From 64fd5f9e91961dedc16118fcc7ad71ee82efe28f Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Tue, 13 Oct 2026 18:10:44 -0500 Subject: [PATCH] Research: certify P112 rank-six frame coverage and sharp bill60 relaxation --- research/p112-rank6-frame-coverage/CLAIM.json | 43 + .../p112-rank6-frame-coverage/COVERING.json | 77 + .../DIAGONAL-SEARCH.json | 18 + research/p112-rank6-frame-coverage/LICENSE | 201 + .../p112-rank6-frame-coverage/OVERLAP.json | 62 + research/p112-rank6-frame-coverage/PROOF.md | 181 + research/p112-rank6-frame-coverage/README.md | 129 + .../p112-rank6-frame-coverage/SEARCH.json | 69 + .../p112-rank6-frame-coverage/SOURCES.json | 54 + research/p112-rank6-frame-coverage/TASK.json | 60 + .../p112-rank6-frame-coverage/VALIDATION.json | 30 + .../p112-rank6-frame-coverage/VERIFY.json | 47 + research/p112-rank6-frame-coverage/engine.py | 229 + .../generated/CERTIFICATE.json | 144 + .../generated/COVERAGE.jsonl | 7616 +++++++++++++++++ .../p112-rank6-frame-coverage/independent.py | 231 + .../inputs/PR1226-NOTICE.md | 21 + .../inputs/PR1323-CERTIFICATE.json | 110 + .../inputs/PR1323-MODEL.json | 1328 +++ .../p112-rank6-frame-coverage/search_cover.py | 110 + .../p112-rank6-frame-coverage/test_package.py | 142 + research/p112-rank6-frame-coverage/verify.py | 58 + 22 files changed, 10960 insertions(+) create mode 100644 research/p112-rank6-frame-coverage/CLAIM.json create mode 100644 research/p112-rank6-frame-coverage/COVERING.json create mode 100644 research/p112-rank6-frame-coverage/DIAGONAL-SEARCH.json create mode 100644 research/p112-rank6-frame-coverage/LICENSE create mode 100644 research/p112-rank6-frame-coverage/OVERLAP.json create mode 100644 research/p112-rank6-frame-coverage/PROOF.md create mode 100644 research/p112-rank6-frame-coverage/README.md create mode 100644 research/p112-rank6-frame-coverage/SEARCH.json create mode 100644 research/p112-rank6-frame-coverage/SOURCES.json create mode 100644 research/p112-rank6-frame-coverage/TASK.json create mode 100644 research/p112-rank6-frame-coverage/VALIDATION.json create mode 100644 research/p112-rank6-frame-coverage/VERIFY.json create mode 100644 research/p112-rank6-frame-coverage/engine.py create mode 100644 research/p112-rank6-frame-coverage/generated/CERTIFICATE.json create mode 100644 research/p112-rank6-frame-coverage/generated/COVERAGE.jsonl create mode 100644 research/p112-rank6-frame-coverage/independent.py create mode 100644 research/p112-rank6-frame-coverage/inputs/PR1226-NOTICE.md create mode 100644 research/p112-rank6-frame-coverage/inputs/PR1323-CERTIFICATE.json create mode 100644 research/p112-rank6-frame-coverage/inputs/PR1323-MODEL.json create mode 100644 research/p112-rank6-frame-coverage/search_cover.py create mode 100644 research/p112-rank6-frame-coverage/test_package.py create mode 100644 research/p112-rank6-frame-coverage/verify.py diff --git a/research/p112-rank6-frame-coverage/CLAIM.json b/research/p112-rank6-frame-coverage/CLAIM.json new file mode 100644 index 0000000000..eece3b76d4 --- /dev/null +++ b/research/p112-rank6-frame-coverage/CLAIM.json @@ -0,0 +1,43 @@ +{ + "seed": 20, + "track": "complex supplier", + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "start_utc": "2026-10-13T22:44:49Z", + "expected_finish_utc": "2026-10-13T23:44:49Z", + "verification_reserve_start_utc": "2026-10-13T23:29:49Z", + "predecessor": { + "pr": 1323, + "head": "c1144855242a56ffc1090be2f075f977d123d947" + }, + "candidates": [ + { + "object": "Selected k8 helper boundary donor census", + "disposition": "Active overlapping claims 1258/1314; not selected." + }, + { + "object": "P112 fixed nine co-star decoder", + "disposition": "Discussion1267 completed a separate obstruction; not reopened." + }, + { + "object": "All rank-six arbitrary support trims of original cost-seven P112 C/N parents", + "disposition": "Chosen: frame coverage and optimistic assembly demand are beyond PR1323 first-erasure threshold." + } + ], + "domain": "All 7616 tagged original rank-seven parents; enumerate their 127 nonzero column-code words and transposes to dominate every arbitrary joint rank-six support restriction. Rank below six and trimmed original rank-eight/nine parents are excluded.", + "seed_use": "Choose ties and explicit witnesses by cyclic ordering beginning at support tag20; coverage is exhaustive, not seed-dependent.", + "deliverable": "Exact maximum frame-hit coverage, per-parent receipts, an all-cuts domination proof, and the sharp implication for the optimistic ten-cost-six frame-demand relaxation. No coefficients, physical supplier or kappa claimed.", + "initial_body": "CLAIM \u2014 complex supplier track, OS assignment seed 20.\n\nBase: `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Predecessors: PR1226/PR1236/PR1242; first-erasure result PR1323 at `c1144855242a56ffc1090be2f075f977d123d947`.\n\nExact question: how many of the 1260 live P112 frames can a rank-six term retain when both supports are arbitrary subsets of an original cost-seven C/N root-star pair? Enumerate all 127 maximal one-axis codeword cuts per tagged parent, prove these dominate every joint rank-six cut, and test the favorable ten-term copy bill 60 against the required eight hits per frame. This measures assembly coverage after the first copy saving; it does not repeat PR1323 erasure thresholds or the exact-support cost 64 theorem.\n\nExpected artifact: complete exact coverage census and scoped proof or explicit favorable relaxation witness, with separate checks and source pins. Additional helpers/source access/frame/restoration/recursive charges are optimistically zero for this screen; no decoder, supplier admission or new kappa claim.\n\nExpected finish: 2026-10-13 23:44 UTC; final quarter reserved for verification. Claim expires 2026-10-14 00:44 UTC. Cinna Davis, with substantial OpenAI Codex assistance.", + "discussion": { + "id": "D_kwDOU-508s4AqApC", + "number": 1330, + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1330" + }, + "result": { + "status": "verified", + "statement": "All rank-six descendants retain at most 1120 frames; exact frame-demand bill 60 is attained by 10 terms, but this witness leaves 21 diagonals uncovered.", + "artifact": "research/p112-rank6-frame-coverage/", + "validation": "Full registered Python3.12.15 replay and eight tests pass; local Python3.14.7 eight tests pass.", + "actual_verification_start_utc": "2026-10-13T23:02:38Z", + "handoff_discussion": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1330" + } +} diff --git a/research/p112-rank6-frame-coverage/COVERING.json b/research/p112-rank6-frame-coverage/COVERING.json new file mode 100644 index 0000000000..b762571ef9 --- /dev/null +++ b/research/p112-rank6-frame-coverage/COVERING.json @@ -0,0 +1,77 @@ +{ + "scope": "Frame-demand relaxation only; arbitrary coefficients are not supplied. All helpers, source access, frame changes, copies beyond per-term rank, restoration, hosting and recursive overhead are optimistically zero.", + "terms": [ + [ + 7, + 0, + "0x187100008e18000000000560009590" + ], + [ + 29, + 0, + "0x187100000000187100000562a60004" + ], + [ + 19, + 2, + "0x80c8048004804c0424008040102464" + ], + [ + 105, + 88, + "0xaa00550a00a50050c000cc0000000" + ], + [ + 207, + 54, + "0x6801168001018080044402a1012020" + ], + [ + 215, + 90, + "0xa42180a0084210020848840480840" + ], + [ + 183, + 2, + "0x88a04452008100404820890408804" + ], + [ + 213, + 90, + "0x9422409004422000a018241082040" + ], + [ + 229, + 52, + "0x490404200420209221080802000668" + ], + [ + 135, + 54, + "0x81008100810618604816802006004" + ] + ], + "exact_check": { + "terms": 10, + "copy_bill": 60, + "minimum_hits": 8, + "hit_histogram": { + "8": 376, + "9": 648, + "10": 236 + }, + "frame_counts_sha256": "279d8390f77b13fd387f708b71988d62d021934b27a5868e7d776dc6b552327b" + }, + "diagonal_support_coverage": { + "minimum": 0, + "histogram": { + "0": 21, + "1": 41, + "2": 37, + "3": 9, + "4": 2, + "5": 2 + } + } +} diff --git a/research/p112-rank6-frame-coverage/DIAGONAL-SEARCH.json b/research/p112-rank6-frame-coverage/DIAGONAL-SEARCH.json new file mode 100644 index 0000000000..899a67a9cd --- /dev/null +++ b/research/p112-rank6-frame-coverage/DIAGONAL-SEARCH.json @@ -0,0 +1,18 @@ +{ + "solver": "scipy.optimize.milp", + "seed": 20, + "domain": "5376 distinct 1120-hit maximal row-cut frame patterns; sorted index20 forced; choose10 distinct patterns", + "require_diagonal_coverage": true, + "time_limit_seconds": 120, + "stopping_rule": "Return one feasible incumbent or stop at the 120-second solver limit; no exclusion theorem from failure.", + "elapsed_seconds": 120.14608920499813, + "status": 1, + "message": "Time limit reached. (HiGHS Status 13: model_status is Time limit reached; primal_status is None)", + "candidate_sha256": "1c72aaca41bfb34b664ea21888e53a4406acdd536f09aa488073aa11a37499b7", + "environment": { + "python": "3.14.7", + "numpy": "2.5.3", + "scipy": "1.18.1" + }, + "feasible": false +} diff --git a/research/p112-rank6-frame-coverage/LICENSE b/research/p112-rank6-frame-coverage/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/p112-rank6-frame-coverage/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/p112-rank6-frame-coverage/OVERLAP.json b/research/p112-rank6-frame-coverage/OVERLAP.json new file mode 100644 index 0000000000..f8bd799f6d --- /dev/null +++ b/research/p112-rank6-frame-coverage/OVERLAP.json @@ -0,0 +1,62 @@ +{ + "searched_at": "2026-10-13T23:04:46.512662+00:00", + "coverage": { + "open_prs": { + "fetched_at": "2026-10-13T23:04:16.536068+00:00", + "complete_pagination": true, + "records": 821 + }, + "discussions": { + "fetched_at": "2026-10-13T23:04:46.426187+00:00", + "complete_pagination": true, + "records": 73 + } + }, + "warnings": [], + "recent_all_state_prs_checked": 60, + "related": [ + { + "pr": 1331, + "head": "f08b698cc2bd74e2425486728a008e531fc35f0e", + "title": "Scoped obstruction: one free P112 rectangle cannot improve one coordinate COPY", + "state": "OPEN", + "scope_difference": "One free rectangle mixed with one coordinate total; not the arbitrary rank-six descendant support class." + }, + { + "pr": 1327, + "head": "0462379659388acdb271f2e769986475d8a0646c", + "title": "Scoped negative result: copy-rank floor for two-sided P112 parity lifts", + "state": "OPEN", + "scope_difference": "Two-sided parity-lift exact identities and compensation bills; not rank-six star-subset frame covers." + }, + { + "pr": 1323, + "head": "c1144855242a56ffc1090be2f075f977d123d947", + "title": "Scoped bound: P112 star copy-cost drops need at least 20 trims", + "state": "OPEN", + "scope_difference": "Direct predecessor: first-erasure thresholds; current package adds complete slice frame capacities and a sharp frame-only cover." + }, + { + "pr": 1320, + "head": "ab2061c1249b027e08cf7b9426d6c913526d1e39", + "title": "Prove a nine-root obstruction for one masked P112 co-star decoder", + "state": "OPEN", + "scope_difference": "One fixed nine-term co-star assignment; no overlap with the complete codeword coverage census." + }, + { + "pr": 1313, + "head": "cd3ed178ba7b4edba818f7892e61a71cd11e72a2", + "title": "Research: classify low-rank P112 diagonal-mask completions", + "state": "OPEN", + "scope_difference": "Adjacent diagonal-mask completion research; body was a template at refresh, so no detailed claim imported." + } + ], + "result": "No competing all-rank-six descendant frame-coverage census or sharp frame-demand covering result found; title/body/comment coverage is not proof of novelty.", + "predecessor_heads_rechecked": { + "1226": "8b10989e4e45f0f9ce41004d7898a21a32f87e11", + "1236": "ee8437bd9879272094e20c024cd34a53c4e84cd8", + "1242": "7f31a561787864f26eb2242ef35179d07223accf", + "1323": "c1144855242a56ffc1090be2f075f977d123d947" + }, + "selected_record_sha256_after_fetch": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" +} diff --git a/research/p112-rank6-frame-coverage/PROOF.md b/research/p112-rank6-frame-coverage/PROOF.md new file mode 100644 index 0000000000..e8367c86c2 --- /dev/null +++ b/research/p112-rank6-frame-coverage/PROOF.md @@ -0,0 +1,181 @@ +# Rank-six P112 star slices and the sharp frame-demand relaxation + +## 1. Fixed object and theorem + +Use the 120 E8 root lines in the doubled coordinates and order archived in +`inputs/PR1323-MODEL.json`. Remove the standard orthogonal eight-frame F0 to +obtain the fixed 112 live lines. For norm-two representatives, write +`G(i,j) = ` and `N(i,j) = (G(i,j)+1) mod 2`. + +The 240 tagged supports are `C(alpha)`, the live lines not orthogonal to alpha, +and `N(alpha)`, that support with alpha itself removed. A tag is +`2*normal_line + self_trimmed`. Duplicate tags for punctured normals are retained. +The original support-pair matrix has rank seven for 7,616 ordered tagged pairs +(6,720 distinct support pairs), as in Navinor's PR1226 and David Arias's PR1236. + +Here a **rank-six descendant** is any pair of subsets of one of those original +rank-seven parent pairs whose binary pairing matrix has rank exactly six. +Both factors may be trimmed simultaneously. This is a larger support class +than the original exact C/N theorem. Parents of rank eight or nine, descendants +of rank at most five, other punctures and shared-copy contracts are excluded. + +The exact census and the domination lemma below establish: + +1. Every maximal one-axis nonzero-codeword cut has rank exactly six in this + fixed model: 127 per tagged parent, 967,232 cases in total. +2. A rank-six descendant meets at most 1,120 of the 1,260 live orthogonal + eight-frames on both factors. That maximum is attained. The sharp per-parent + joint maxima are 1,080 for 5,824 tagged parents and 1,120 for 1,792. +3. The averaged frame-demand lower bound for this class is exactly 54. +4. The integer **frame-demand relaxation** over rank-six descendants has sharp + copy bill 60. Its exact ten-term witness is in `COVERING.json`. + +Item 4 concerns supports and necessary rank demand. It does not assert an exact +masked identity, a realized supplier, or any value of kappa. + +## 2. Why one-axis codewords cover arbitrary joint rank-six cuts + +Let M be a binary matrix of rank r and factor it as `M = A B`, where A has full +column rank r and B has full row rank r. Its column code consists of the +vectors `A z` for `z in F2^r`: B maps its coefficient space onto F2^r. + +For a nonzero z, the zero set `Z(z) = {i : (A z)_i = 0}` is the largest row +support lying in that functional's kernel. Deleting the nonzero codeword's +support leaves `M[Z(z), all columns]` with rank at most r-1. For a row +restriction of rank exactly r-1, choose a nonzero z in the one-dimensional +kernel of its A factor. Its retained rows lie in Z(z). Since that restriction already has +rank r-1, the larger maximal restriction also has rank exactly r-1. + +Now suppose a simultaneous row and column restriction `A_S B_T` has rank r-1. +Each of A_S and B_T has rank at least r-1. If both had rank r, B_T would still +map onto F2^r and A_S would remain injective, so their product would have rank r. +Thus at least one of the two one-axis restrictions has rank exactly r-1. +Extend that restriction to one of the maximal functional zero sets on its +axis, and restore the other factor to its full parent support. The resulting +one-axis slice: + +- contains the joint descendant on both factors; +- still has rank exactly r-1; +- meets every frame that the joint descendant meets. + +This proves that the maximum frame coverage over **all** joint rank-six +descendants of a rank-seven parent equals the larger of its maximal row-cut +and maximal column-cut coverages. No bound on the number of deleted labels is +assumed. This argument does not extend an optimization priced at rank five +to one priced at rank six: rank exactly r-1 is essential to the claim. + +The two orientations of every tagged parent occur in the ordered census, so +the transposed record supplies the complete column-cut maximum. Every nonzero +word in each seven-dimensional column code is enumerated, not just words of +minimum Hamming weight from PR1323. + +## 3. Exact census and averaged bill + +Both implementations construct every live orthogonal frame and every original +support-pair rank. They then enumerate all 127 nonzero words for every rank-seven +parent, check the rank of each retained support pair, and count its frame hits. + +The primary implementation generates the root lines explicitly, enumerates +column spans, and uses bit-set clique recursion. The separate implementation +validates the roots using simple-root Weyl reflections, enumerates linear +functionals on independently obtained row coordinates, and lists frames using +sets. They agree on every per-parent maximum, witness, minimizer count, and +digest of all 127 `(cut, frame_hits)` records, and on every certificate field. +Both belong to this AI-assisted contribution; this is not an independent human +review or a proof-assistant formalization. + +The one-axis per-parent maxima are 1,080 (5,824 pairs), 1,110 (896), and 1,120 +(896). Restoring the opposite factor by the lemma and using transposed records +gives the joint maxima in Section 1. There are 23,340 distinct retained row +supports across the full tagged census. + +On each live frame F, the constrained masked identity has right side `4 I_8`. +Each paid outer product has rank at most one, so at least eight terms must meet +F on both factors. A cost-zero term has a zero binary pairing matrix on its +support rectangle. Since N is one everywhere on F-by-F, such a term cannot +meet F on both factors and cannot supply any of those eight ranks. + +Summing the required hits over 1,260 frames gives 10,080. A rank-six term supplies +at most 1,120 hits. Thus the uniform averaged inequality gives + +``` +copy bill >= 10080 * (6/1120) = 54. +``` + +The maximum-hit witness attains the per-term efficiency in this calculation. +This is a sharp single-term capacity bound; it is weaker than the simultaneous +integer frame constraint. + +## 4. At least ten rank-six terms + +The rank-seven parent classification says both supports are self-trimmed +(or identical C/N supports for a punctured normal), with the two normals having +odd inner product. Two punctured normals are orthogonal, so at least one normal +of each parent is live. Choose one such live normal a for each descendant. + +The parent's support N(a) avoids every live frame containing a. Every subset of +that support also avoids those frames. Thus a descendant misses all 90 frames +through its chosen live normal. + +Seven or fewer terms cannot satisfy the rank-eight demand. Eight terms would each have to +meet every frame; none of these descendants does. Suppose nine terms were +feasible. A frame could then be missed by at most one term. The nine chosen +live normals must be distinct, and no two can be orthogonal: every orthogonal +live pair belongs to a live eight-frame, as recounted by PR1236/PR1242 and the +frame enumeration. We would have nine pairwise odd root lines. + +For completeness, the predecessor's integer-dependence proof excludes those +nine lines. Nine rational norm-two roots in eight dimensions have a primitive +integer dependence `sum c_i v_i = 0`, with some c_i odd. Their Gram matrix +modulo two is J+I of size nine; its kernel consists of the constant vectors. +Hence every c_i is odd. But + +``` +(1/2) ||sum c_i v_i||^2 + = sum c_i^2 + sum_(i + = 9 + 36 = 1 mod 2, +``` + +contradicting the zero dependence. This obstruction is credited to David +Arias's PR1236 and independently corroborated by Hanson Sun's PR1242. Trimming +more support cannot undo the inherited misses. + +Consequently any feasible all-rank-six frame cover has at least ten terms and +copy bill at least 60. `COVERING.json` attains ten terms: both exact checkers +recompute each parent rank, each cut's code membership, the actual rank six, +and all 1,260 frame hit counts. This proves the relaxation's optimum is 60. + +## 5. Search and limits + +The complete capacity census is exhaustive. The optional MILP proposal search +is narrower: 5,376 distinct maximum-hit frame patterns, sorted by their missing +frame masks, with pattern index 20 forced by the assignment seed, and ten +distinct patterns chosen. It stops after a feasible incumbent or a 120-second +solver limit. The search receipts record the runtime, versions, candidate hash +and explicit terms. A floating-point proposal is accepted only after exact +standard-library checking. Search failure would not be an impossibility theorem. + +The recorded first witness has frame-hit counts 8 (376 frames), 9 (648), and +10 (236), but leaves 21 live diagonals outside all ten support rectangles. +That is a concrete obstruction to this particular witness being a decoder: +its diagonal sum is zero there for every possible coefficient choice, whereas +the required diagonal is four. Cost-zero odd corrections cannot touch those +diagonals. This distinguishes the sharp frame relaxation from masked exactness. +One bounded refinement added coverage of every live diagonal to the same +5,376-pattern search. It timed out after 120 seconds without a feasible +incumbent; the finite coverage class was not exhausted and no infeasibility +conclusion is drawn. See `DIAGONAL-SEARCH.json`. +The refinement retained the first enumerated support representative of each +frame pattern. Deduplicating by frame pattern preserves the frame-only +problem, but does not preserve diagonal-coverage possibilities. The failed +refinement is therefore also restricted by this representative choice. + +The complete supplier cost has not been realized. For this optimistic screen, +all helper endpoints, source access, frame changes, extra copied information, +dirty restoration, hosting and recursive overhead are assigned zero cost; +only the separate-term copied rank is priced. Even this favorable screen does +not supply coefficient exactness. Necessary frame coverage is not sufficient +for the diagonal and orthogonal-entry equations. Free odd-entry corrections +cannot repair a wrong diagonal. A complete decoder would have to satisfy +`sum d_k(i) t_k(j) = 2 G(i,j)` on all N(i,j)=1 entries with these actual supports, +then pay every physical and recursive charge. No such decoder is claimed. diff --git a/research/p112-rank6-frame-coverage/README.md b/research/p112-rank6-frame-coverage/README.md new file mode 100644 index 0000000000..2c4118013e --- /dev/null +++ b/research/p112-rank6-frame-coverage/README.md @@ -0,0 +1,129 @@ +# P112 rank-six star trims: sharp frame-demand copy bill 60 + +**Scoped structural result and exact census. No masked decoder, supplier or new kappa.** + +The exact C/N support theorem in David Arias's PR1236 has copy floor 64 and +excludes further support trims. Cinna Davis's PR1323 showed that a first copy +saving from an original cost-seven atom needs at least 20 support deletions. +This contribution asks what frame coverage survives that saving, including +arbitrary simultaneous trims of both factors, on the same fixed P112 model. + +## Result + +Every rank-six descendant of an original cost-seven atom meets at most **1,120 +of the 1,260 live frames**. A rank-factorization argument reduces all arbitrary +joint cuts to maximal one-axis functional zero sets. Both checkers agree across +all **7,616 tagged parents and 967,232 maximal slices**, not just the minimum +deletion witnesses of PR1323. + +| Maximum hits after arbitrary joint rank-six trimming | Tagged parents | +|---:|---:| +| 1,080 | 5,824 | +| 1,120 | 1,792 | + +The averaged copy bound is only `10080*6/1120 = 54`. Simultaneous frame demands +give the stronger, sharp **integer relaxation optimum 60**: nine terms are +excluded by the inherited nine-root obstruction, while `COVERING.json` supplies +ten cost-six support pairs meeting every frame at least eight times. The exact +hit counts are 8 on 376 frames, 9 on 648, and 10 on 236. + +This ten-term frame witness leaves **21 diagonals uncovered**. It therefore +cannot be a masked decoder, regardless of coefficients. That concrete failure +is a negative control and shows why the relaxation's value must not be promoted +to a construction. A 120-second search adding diagonal coverage found no +feasible incumbent; it did not exhaust that search or prove infeasibility. + +The [proof](PROOF.md) gives the all-cuts reduction, the inherited ten-term +obstruction, the exact relaxation definition and the limits. In particular, +original rank-eight/nine parents, descendants of rank five or lower, mixtures +with other cost classes, different punctures and shared-copy pricing are outside +this optimization. Other term classes may have different frame efficiencies. + +## Reproduce + +From the repository root, standard-library Python: + +```sh +python3 -I -O -B research/p112-rank6-frame-coverage/verify.py +python3 -I -O -B research/p112-rank6-frame-coverage/independent.py +``` + +Expected markers: + +```text +PASS_P112_RANK6_FRAME_COVERAGE atoms=7616 slices=967232 max_hits=1120 average_floor=54 cover_bill=60 +PASS_INDEPENDENT_P112_RANK6_COVERAGE atoms=7616 slices=967232 max_hits=1120 cover_bill=60 +``` + +`generated/COVERAGE.jsonl` stores one record per tagged parent: +`[left_tag, right_tag, maximum_row_hits, attaining_cut_hex, attaining_cut_size, +maximizer_count, all_127_cut_hit_digest]`. Each digest encodes sorted nonzero +cuts as `hex_cut`, tab, decimal hits, newline. Bit positions refer to original +root IDs 0 through 119. Transposed parent records supply column maxima. +`generated/CERTIFICATE.json` records the full distributions and a maximum-hit +witness. The explicit writer option refuses existing output directories. + +The separate implementation imports no primary or predecessor program. It uses +Weyl reflections, row-coordinate duals and set-based frame enumeration. Both +engines belong to this contribution; independent human review is not claimed. + +Eight tests cover all 4,096 binary 3-by-4 matrices and 524,160 joint restrictions, +the rank-factorization domination lemma, exact frame receipts, the uncovered +diagonal obstruction, deliberately false copy/frame witnesses, source and table +corruption, overwrite refusal and optimized relocation. Finite regressions test +the implementations; the written argument supplies the arbitrary-cut scope. + +The optional `search_cover.py` proposes witnesses with NumPy 2.5.3 and SciPy +1.18.1, as used in the recorded run. Its exhaustive candidate generation yields +5,376 distinct maximum-hit frame patterns. Assignment seed 20 forces sorted +pattern index 20. It chooses ten distinct patterns and has a 120-second solver +limit. `SEARCH.json` records the feasible first run; `DIAGONAL-SEARCH.json` +records the single bounded refinement without a feasible incumbent. Solver +arithmetic is not part of acceptance: both standard-library engines check the +fixed witness exactly. +The refinement keeps one first-enumerated support representative per frame +pattern. Other representatives with the same frame hits may have different +diagonal coverage, so the refinement does not exhaust even the maximum-hit +support dictionary. + +```sh +OPENBLAS_NUM_THREADS=1 python3 -B research/p112-rank6-frame-coverage/search_cover.py --output /tmp/new-frame-search.json +``` + +The search may return a different witness or hit its time limit; neither outcome +changes the committed exact certificate. Add `--diagonal` to reproduce the +stronger searched constraint. Output paths must be new. + +## Open next questions + +Can rank-six support cuts participate in an exact masked identity below cost +64 once diagonal and orthogonal-entry equations are imposed? A feasible first +step is a support-level relaxation adding diagonal coverage and stronger +per-frame rank constraints across the **full** slice dictionary. The recorded +search used only maximum-hit patterns and did not decide even its restricted +diagonal-cover problem. A favorable support relaxation would still require +exact coefficients, helpers, source access, frame changes, restoration, hosting +and a complete recursive cost recurrence. The current frame-only certificate +does not supply any of these obligations. + +## Provenance and credit + +Base: `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Fresh OS assignment seed **20**, +complex supplier track. Coordination: [discussion 1330](https://github.com/CrocSwap/integer-mult-bounds/discussions/1330). +Exact commits, Git blobs and archive hashes are in `SOURCES.json`; source archives +and their original notice are unchanged. + +Navinor (@navinor), PR1226 at `8b10989e4e45f0f9ce41004d7898a21a32f87e11`, +supplies the P112 model and root-star census. David Arias (@DavidAriasC), PR1236 +at `ee8437bd9879272094e20c024cd34a53c4e84cd8`, supplies the original sharp cost64 +theorem and nine-root obstruction; Hanson Sun (@bbMisk), PR1242 at +`7f31a561787864f26eb2242ef35179d07223accf`, independently corroborates it and +identifies further trims as open. Cinna Davis, PR1323 at +`c1144855242a56ffc1090be2f075f977d123d947`, supplies the first-erasure result and +ordered model. PR717 by DreamingOfClouds and retained PR968 geometry are credited +in the frozen notice. None of these pending packages is silently adopted as +the selected frontier. + +New work by **Cinna Davis (@1337isnot1337)** with substantial **OpenAI Codex +assistance** in proof analysis, code, experiments, checks and writing. +Apache-2.0; `LICENSE` and the predecessor notice are retained. diff --git a/research/p112-rank6-frame-coverage/SEARCH.json b/research/p112-rank6-frame-coverage/SEARCH.json new file mode 100644 index 0000000000..f0ed856e55 --- /dev/null +++ b/research/p112-rank6-frame-coverage/SEARCH.json @@ -0,0 +1,69 @@ +{ + "solver": "scipy.optimize.milp", + "seed": 20, + "domain": "5376 distinct 1120-hit maximal row-cut frame patterns; one candidate at sorted index20 is forced; choose exactly10 distinct patterns", + "time_limit_seconds": 120, + "elapsed_seconds": 11.080449060002138, + "status": 0, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "candidate_sha256": "1c72aaca41bfb34b664ea21888e53a4406acdd536f09aa488073aa11a37499b7", + "feasible": true, + "terms": [ + [ + 7, + 0, + "0x187100008e18000000000560009590" + ], + [ + 29, + 0, + "0x187100000000187100000562a60004" + ], + [ + 19, + 2, + "0x80c8048004804c0424008040102464" + ], + [ + 105, + 88, + "0xaa00550a00a50050c000cc0000000" + ], + [ + 207, + 54, + "0x6801168001018080044402a1012020" + ], + [ + 215, + 90, + "0xa42180a0084210020848840480840" + ], + [ + 183, + 2, + "0x88a04452008100404820890408804" + ], + [ + 213, + 90, + "0x9422409004422000a018241082040" + ], + [ + 229, + 52, + "0x490404200420209221080802000668" + ], + [ + 135, + 54, + "0x81008100810618604816802006004" + ] + ], + "minimum_hits": 8, + "environment": { + "python": "3.14.7", + "numpy": "2.5.3", + "scipy": "1.18.1" + } +} diff --git a/research/p112-rank6-frame-coverage/SOURCES.json b/research/p112-rank6-frame-coverage/SOURCES.json new file mode 100644 index 0000000000..37d0d7cd49 --- /dev/null +++ b/research/p112-rank6-frame-coverage/SOURCES.json @@ -0,0 +1,54 @@ +{ + "schema_version": 1, + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb", + "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce" + } + ], + "archives": [ + { + "local_path": "inputs/PR1323-MODEL.json", + "source_commit": "c1144855242a56ffc1090be2f075f977d123d947", + "source_path": "research/p112-star-first-cost-drop/generated/MODEL.json", + "git_blob": "99474a0444b466fbeebd74f2bbe12c9f210c486b", + "sha256": "899a5a0c604a244b06d59d1b1807927c4495cafd2eb6d581479c7f0da1d5b142" + }, + { + "local_path": "inputs/PR1323-CERTIFICATE.json", + "source_commit": "c1144855242a56ffc1090be2f075f977d123d947", + "source_path": "research/p112-star-first-cost-drop/generated/CERTIFICATE.json", + "git_blob": "7e5ed1e27bef94be33c444803e61812356992e42", + "sha256": "871540917b3d92895d2900e76f378da202b49f7943ecef6a600a9275619dea75" + }, + { + "local_path": "inputs/PR1226-NOTICE.md", + "source_commit": "8b10989e4e45f0f9ce41004d7898a21a32f87e11", + "source_path": "research/masked-root-star-floor/NOTICE.md", + "git_blob": "767d5458bc299cb2ac0fa04cb061eb174c25f95f", + "sha256": "e072c0269eae7bdfc438e0b9b980be79cf0b2b7618bc66656fac9c24ce32c256" + }, + { + "local_path": "LICENSE", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "LICENSE", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + } + ], + "predecessors": { + "1226": "8b10989e4e45f0f9ce41004d7898a21a32f87e11", + "1236": "ee8437bd9879272094e20c024cd34a53c4e84cd8", + "1242": "7f31a561787864f26eb2242ef35179d07223accf", + "1323": "c1144855242a56ffc1090be2f075f977d123d947" + } +} diff --git a/research/p112-rank6-frame-coverage/TASK.json b/research/p112-rank6-frame-coverage/TASK.json new file mode 100644 index 0000000000..04244d60ae --- /dev/null +++ b/research/p112-rank6-frame-coverage/TASK.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "task_id": "complex-masked-decoder", + "priority_revision": 2, + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "original_card": { + "id": "complex-masked-decoder", + "question": "Can one specified masked or overcomplete decoder improve the complete moment budget?", + "starting_points": [ + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md" + ], + "methods": [ + "Synthesize a decoder with exact coefficients and fully priced helper endpoints.", + "Bound the best possible budget for a fixed support alphabet before synthesis." + ], + "acceptance_gate": "Change an assumption of the eight-term all-pairs bound and count all copied information, frames and restoration.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-decoder-field-extension-seed44/verify.py" + ], + "expected": "PASS_COMPLEX_DECODER_FIELD_EXTENSION_S44", + "inspect": "Locate the excluded classes: masked identities, at least nine terms, and deeper punctures.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Choose one finite support alphabet and test exact decoding constraints before building a whole network.", + "bottleneck_link": "A cheaper fully realized decoder could increase deficit or lower recursive cost on the binding complex side.", + "allowed_variations": [ + "Select a specific masked or overcomplete family with exact labels and supports." + ], + "scope_change_triggers": [ + "Repeating the exact eight-term all-pairs search inside its proved scope." + ], + "overlap_terms": [ + "masked decoder", + "overcomplete", + "eight-term" + ] + }, + "scope_status": "changed", + "actual_scope": "Complete frame-capacity census for every arbitrary rank-six descendant of an original rank-seven P112 C/N atom, and the sharp all-rank-six integer frame-demand relaxation.", + "scope_change_reason": "The actual experiment is a necessary-condition bound and covering witness for a changed support class. It does not synthesize an exact masked decoder or a fully realized moment budget. All other complete-cost charges are optimistically zero.", + "bottleneck_link": "The complex supplier is binding at the selected base. Further support cuts evade the original exact-star theorem; this screen establishes what frame constraints can and cannot exclude before expensive coefficient or compiler work.", + "budget_minutes": 60, + "stop_rule": "Complete all 7616*127 maximal slices; one 120-second restricted frame-cover search and one 120-second diagonal-cover refinement. Reserve final quarter for independent replay, rejection controls and handoff.", + "outcome": "completed", + "evidence": "PROOF.md, generated/CERTIFICATE.json, generated/COVERAGE.jsonl, COVERING.json, SEARCH.json and DIAGONAL-SEARCH.json", + "author": "Cinna Davis (@1337isnot1337)", + "ai_assistance": "Substantial OpenAI Codex assistance in analysis, implementation, experiments, verification and writing.", + "open_questions": [ + { + "question": "Can rank-six descendants participate in an exact masked decoder below copy cost 64?", + "why_it_matters": "Frame-only demands admit cost60, so an exclusion needs additional constraints; a construction needs coefficient exactness and a complete physical invoice.", + "first_step": "Test a full-dictionary diagonal and per-frame rank relaxation before nonlinear coefficient synthesis. The maximum-hit-only bounded diagonal search was not decided.", + "blocked_by": "No feasible diagonal-cover incumbent, no coefficient identity, no helper/frame/source/restoration/hosting or recursive realization is supplied." + } + ] +} diff --git a/research/p112-rank6-frame-coverage/VALIDATION.json b/research/p112-rank6-frame-coverage/VALIDATION.json new file mode 100644 index 0000000000..5be822ee0b --- /dev/null +++ b/research/p112-rank6-frame-coverage/VALIDATION.json @@ -0,0 +1,30 @@ +{ + "status": "PASS", + "local_python": "3.14.7", + "registered_python": "3.12.15", + "standalone_release": "20261009", + "runtime_asset": { + "browser_download_url": "https://github.com/astral-sh/python-build-standalone/releases/download/20261009/cpython-3.12.15%2B20261009-x86_64-unknown-linux-gnu-install_only_stripped.tar.gz", + "digest": "sha256:ffa8f85f1b56e88b687f08d743d817015524b86a9365fd921243132b80f1a36d", + "name": "cpython-3.12.15+20261009-x86_64-unknown-linux-gnu-install_only_stripped.tar.gz" + }, + "runtime_checks": "GitHub release digest and official SHA256SUMS both match.", + "local_tests": { + "passed": 8, + "seconds": 107.738 + }, + "registered_tests": { + "passed": 8, + "seconds": 119.289 + }, + "command": "python3.12 scripts/research_package.py --package research/p112-rank6-frame-coverage", + "domain": { + "tagged_rank7_parents": 7616, + "maximal_slices": 967232, + "binary_3_by_4_matrices": 4096, + "nonzero_matrix_joint_restrictions": 524160 + }, + "source_archives_checked_against_exact_git_blobs": 4, + "finite_result": "Both complete coverage tables and certificates match; ten rank-six terms meet all frame demands with copy bill 60; the same terms leave21 diagonals uncovered.", + "scope": "Final registered replay includes all code changes. No native supplier admission, selected cold replay, full multiplication formalization or remote CI is claimed." +} diff --git a/research/p112-rank6-frame-coverage/VERIFY.json b/research/p112-rank6-frame-coverage/VERIFY.json new file mode 100644 index 0000000000..f057a8ef73 --- /dev/null +++ b/research/p112-rank6-frame-coverage/VERIFY.json @@ -0,0 +1,47 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p112-rank6-frame-coverage/inputs/PR1323-MODEL.json", + "research/p112-rank6-frame-coverage/inputs/PR1323-CERTIFICATE.json", + "research/p112-rank6-frame-coverage/inputs/PR1226-NOTICE.md", + "research/p112-rank6-frame-coverage/LICENSE" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Complete maximal-slice census and exact ten-term frame witness." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/independent.py" + ], + "timeout_seconds": 240, + "checks": "Separate Weyl-root, row-dual and set-frame complete replay." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/test_package.py" + ], + "timeout_seconds": 360, + "checks": "Eight mathematical and package failure controls, including all binary3x4 matrices, diagonal obstruction and relocation." + } + ] +} diff --git a/research/p112-rank6-frame-coverage/engine.py b/research/p112-rank6-frame-coverage/engine.py new file mode 100644 index 0000000000..6afabd3777 --- /dev/null +++ b/research/p112-rank6-frame-coverage/engine.py @@ -0,0 +1,229 @@ +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Complete maximal rank-six slice census; E8 model from PR1226/PR1323.""" +from collections import Counter +from fractions import Fraction +import hashlib +import itertools +import json + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def bits(mask): + while mask: + bit = mask & -mask + yield bit.bit_length() - 1 + mask ^= bit + + +def model(): + roots = [] + for i, j in itertools.combinations(range(8), 2): + for si in (1, -1): + for sj in (1, -1): + root = [0] * 8 + root[i], root[j] = 2 * si, 2 * sj + roots.append(tuple(root)) + roots.extend(r for r in itertools.product((1, -1), repeat=8) + if r.count(-1) % 2 == 0) + lines, seen = [], set() + for root in roots: + key = max(root, tuple(-x for x in root)) + if key not in seen: + seen.add(key) + lines.append(root) + puncture = [] + for k in range(4): + for sign in (1, -1): + root = [0] * 8 + root[2*k], root[2*k+1] = 2, 2*sign + puncture.append(lines.index(tuple(root))) + return dict(lines=[list(r) for r in lines], punctured_frame=puncture, + live=[i for i in range(120) if i not in puncture]) + + +def geometry(data): + roots, live = data["lines"], data["live"] + require(len(roots) == 120 and len(live) == 112, "wrong model size") + require(all(sum(x*x for x in r) == 8 for r in roots), "wrong root norm") + products = [[sum(x*y for x, y in zip(a, b)) for b in roots] for a in roots] + require(all(v % 4 == 0 for row in products for v in row), "nonintegral pairing") + ip = [[v // 4 for v in row] for row in products] + n = [sum(((v+1) % 2) << j for j, v in enumerate(row)) for row in ip] + supports = [] + for a in range(120): + star = sum(1 << i for i in live if ip[a][i] != 0) + supports.extend((star, star & ~(1 << a))) + adjacent = [sum(1 << j for j in live if i != j and ip[i][j] == 0) + for i in range(120)] + frames = [] + + def extend(chosen, candidates): + if len(chosen) == 8: + frames.append(tuple(chosen)) + return + while candidates: + if candidates.bit_count() < 8-len(chosen): + return + bit = candidates & -candidates + candidates ^= bit + i = bit.bit_length()-1 + extend(chosen + [i], candidates & adjacent[i]) + extend([], sum(1 << i for i in live)) + require(len(frames) == 1260, "live frame census changed") + incidence = Counter(i for f in frames for i in f) + require(set(incidence) == set(live) and set(incidence.values()) == {90}, + "live frame incidence changed") + coframe = {pair for f in frames for pair in itertools.combinations(f, 2)} + require(all((i, j) in coframe for i, j in itertools.combinations(live, 2) + if ip[i][j] == 0), "an orthogonal live pair has no live frame") + return ip, n, supports, frames + + +def basis(values): + pivots = {} + for v in values: + while v: + p = v.bit_length()-1 + if p in pivots: + v ^= pivots[p] + else: + pivots[p] = v + break + return tuple(pivots.values()) + + +def rank(n, left, right): + return len(basis(n[i] & right for i in bits(left))) + + +def column_code(n, left, right): + generators = basis(n[j] & left for j in bits(right)) + code = [0] + for g in generators: + code += [v ^ g for v in code] + return sorted(code[1:]) + + +def word_digest(records): + return hashlib.sha256("".join(f"{w:x}\t{h}\n" for w, h in records).encode()).hexdigest() + + +def table_bytes(table): + return "".join(json.dumps(row, separators=(",", ":"))+"\n" for row in table).encode() + + +def census(data): + ip, n, supports, frames = geometry(data) + frame_masks = [sum(1 << i for i in f) for f in frames] + hit_cache, row_masks = {}, set() + + def hits(mask): + if mask not in hit_cache: + hit_cache[mask] = sum(1 << k for k, f in enumerate(frame_masks) if mask & f) + return hit_cache[mask] + + parent_ranks, cut_ranks, hit_counts = Counter(), Counter(), Counter() + table = [] + for a, left in enumerate(supports): + for b, right in enumerate(supports): + r = rank(n, left, right) + parent_ranks[r] += 1 + if r != 7: + continue + require((a % 2 or a//2 in data["punctured_frame"]) and + (b % 2 or b//2 in data["punctured_frame"]) and + ip[a//2][b//2] % 2, "rank-seven parent classification failed") + words = column_code(n, left, right) + require(len(words) == len(set(words)) == 127 and all(words), "incomplete code") + values = [] + right_hits = hits(right) + for word in words: + row = left ^ word + require(word & ~left == 0, "codeword leaves parent support") + r = rank(n, row, right) + require(r == 6, "maximal one-axis slice is not rank six") + cut_ranks[r] += 1 + row_masks.add(row) + h = (hits(row) & right_hits).bit_count() + hit_counts[h] += 1 + values.append((word, h)) + maximum = max(h for _, h in values) + maximizers = [w for w, h in values if h == maximum] + cut = min(maximizers, key=lambda w: (w.bit_count(), w)) + table.append([a, b, maximum, format(cut, "x"), cut.bit_count(), + len(maximizers), word_digest(values)]) + require(parent_ranks == {7: 7616, 8: 37440, 9: 12544}, "parent census changed") + lookup = {(row[0], row[1]): row for row in table} + one_axis = Counter(row[2] for row in table) + joint = Counter(max(row[2], lookup[row[1], row[0]][2]) for row in table) + maximum = max(one_axis) + selected = min((row for row in table if row[2] == maximum), + key=lambda row: ((row[0]-20) % 240, (row[1]-20) % 240, + int(row[3], 16))) + a, b, h, cut_hex = selected[:4] + cut = int(cut_hex, 16) + summary = dict( + status="PASS_COMPLETE_RANK6_FRAME_CENSUS", frames=1260, + required_frame_hits=10080, rank7_tagged_parents=len(table), + codeword_cases=sum(cut_ranks.values()), distinct_row_slice_supports=len(row_masks), + parent_rank_histogram=dict(sorted(parent_ranks.items())), + slice_rank_histogram=dict(cut_ranks), slice_frame_hit_histogram=dict(sorted(hit_counts.items())), + one_axis_parent_maximum_histogram=dict(sorted(one_axis.items())), + arbitrary_joint_parent_maximum_histogram=dict(sorted(joint.items())), + maximum_frame_hits=maximum, + averaged_frame_bound=str(Fraction(10080 * 6, maximum)), + all_rank6_term_count_lower_bound=10, + witness=dict(left_tag=a, right_tag=b, row_cut_hex=cut_hex, + retained_row_ids=list(bits(supports[a] ^ cut)), + column_ids=list(bits(supports[b])), copy_rank=6, frame_hits=h), + table_sha256=hashlib.sha256(table_bytes(table)).hexdigest()) + return table, summary + + +def check_cover(data, cover): + """Check a necessary-condition witness with exact bit ranks, not an LP solver.""" + _, n, supports, frames = geometry(data) + counts = [0] * len(frames) + diagonal = {i: 0 for i in data["live"]} + masks = [sum(1 << i for i in f) for f in frames] + terms = cover["terms"] + require(len(terms) == 10, "cover must contain ten terms") + for term in terms: + a, b, cut_hex = term + require(type(a) is int and type(b) is int and 0 <= a < 240 and 0 <= b < 240, + "invalid parent tags") + cut = int(cut_hex, 16) + left, right = supports[a], supports[b] + require(rank(n, left, right) == 7 and cut in column_code(n, left, right), + "cover term is outside the maximal-cut dictionary") + row = left ^ cut + require(rank(n, row, right) == 6, "cover term does not cost six") + for i, mask in enumerate(masks): + counts[i] += bool(row & mask and right & mask) + for i in diagonal: + diagonal[i] += bool(row & right & (1 << i)) + require(min(counts) >= 8, "cover misses a frame demand") + result = dict(terms=10, copy_bill=60, minimum_hits=min(counts), + hit_histogram=dict(sorted(Counter(counts).items())), + frame_counts_sha256=hashlib.sha256(bytes(counts)).hexdigest()) + require(json.loads(json.dumps(result)) == cover["exact_check"], "cover receipt changed") + diagonal_result = dict(minimum=min(diagonal.values()), + histogram=dict(sorted(Counter(diagonal.values()).items()))) + require(json.loads(json.dumps(diagonal_result)) == cover["diagonal_support_coverage"], + "diagonal support receipt changed") + return result + + +def check_diagonal_coverage(data, cover): + """Separate necessary identity check; frame feasibility does not imply it.""" + _, _, supports, _ = geometry(data) + covered = 0 + for a, b, cut in cover["terms"]: + covered |= (supports[a] ^ int(cut, 16)) & supports[b] + missing = [i for i in data["live"] if not covered & (1 << i)] + require(not missing, "uncovered diagonal prevents a masked identity: " + str(missing)) diff --git a/research/p112-rank6-frame-coverage/generated/CERTIFICATE.json b/research/p112-rank6-frame-coverage/generated/CERTIFICATE.json new file mode 100644 index 0000000000..31377026ed --- /dev/null +++ b/research/p112-rank6-frame-coverage/generated/CERTIFICATE.json @@ -0,0 +1,144 @@ +{ + "all_rank6_term_count_lower_bound": 10, + "arbitrary_joint_parent_maximum_histogram": { + "1080": 5824, + "1120": 1792 + }, + "averaged_frame_bound": "54", + "codeword_cases": 967232, + "distinct_row_slice_supports": 23340, + "frames": 1260, + "maximum_frame_hits": 1120, + "one_axis_parent_maximum_histogram": { + "1080": 5824, + "1110": 896, + "1120": 896 + }, + "parent_rank_histogram": { + "7": 7616, + "8": 37440, + "9": 12544 + }, + "rank7_tagged_parents": 7616, + "required_frame_hits": 10080, + "slice_frame_hit_histogram": { + "1020": 12544, + "1030": 172032, + "1080": 69888, + "1110": 35840, + "1120": 21504, + "760": 6720, + "810": 10752, + "840": 21504, + "850": 120960, + "890": 139776, + "900": 37632, + "930": 67200, + "940": 21504, + "960": 32256, + "980": 21504, + "990": 175616 + }, + "slice_rank_histogram": { + "6": 967232 + }, + "status": "PASS_COMPLETE_RANK6_FRAME_CENSUS", + "table_sha256": "79583495e513a4fc73d5f26917286dcfd2b0a9fb77e0a86a45ae36222bbe028d", + "witness": { + "column_ids": [ + 10, + 11, + 12, + 13, + 22, + 23, + 24, + 25, + 32, + 33, + 34, + 35, + 40, + 41, + 42, + 43, + 46, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 56, + 57, + 62, + 63, + 66, + 67, + 68, + 69, + 74, + 75, + 76, + 77, + 80, + 81, + 86, + 87, + 90, + 91, + 92, + 93, + 96, + 97, + 102, + 103, + 104, + 105, + 110, + 111, + 114, + 115, + 116, + 117 + ], + "copy_rank": 6, + "frame_hits": 1120, + "left_tag": 21, + "retained_row_ids": [ + 4, + 5, + 6, + 7, + 8, + 9, + 12, + 13, + 40, + 41, + 46, + 47, + 50, + 51, + 56, + 58, + 60, + 62, + 64, + 66, + 68, + 70, + 104, + 106, + 108, + 110, + 112, + 114, + 116, + 118 + ], + "right_tag": 108, + "row_cut_hex": "55555555000000000300c0000c" + } +} diff --git a/research/p112-rank6-frame-coverage/generated/COVERAGE.jsonl 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b/research/p112-rank6-frame-coverage/independent.py new file mode 100644 index 0000000000..852c186900 --- /dev/null +++ b/research/p112-rank6-frame-coverage/independent.py @@ -0,0 +1,231 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Weyl roots, set-based frames and row-dual enumeration; no primary imports.""" +from collections import Counter +from fractions import Fraction +import hashlib +import itertools +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def indices(mask): + return [i for i in range(120) if mask & (1 << i)] + + +def check_roots(lines): + simple = [(1, -1, -1, -1, -1, -1, -1, 1), (2, 2, 0, 0, 0, 0, 0, 0)] + for i in range(6): + root = [0] * 8 + root[i], root[i+1] = -2, 2 + simple.append(tuple(root)) + roots, pending = {simple[0]}, [simple[0]] + while pending: + root = pending.pop() + for normal in simple: + dot = sum(x*y for x, y in zip(root, normal)) + require(dot % 4 == 0, "nonintegral Weyl reflection") + reflected = tuple(x-(dot//4)*y for x, y in zip(root, normal)) + if reflected not in roots: + roots.add(reflected) + pending.append(reflected) + advertised = {tuple(r) for r in lines} | {tuple(-x for x in r) for r in lines} + require(len(roots) == 240 and roots == advertised, "Weyl root model disagreement") + + +def row_coordinates(rows): + pivots, dimension = {}, 0 + for value in rows: + coefficients = 0 + while value: + pivot = value.bit_length()-1 + if pivot in pivots: + value ^= pivots[pivot][0] + coefficients ^= pivots[pivot][1] + else: + pivots[pivot] = (value, coefficients ^ (1 << dimension)) + dimension += 1 + break + coordinates = [] + for value in rows: + coefficients = 0 + while value: + pivot = value.bit_length()-1 + require(pivot in pivots, "row outside selected span") + value ^= pivots[pivot][0] + coefficients ^= pivots[pivot][1] + coordinates.append(coefficients) + return dimension, coordinates + + +def independent_geometry(data): + lines, live = data["lines"], data["live"] + check_roots(lines) + require(len(live) == 112 and set(live) == set(range(120))-set(data["punctured_frame"]), + "invalid puncture") + puncture_roots = [] + for k in range(4): + for sign in (1, -1): + root = [0] * 8 + root[2*k], root[2*k+1] = 2, 2*sign + puncture_roots.append(root) + require([lines[i] for i in data["punctured_frame"]] == puncture_roots, "wrong punctured frame") + ip = [[sum(x*y for x, y in zip(a, b))//4 for b in lines] for a in lines] + n = [sum(((v+1) % 2) << j for j, v in enumerate(row)) for row in ip] + supports = [] + for a in range(120): + star = sum(1 << i for i in live if ip[a][i] != 0) + supports.extend((star, star & ~(1 << a))) + orthogonal = [{j for j in live if j != i and ip[i][j] == 0} for i in range(120)] + frames = [] + + def complete(prefix, candidates): + if len(prefix) == 8: + frames.append(tuple(prefix)) + return + if len(candidates) < 8-len(prefix): + return + candidates = set(candidates) + while candidates: + i = min(candidates) + candidates.remove(i) + complete(prefix+[i], candidates.intersection(orthogonal[i])) + complete([], set(live)) + require(len(frames) == 1260, "independent frame census changed") + through = Counter(i for frame in frames for i in frame) + require(set(through) == set(live) and set(through.values()) == {90}, "independent incidence failed") + coframe = {pair for frame in frames for pair in itertools.combinations(frame, 2)} + require(all((i, j) in coframe for i, j in itertools.combinations(live, 2) + if ip[i][j] == 0), "independent orthogonal pair has no live frame") + return ip, n, supports, frames + + +def check_cover(data, n, supports, frames, cover): + terms = cover["terms"] + require(len(terms) == 10, "wrong cover term count") + counts = [0] * len(frames) + diagonal = {i: 0 for i in data["live"]} + for a, b, cut_hex in terms: + require(type(a) is int and type(b) is int and 0 <= a < 240 and 0 <= b < 240, + "invalid cover tags") + left, right = supports[a], supports[b] + ids = indices(left) + rows = [n[i] & right for i in ids] + dimension, coords = row_coordinates(rows) + require(dimension == 7, "cover parent not rank seven") + cut = int(cut_hex, 16) + codes = {sum(((c & dual).bit_count() % 2) << i for i, c in zip(ids, coords)) + for dual in range(1, 128)} + require(cut in codes, "cover cut not a dual-functional zero set") + kept = left ^ cut + dimension, _ = row_coordinates([n[i] & right for i in indices(kept)]) + require(dimension == 6, "cover term not rank six") + for k, frame in enumerate(frames): + counts[k] += (any(kept & (1 << i) for i in frame) and + any(right & (1 << i) for i in frame)) + for i in diagonal: + diagonal[i] += bool(kept & right & (1 << i)) + require(min(counts) >= 8, "independent cover fails frame demand") + actual = dict(terms=10, copy_bill=60, minimum_hits=min(counts), + hit_histogram=dict(sorted(Counter(counts).items())), + frame_counts_sha256=hashlib.sha256(bytes(counts)).hexdigest()) + actual_diagonal = dict(minimum=min(diagonal.values()), + histogram=dict(sorted(Counter(diagonal.values()).items()))) + require(json.loads(json.dumps(actual)) == cover["exact_check"], "cover counts disagree") + require(json.loads(json.dumps(actual_diagonal)) == cover["diagonal_support_coverage"], + "diagonal counts disagree") + + +def main(): + try: + sources = json.loads((HERE / "SOURCES.json").read_text()) + for source in sources["archives"]: + path = Path(source["local_path"]) + require(not path.is_absolute() and ".." not in path.parts, "unsafe archive path") + require(hashlib.sha256((HERE/path).read_bytes()).hexdigest() == source["sha256"], "archive drift") + data = json.loads((HERE / "inputs/PR1323-MODEL.json").read_text()) + ip, n, supports, frames = independent_geometry(data) + frame_masks = [sum(1 << i for i in f) for f in frames] + cache, row_masks = {}, set() + + def hits(mask): + if mask not in cache: + cache[mask] = sum(1 << i for i, f in enumerate(frame_masks) if mask & f) + return cache[mask] + parent_ranks, cut_ranks, hit_counts = Counter(), Counter(), Counter() + table = [] + for a, left in enumerate(supports): + ids = indices(left) + for b, right in enumerate(supports): + rows = [n[i] & right for i in ids] + dimension, coordinates = row_coordinates(rows) + parent_ranks[dimension] += 1 + if dimension != 7: + continue + require((a % 2 or a//2 in data["punctured_frame"]) and + (b % 2 or b//2 in data["punctured_frame"]) and + ip[a//2][b//2] % 2, "independent cheap-parent classification failed") + words = sorted(sum(((c & dual).bit_count() % 2) << i + for i, c in zip(ids, coordinates)) for dual in range(1, 128)) + require(len(words) == len(set(words)) == 127 and words[0] > 0, "incomplete dual code") + values = [] + right_hits = hits(right) + for word in words: + kept = left ^ word + dimension, _ = row_coordinates([row for i, row in zip(ids, rows) + if not word & (1 << i)]) + require(dimension == 6, "independent maximal slice not rank six") + cut_ranks[dimension] += 1 + row_masks.add(kept) + met = (hits(kept) & right_hits).bit_count() + hit_counts[met] += 1 + values.append((word, met)) + maximum = max(h for _, h in values) + choices = [word for word, h in values if h == maximum] + cut = min(choices, key=lambda w: (w.bit_count(), w)) + digest = hashlib.sha256("".join(f"{w:x}\t{h}\n" for w, h in values).encode()).hexdigest() + table.append([a, b, maximum, format(cut, "x"), cut.bit_count(), len(choices), digest]) + recorded = [json.loads(line) for line in (HERE / "generated/COVERAGE.jsonl").read_text().splitlines()] + require(table == recorded, "independent complete coverage table disagreement") + lookup = {(row[0], row[1]): row for row in table} + one_axis = Counter(row[2] for row in table) + joint = Counter(max(row[2], lookup[row[1], row[0]][2]) for row in table) + maximum = max(one_axis) + selected = min((row for row in table if row[2] == maximum), + key=lambda row: ((row[0]-20) % 240, (row[1]-20) % 240, int(row[3], 16))) + a, b, h, cut_hex = selected[:4] + table_raw = "".join(json.dumps(row, separators=(",", ":"))+"\n" for row in table).encode() + certificate = dict( + status="PASS_COMPLETE_RANK6_FRAME_CENSUS", frames=1260, required_frame_hits=10080, + rank7_tagged_parents=len(table), codeword_cases=sum(cut_ranks.values()), + distinct_row_slice_supports=len(row_masks), parent_rank_histogram=dict(sorted(parent_ranks.items())), + slice_rank_histogram=dict(cut_ranks), slice_frame_hit_histogram=dict(sorted(hit_counts.items())), + one_axis_parent_maximum_histogram=dict(sorted(one_axis.items())), + arbitrary_joint_parent_maximum_histogram=dict(sorted(joint.items())), + maximum_frame_hits=maximum, averaged_frame_bound=str(Fraction(10080*6, maximum)), + all_rank6_term_count_lower_bound=10, + witness=dict(left_tag=a, right_tag=b, row_cut_hex=cut_hex, + retained_row_ids=indices(supports[a] ^ int(cut_hex, 16)), + column_ids=indices(supports[b]), copy_rank=6, frame_hits=h), + table_sha256=hashlib.sha256(table_raw).hexdigest()) + require(json.loads(json.dumps(certificate)) == json.loads((HERE / "generated/CERTIFICATE.json").read_text()), + "independent full certificate disagreement") + check_cover(data, n, supports, frames, json.loads((HERE / "COVERING.json").read_text())) + print("PASS_INDEPENDENT_P112_RANK6_COVERAGE atoms=7616 slices=967232 max_hits=1120 cover_bill=60") + except (OSError, ValueError, KeyError, TypeError) as error: + print("REJECT_INDEPENDENT_P112_RANK6_COVERAGE: " + str(error), file=sys.stderr) + return 1 + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/research/p112-rank6-frame-coverage/inputs/PR1226-NOTICE.md b/research/p112-rank6-frame-coverage/inputs/PR1226-NOTICE.md new file mode 100644 index 0000000000..767d5458bc --- /dev/null +++ b/research/p112-rank6-frame-coverage/inputs/PR1226-NOTICE.md @@ -0,0 +1,21 @@ +# Notice and attribution + +Prepared by **Navinor** with help from opencode (research, proof development, +implementation, verification and documentation). Apache-2.0; new contributions are under +the repository's license. + +Model and question: CrocSwap/integer-mult-bounds#717 (DreamingOfClouds), `research/format-limits-2/` at head +`4a97676294f9fa413b65986e9984fddeda71e4cc` (B14 decoder model, D1(a) masked reduction, +D1 mixed-beta open problem, D1(e) sampled covering bound; read for definitions only, not +vendored or executed). Prior decoder floors: CrocSwap/integer-mult-bounds#620 (Joel Pulikkan / GamingPuzzled), +CrocSwap/integer-mult-bounds#968 and CrocSwap/integer-mult-bounds#1077 (woklerx and the seed44/seed48 packages; both defer masked E-graph +identities), CrocSwap/integer-mult-bounds#845 (Mihir Srivastava; fixed-reader ninth total). The E8 line enumeration +is adapted from `research/complex-frame-pair-decoders/verify.py` (Apache-2.0, same +repository) with attribution; no predecessor file is modified or imported at runtime. + +The selected construction chain (see `certificates/selected-result.json`) is read only: +Jonathan Capalbo, Chafik Boukhalfa, Jeremy Kothe, Hao Yan, DreamingOfClouds, eumemic and +the other credited authors of the T37/CrocSwap/integer-mult-bounds#589 chain. No selected-frontier change is proposed. + +Third-party code: none. Standard library only. Retained source attribution and licenses of +all predecessor packages apply to their own files. diff --git a/research/p112-rank6-frame-coverage/inputs/PR1323-CERTIFICATE.json b/research/p112-rank6-frame-coverage/inputs/PR1323-CERTIFICATE.json new file mode 100644 index 0000000000..7e5ed1e27b --- /dev/null +++ b/research/p112-rank6-frame-coverage/inputs/PR1323-CERTIFICATE.json @@ -0,0 +1,110 @@ +{ + "assignment_seed": 46, + "completed_codewords": 967232, + "distinct_supports": 232, + "first_frame_hit_change": 4, + "frames_per_line": 90, + "global_even_position_loss_floor": 560, + "global_first_copy_drop": 20, + "joint_even_position_loss_histogram": { + "560": 5376, + "624": 448, + "656": 1792 + }, + "joint_first_drop_histogram": { + "20": 5376, + "22": 2240 + }, + "lines": 120, + "live_frames": 1260, + "live_lines": 112, + "nonzero_column_codewords_per_orientation": 127, + "ordered_parent_pairs": 57600, + "parent_pair_rank_histogram": { + "7": 7616, + "8": 37440, + "9": 12544 + }, + "rank7_distinct_support_pairs": 6720, + "rank7_tagged_pairs": 7616, + "row_first_drop_histogram": { + "20": 5376, + "22": 1344, + "24": 896 + }, + "scope": "Arbitrary row and/or column support deletions within original rank-seven C/N atoms on fixed P112. Constrained-position loss is support coverage, not a count of added repair terms or paid operations. No decoder assembly, physical admission or new kappa.", + "status": "PASS_P112_STAR_FIRST_COST_DROP", + "table_sha256": "74e52306580d98e3def63d4cbdd9f033c0b94fe5fc49e435f271d3b7aff07e94", + "tagged_supports": 240, + "witness": { + "deleted_rows": [ + 10, + 11, + 24, + 25, + 59, + 61, + 65, + 71, + 73, + 79, + 83, + 85, + 90, + 92, + 96, + 102, + 104, + 110, + 114, + 116 + ], + "even_positions_removed": 560, + "frame": [ + 2, + 3, + 16, + 17, + 46, + 47, + 52, + 53 + ], + "frame_change_deleted_rows": [ + 16, + 17, + 46, + 47 + ], + "frame_change_rank": 7, + "frames_met_after": 1077, + "frames_met_before": 1080, + "left_normal": 23, + "left_tag": 47, + "minimum_even_loss_deleted_rows": [ + 10, + 11, + 24, + 25, + 59, + 61, + 65, + 71, + 73, + 79, + 83, + 85, + 90, + 92, + 96, + 102, + 104, + 110, + 114, + 116 + ], + "right_normal": 32, + "right_tag": 65, + "row_rank_after": 6 + } +} diff --git a/research/p112-rank6-frame-coverage/inputs/PR1323-MODEL.json 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1, + -1, + -1, + -1 + ], + [ + 1, + -1, + -1, + -1, + -1, + 1, + 1, + 1 + ], + [ + 1, + -1, + -1, + -1, + -1, + 1, + -1, + -1 + ], + [ + 1, + -1, + -1, + -1, + -1, + -1, + 1, + -1 + ], + [ + 1, + -1, + -1, + -1, + -1, + -1, + -1, + 1 + ] + ], + "punctured_frame": [ + 0, + 1, + 26, + 27, + 44, + 45, + 54, + 55 + ], + "live": [ + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 23, + 24, + 25, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 36, + 37, + 38, + 39, + 40, + 41, + 42, + 43, + 46, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 56, + 57, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72, + 73, + 74, + 75, + 76, + 77, + 78, + 79, + 80, + 81, + 82, + 83, + 84, + 85, + 86, + 87, + 88, + 89, + 90, + 91, + 92, + 93, + 94, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 103, + 104, + 105, + 106, + 107, + 108, + 109, + 110, + 111, + 112, + 113, + 114, + 115, + 116, + 117, + 118, + 119 + ] +} diff --git a/research/p112-rank6-frame-coverage/search_cover.py b/research/p112-rank6-frame-coverage/search_cover.py new file mode 100644 index 0000000000..fe0104232d --- /dev/null +++ b/research/p112-rank6-frame-coverage/search_cover.py @@ -0,0 +1,110 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Optional bounded MILP proposal search; the standard-library replay is exact.""" +import argparse +import hashlib +import json +from pathlib import Path +import sys +import time + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import engine + + +def candidates(): + data = engine.model() + _, n, support, frames = engine.geometry(data) + frame_masks = [sum(1 << i for i in f) for f in frames] + cache, dictionary = {}, {} + + def hits(mask): + if mask not in cache: + cache[mask] = sum(1 << i for i, f in enumerate(frame_masks) if f & mask) + return cache[mask] + for a, left in enumerate(support): + for b, right in enumerate(support): + if engine.rank(n, left, right) != 7: + continue + code = [0] + for generator in engine.basis(n[j] & left for j in engine.bits(right)): + code += [v ^ generator for v in code] + for word in code[1:]: + met = hits(left ^ word) & hits(right) + if met.bit_count() == 1120: + missing = ((1 << len(frames))-1) ^ met + dictionary.setdefault(missing, (a, b, hex(word))) + return [[a, b, cut, format(missing, "x")] + for missing, (a, b, cut) in sorted(dictionary.items())] + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--output", type=Path, required=True) + parser.add_argument("--diagonal", action="store_true", help="also cover every live diagonal position") + args = parser.parse_args() + engine.require(not args.output.exists(), "search output already exists") + import numpy as np + import scipy + from scipy.optimize import Bounds, LinearConstraint, milp + from scipy.sparse import coo_matrix + records = candidates() + engine.require(len(records) == 5376, "restricted candidate census changed") + data = engine.model() + _, _, support, _ = engine.geometry(data) + rr, cc = [], [] + for j, (a, b, cut, missing) in enumerate(records): + rr.extend(engine.bits(int(missing, 16))) + cc.extend([j] * int(missing, 16).bit_count()) + rr.append(1260) + cc.append(j) + if args.diagonal: + both = (support[a] ^ int(cut, 16)) & support[b] + for k, i in enumerate(data["live"]): + if both & (1 << i): + rr.append(1261 + k) + cc.append(j) + size = 1373 if args.diagonal else 1261 + matrix = coo_matrix((np.ones(len(rr)), (rr, cc)), shape=(size, len(records))).tocsc() + low, high = np.full(size, -np.inf), np.full(size, 2.) + low[1260] = high[1260] = 10 + if args.diagonal: + low[1261:], high[1261:] = 1., np.inf + lower, upper = np.zeros(len(records)), np.ones(len(records)) + lower[20] = 1 # Assignment seed chooses the forced frame pattern. + start = time.monotonic() + result = milp(np.zeros(len(records)), integrality=np.ones(len(records)), + bounds=Bounds(lower, upper), constraints=LinearConstraint(matrix, low, high), + options={"time_limit": 120., "mip_rel_gap": 0.}) + receipt = dict(solver="scipy.optimize.milp", seed=20, + domain="5376 distinct 1120-hit maximal row-cut frame patterns; sorted index20 forced; choose10 distinct patterns", + require_diagonal_coverage=args.diagonal, time_limit_seconds=120, + stopping_rule="Return one feasible incumbent or stop at the 120-second solver limit; no exclusion theorem from failure.", + elapsed_seconds=time.monotonic()-start, status=int(result.status), + message=result.message, + candidate_sha256=hashlib.sha256(json.dumps(records).encode()).hexdigest(), + environment=dict(python=sys.version.split()[0], numpy=np.__version__, scipy=scipy.__version__), + feasible=False) + if result.x is not None: + selected = [int(i) for i, value in enumerate(result.x) if value > .5] + misses = [0] * 1260 + diagonals = [0] * 112 + for index in selected: + a, b, cut, missing = records[index] + for f in engine.bits(int(missing, 16)): + misses[f] += 1 + both = (support[a] ^ int(cut, 16)) & support[b] + for k, i in enumerate(data["live"]): + diagonals[k] += bool(both & (1 << i)) + receipt.update(terms=[records[i][:3] for i in selected], minimum_hits=10-max(misses), + minimum_diagonal_coverage=min(diagonals)) + receipt["feasible"] = (len(selected) == 10 and max(misses) <= 2 and + (not args.diagonal or min(diagonals) >= 1)) + args.output.write_text(json.dumps(receipt, indent=2)+"\n") + print("SEARCH_RESULT", receipt["feasible"], receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/p112-rank6-frame-coverage/test_package.py b/research/p112-rank6-frame-coverage/test_package.py new file mode 100644 index 0000000000..2ff4c7cfe2 --- /dev/null +++ b/research/p112-rank6-frame-coverage/test_package.py @@ -0,0 +1,142 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Finite mathematical regressions and package rejection controls.""" +import itertools +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile +import unittest + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import engine +import independent + + +def span(values): + result = {0} + for value in values: + result |= {v ^ value for v in result} + return result + + +def oracle_rank(values): + return len(span(values)).bit_length()-1 + + +def run(script, *args, cwd=None): + return subprocess.run([sys.executable, "-I", "-O", "-B", str(script), *map(str, args)], + cwd=cwd, capture_output=True, text=True, timeout=240) + + +class PackageTests(unittest.TestCase): + def test_joint_domination_all_binary_3_by_4_matrices(self): + matrices, cases, codimension_one = 0, 0, 0 + for rows in itertools.product(range(16), repeat=3): + matrices += 1 + r = oracle_rank(rows) + self.assertEqual(r, len(engine.basis(rows))) + if r == 0: + continue + columns = [sum(((rows[i] >> j) & 1) << i for i in range(3)) for j in range(4)] + row_zero_sets = [7 ^ word for word in span(columns) if word] + column_zero_sets = [15 ^ word for word in span(rows) if word] + row_ranks = [oracle_rank(rows[i] for i in range(3) if s & (1 << i)) for s in range(8)] + column_ranks = [oracle_rank(row & t for row in rows) for t in range(16)] + for s in range(8): + for t in range(16): + cases += 1 + joint = oracle_rank(rows[i] & t for i in range(3) if s & (1 << i)) + if row_ranks[s] == r and column_ranks[t] == r: + self.assertEqual(joint, r) + if joint != r-1: + continue + codimension_one += 1 + self.assertTrue(row_ranks[s] == r-1 or column_ranks[t] == r-1) + row_extension = (row_ranks[s] == r-1 and any( + s & ~z == 0 and row_ranks[z] == r-1 for z in row_zero_sets)) + column_extension = (column_ranks[t] == r-1 and any( + t & ~z == 0 and column_ranks[z] == r-1 for z in column_zero_sets)) + self.assertTrue(row_extension or column_extension) + self.assertEqual((matrices, cases), (4096, 524160)) + self.assertGreater(codimension_one, 0) + + def test_cover_exactly_and_diagonal_obstruction(self): + data = engine.model() + cover = json.loads((HERE / "COVERING.json").read_text()) + result = engine.check_cover(data, cover) + self.assertEqual(result["copy_bill"], 60) + self.assertEqual(result["hit_histogram"], {8: 376, 9: 648, 10: 236}) + with self.assertRaisesRegex(ValueError, "uncovered diagonal"): + engine.check_diagonal_coverage(data, cover) + _, n, support, frames = independent.independent_geometry(data) + independent.check_cover(data, n, support, frames, cover) + self.assertEqual(cover["diagonal_support_coverage"]["histogram"]["0"], 21) + + def test_invalid_copy_and_frame_witnesses_rejected(self): + data = engine.model() + cover = json.loads((HERE / "COVERING.json").read_text()) + zero_cut = json.loads(json.dumps(cover)) + zero_cut["terms"][0][2] = "0" + with self.assertRaisesRegex(ValueError, "maximal-cut dictionary"): + engine.check_cover(data, zero_cut) + repeated = json.loads(json.dumps(cover)) + repeated["terms"] = [cover["terms"][0]] * 10 + with self.assertRaisesRegex(ValueError, "misses a frame"): + engine.check_cover(data, repeated) + + def test_both_replays_reject_archive_mutation(self): + with tempfile.TemporaryDirectory(prefix="p112-rank6-source-") as root: + copy = Path(root) / "package" + shutil.copytree(HERE, copy, ignore=shutil.ignore_patterns("__pycache__")) + with (copy / "inputs/PR1323-MODEL.json").open("ab") as stream: + stream.write(b" ") + for script in ("verify.py", "independent.py"): + result = run(copy / script) + self.assertNotEqual(result.returncode, 0) + self.assertIn("REJECT_", result.stderr) + + def test_independent_rejects_wrong_roots(self): + lines = engine.model()["lines"] + lines[0] = [2*x for x in lines[0]] + with self.assertRaisesRegex(ValueError, "Weyl root"): + independent.check_roots(lines) + + def test_false_coverage_table_rejected(self): + with tempfile.TemporaryDirectory(prefix="p112-rank6-table-") as root: + copy = Path(root) / "package" + shutil.copytree(HERE, copy, ignore=shutil.ignore_patterns("__pycache__")) + path = copy / "generated/COVERAGE.jsonl" + rows = [json.loads(line) for line in path.read_text().splitlines()] + rows[0][2] += 1 + path.write_bytes(engine.table_bytes(rows)) + result = run(copy / "verify.py") + self.assertNotEqual(result.returncode, 0) + self.assertIn("coverage table disagreement", result.stderr) + + def test_writer_refuses_existing_directory(self): + with tempfile.TemporaryDirectory(prefix="p112-rank6-write-") as root: + sentinel = Path(root) / "sentinel" + sentinel.write_text("preserve me") + result = run(HERE / "verify.py", "--write-directory", root) + self.assertNotEqual(result.returncode, 0) + self.assertIn("output directory already exists", result.stderr) + self.assertEqual(sentinel.read_text(), "preserve me") + + def test_optimized_relocation_both_replays(self): + with tempfile.TemporaryDirectory(prefix="p112 rank6 relocation ") as root: + copy = Path(root) / "package with spaces" + shutil.copytree(HERE, copy, ignore=shutil.ignore_patterns("__pycache__")) + for script, marker in (("verify.py", "PASS_P112_RANK6_FRAME_COVERAGE"), + ("independent.py", "PASS_INDEPENDENT_P112_RANK6_COVERAGE")): + result = run(copy / script, cwd=root) + self.assertEqual(result.returncode, 0, result.stderr) + self.assertIn(marker, result.stdout) + + +if __name__ == "__main__": + unittest.main(verbosity=2) diff --git a/research/p112-rank6-frame-coverage/verify.py b/research/p112-rank6-frame-coverage/verify.py new file mode 100644 index 0000000000..21c62771e4 --- /dev/null +++ b/research/p112-rank6-frame-coverage/verify.py @@ -0,0 +1,58 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Recompute every rank-six maximal slice and its exact frame coverage.""" +import argparse +import hashlib +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import engine + + +def check_sources(): + sources = json.loads((HERE / "SOURCES.json").read_text()) + for source in sources["archives"]: + name = Path(source["local_path"]) + engine.require(not name.is_absolute() and ".." not in name.parts, "unsafe archive path") + engine.require(hashlib.sha256((HERE / name).read_bytes()).hexdigest() == source["sha256"], + "source archive drift: " + str(name)) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write-directory", type=Path, help="new output directory; existing path is rejected") + args = parser.parse_args() + try: + if args.write_directory: + engine.require(not args.write_directory.exists(), "output directory already exists") + check_sources() + data = engine.model() + engine.require(data == json.loads((HERE / "inputs/PR1323-MODEL.json").read_text()), + "predecessor root model changed") + table, certificate = engine.census(data) + certificate = json.loads(json.dumps(certificate)) + engine.check_cover(data, json.loads((HERE / "COVERING.json").read_text())) + if args.write_directory: + args.write_directory.mkdir() + (args.write_directory / "COVERAGE.jsonl").write_bytes(engine.table_bytes(table)) + (args.write_directory / "CERTIFICATE.json").write_text( + json.dumps(certificate, indent=2, sort_keys=True)+"\n") + else: + generated = HERE / "generated" + recorded = [json.loads(s) for s in (generated / "COVERAGE.jsonl").read_text().splitlines()] + engine.require(table == recorded, "complete coverage table disagreement") + engine.require(certificate == json.loads((generated / "CERTIFICATE.json").read_text()), + "coverage certificate disagreement") + print("PASS_P112_RANK6_FRAME_COVERAGE atoms=7616 slices=967232 max_hits=1120 average_floor=54 cover_bill=60") + except (OSError, ValueError, KeyError, TypeError) as error: + print("REJECT_P112_RANK6_FRAME_COVERAGE: " + str(error), file=sys.stderr) + return 1 + return 0 + + +if __name__ == "__main__": + raise SystemExit(main())