Research: solver-free P111 copied-rank certificate and source-order correction

research/p111-copy-rank-certificate/METHOD.md

@@ -0,0 +1,118 @@
+# Local claim, search budget and verification record
+
+Base commit: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+The clone was clean before this package was added. No applicable `AGENTS.md`
+was present in the workspace ancestry or repository. The Gist, CONTRIBUTING,
+selected certificate, current-status page, review ledger and selected review
+were read. The accepted conditional kappa was
+`51110230636731/31250000000000000`; pending PR titles were not substituted for it.
+
+## Claim and task selection
+
+OS-random assignment seed **41**, drawn with `secrets.randbelow(100)` at
+2026-10-13 04:23 UTC, selects **structural decoder research**.
+
+Three narrow tasks were considered:
+
+1. Asymmetric paired-hypercube star punctures: recent #669 overlaps directly.
+2. Generalized P111 label-functional totals: selected because #620's claimed
+   obstruction lacked proof logs and exact source binding; #555 is the primary
+   fixture (seed 41 is odd), #545 is the predecessor/control.
+3. Repeated-label E8 planes: #446 already reports extensive fixed-dimension
+   SAT results, and broader vector-label mechanisms exceed this bounded task.
+
+The local claim was to establish or improve the minimum of
+`sum rank_Q G[S(x_i),S(y_i)]` subject to `sum x_i y_i^t = B^-1` over F2,
+with arbitrary nonzero nine-bit vectors and repeated terms allowed. Expected
+deliverable: exact witnesses or a scoped obstruction, a deterministic verifier,
+source pins and a local patch. No new supplier or exponent was promised.
+
+No pinned sprint coordination issue was found; the only returned issue was
+#650, requesting a discussion channel. The user's instruction also required
+local review before any public submission, so this claim remained local.
+Six pages of open-PR metadata and the relevant descriptions were read for
+overlap. The read snapshots and source text are preserved outside this package
+in the task's `evidence/` directory.
+
+A final six-page metadata refresh observed PRs through #720 (537 unique
+open PRs; pagination was not atomic). Relevant new descriptions #703,
+#708 and #715, plus the source README section 5 of #717 at its pinned head,
+were read. Their quaternionic, operand-preparation, mixed-port and complex
+decoder scopes differ from this fixed bit-label problem. Main still pointed
+to the same base commit. This is an overlap check, not a global novelty proof.
+
+The pre-submission refresh on 2026-10-13 also inspected all eight PRs returned
+by an all-state `P111` search and the 100 most recently updated PRs, through
+#748. New #728 optimizes punctured-word mini-node XORs, #738 concerns Gaussian
+lines, #747 concerns paired-geometry global stars, and #748 changes an R420
+source representation while retaining copy ranks. Their descriptions add no
+matching proof for these two fixed bit-label fixtures. Main and CONTRIBUTING
+were unchanged. The exact heads are retained in `SOURCES.json`.
+
+## Fork-and-flush adaptation
+
+The installed `fork-and-flush` skill and its execution protocol were followed
+using the supported `collaboration.spawn_agent` API, `fork_turns="none"`, and
+three isolated filesystem copies of one frozen standalone starting artifact.
+The user requested Astra/max. Each branch received the same objective,
+evaluator, fixtures, predecessor context and limits, with no parent reasoning
+or assigned approach. Branches did not spawn additional agents.
+
+Budget: one round, at most three candidate episodes per branch, at most 90
+seconds of search/evaluation per episode, and 12 minutes wall time per branch.
+Each episode could include one bounded exhaustive proof search. Setup,
+coordinator checks and final verification were additional reserved work inside
+a 45-minute overall wall-clock ceiling starting at 04:23 UTC. At least the
+final quarter was reserved for source binding, proof review and packaging.
+Model token consumption was unavailable; episode counts are not token counts.
+
+The primary score was integer copied rank, lower is better; exact reconstruction
+was mandatory. There was no noisy timing selection. Each baseline scored 63.
+Branches used 1, 3 and 3 candidate evaluations respectively, all retaining the
+same baseline. Their exact finite proof experiments included row-space,
+unit-subset and Hamming-distance certificates. Each branch encountered and
+documented one Python 3.9 `int.bit_count` compatibility failure in scratch
+exploration, then used a portable popcount. No branch computation approached
+90 seconds. The coordinator reran all three nominations serially: all scored
+63, so the incumbent was retained on the exact tie.
+
+## Evaluator correction and re-evaluation
+
+Final source binding discovered an input defect in evaluator version 1:
+`hamming_e8()` generates the correct root set in sorted Hamming-word order,
+but numeric deletion indices refer to the supplier's different ordering.
+The initial branch reports now explicitly say **archived-order model**.
+They remain preserved and are not presented as replays of the published words.
+
+The evaluator was corrected to consume the pinned supplier root table, both
+actual baselines were rebuilt, and both still have nine exact cost-seven
+terms. The all-length analytic proof was checked against those corrected
+geometric premises. An independent branch reran its finite obstruction for
+both corrected fixtures: maximum nine-term benefit 9; minimum target distance
+to a nonzero rank-one matrix 27; minimum target ones outside two rows/columns
+31. Both baselines independently passed. The corrected incumbent was retained.
+
+Three bounded review follow-ups (at most five minutes each) reviewed the
+projection proof, reviewed code/source binding, and independently reran the
+corrected finite certificates. These are final verification, not another
+exploration round. No errors remained in the reviewed proof. The compact
+rank-three minor checks in the final package provide another exact obstruction
+for the two actual fixtures.
+
+The original round used **seven** candidate-evaluator calls in aggregate,
+plus three coordinator nomination checks. Input repair added two corrected
+baseline rebuild checks and independent corrected-fixture checks. The full
+standard-library verifier and selected-record integrity checks were then run.
+Raw branch reports, failures, hashes, elapsed times and review receipts are
+preserved in the task's `fork-workspaces/` and `evidence/` directories; this
+package contains only the final mathematical artifact and its deterministic
+receipt. No performance speedup or paper-reported fork-and-flush gain is claimed.
+
+## Verification limits
+
+This adds a standalone research package. Existing generators, suppliers,
+selected-frontier pointers and `upstream/` were not edited. The relevant
+package checks and selected-record source integrity check passed. The expensive
+repository-wide `make verify` / cold supplier replay was not run; this package
+does not claim to re-certify those constructions. No credential change,
+security change or package installation was required.

research/p111-copy-rank-certificate/NOTICE.md

@@ -0,0 +1,38 @@
+# Attribution and license
+
+This local contribution was prepared by OpenAI Codex at Russell Seligmann's
+request, with substantial AI assistance in mathematics, implementation,
+verification and writing. Three fresh Astra/max agents independently explored
+the same fixed objective and subsequently checked the corrected artifact.
+Their reviews are AI reviews, not human-only or Lean reviews.
+
+New material is offered under the repository's Apache-2.0 license. The root
+table in `roots.json` is extracted from the pinned R420 supplier. Its source
+and all consumed word bytes retain their original attribution and notices.
+
+Predecessor credit:
+
+- **Dylan Crow / utcorvusvolat-dotcom (#370)**: E8 bit geometry and the original
+  bit word/checker lineage.
+- **DreamingOfClouds (#545)**: the punctured-star bit unit and nine rank-seven
+  decoder totals.
+- **eumemic (#543, #555)**: the R420 carrier skeleton and the different P111
+  puncture realized on that skeleton.
+- **Joel Pulikkan / GamingPuzzled (#620)**: generalized decoder experiments,
+  the 6/7/8 cost classification and the reported cost-63 SAT obstruction.
+- **DreamingOfClouds (#446, #595)**: the per-total drop-pricing framework and
+  the format-limit analysis that motivated the copied-information question.
+- **Jacob Sussman**, the upstream multiplication framework's authors, and the
+  full contributor lineage retained in those packages: the frame and network
+  setting. This note does not re-verify that full framework.
+- **vectorsss (#631)** and **Sam Sung / the-missionary-company (#669)**:
+  related E8 and paired-hypercube puncture results consulted for overlap.
+- **Douglas R. Colkitt / Mister-Meeseeks (#703)**, **Sagar Thakrar /
+  thakrarsagar (#708, #715)** and **DreamingOfClouds (#717)**: related
+  quaternionic, bit-circuit, mixed-port and complex-decoder work consulted
+  during the final overlap review; no proof or code imported.
+
+The value 63 and its previously reported optimality are not claimed as new.
+The added contribution is the solver-free argument, exact source-bound
+verification for both actual punctures, and the ordering regression evidence.
+No global novelty or priority claim is made.

research/p111-copy-rank-certificate/ORDERING.json

@@ -0,0 +1,172 @@
+{
+  "first_mismatch": {
+    "index": 8,
+    "archived_root": [
+      0,
+      0,
+      0,
+      0,
+      1,
+      1,
+      1,
+      1
+    ],
+    "supplier_root": [
+      0,
+      1,
+      1,
+      0,
+      1,
+      0,
+      0,
+      1
+    ]
+  },
+  "same_signed_root_set": true,
+  "archived_to_supplier_permutation": [
+    0,
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    56,
+    57,
+    58,
+    59,
+    60,
+    61,
+    62,
+    63,
+    88,
+    89,
+    90,
+    91,
+    92,
+    93,
+    94,
+    95,
+    96,
+    97,
+    98,
+    99,
+    100,
+    101,
+    102,
+    103,
+    104,
+    105,
+    106,
+    107,
+    108,
+    109,
+    110,
+    111,
+    80,
+    81,
+    82,
+    83,
+    84,
+    85,
+    86,
+    87,
+    48,
+    49,
+    50,
+    51,
+    52,
+    53,
+    54,
+    55,
+    8,
+    9,
+    10,
+    11,
+    12,
+    13,
+    14,
+    15,
+    112,
+    113,
+    114,
+    115,
+    116,
+    117,
+    118,
+    119,
+    72,
+    73,
+    74,
+    75,
+    76,
+    77,
+    78,
+    79,
+    40,
+    41,
+    42,
+    43,
+    44,
+    45,
+    46,
+    47,
+    16,
+    17,
+    18,
+    19,
+    20,
+    21,
+    22,
+    23,
+    24,
+    25,
+    26,
+    27,
+    28,
+    29,
+    30,
+    31,
+    32,
+    33,
+    34,
+    35,
+    36,
+    37,
+    38,
+    39,
+    64,
+    65,
+    66,
+    67,
+    68,
+    69,
+    70,
+    71
+  ],
+  "mapped_archived_punctures": {
+    "pr545": [
+      9,
+      31,
+      37,
+      52,
+      66,
+      76,
+      78,
+      111,
+      119
+    ],
+    "pr555": [
+      8,
+      17,
+      39,
+      51,
+      53,
+      58,
+      63,
+      72,
+      114
+    ]
+  }
+}