x in row] for row in minor], + "minor_determinant": "8", + "nonzero_response_entries": sum(bool(x) for row in delta for x in row), + "complete_character_comparisons": 2, + "deleted_site_controls": controls, + "scope_controls": ["independent-input subspace restriction", "free odd-q coefficients forbidden"], + "attainment_scope": "Full formal identity is the pinned predecessor theorem; two-point checking alone is insufficient.", + "lower_bound_scope": "Written telescoping proof plus exact finite source minor; no physical or whole-caller optimality.", + "no_new_kappa": True, + } + print(json.dumps(result, sort_keys=True, indent=2)) + + +if __name__ == "__main__": + main()