Audit common24 P112 with the complete colored completion matching

[Clear1nsight]

PR3960's common24 theorem depends on covering every possible shared cut. This separate audit reconstructs all completion records and proves a simpler complete certificate: the entire graph connecting different root normals whose completion cuts have union size at most 24 is a matching, with 2,884 edges and 448 isolated vertices among 6,216 vertices. Three admitted directions under one common cut would force a triangle, so at most two qualify.

The fresh implementation enumerates all 43,435 binary seven-spaces by the unique annihilator pair a<b<a xor b, visits all 5,212,200 root-normal/space pairs, and matches PR3960's full-flat and completion-record digests. It imports no predecessor executable. This replaces the target's special size21/candidate split with an all-cut graph argument; a triangle would only be a necessary condition for a counterexample, and the controls explicitly check that distinction.

The written audit also checks the characteristic-zero rational-kernel bridge, derives distance 53 from that bridge, and proves coefficient independence in the two exact caller transfers: 2^4,3,5,7^5 and 2^4,4^2,7^5, each with eleven pieces, required code-intersection dimension five, quotient dimension six, and common support cap 24. The first caller inherits Nick Petalas's rank-five capacity 12, already audited in #3951; this package does not repeat that census. Historical filter membership is credited to #3960/#3154/#3282 rather than claimed as a new inventory result.

Only research/p112-common24-graph-audit is added. Canonical main was refreshed unchanged at 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Entry/final overlap covered 671/673 live open PR bodies; final snapshot was 2026-10-19 07:30:28 UTC. The local helper searched 2,492 records. Rendered C5/start-here/handoff/active-board coverage was checked by the coordinating agent at 07:24 UTC; all-Discussion/private/diff coverage remains partial. Reviewed target head remains 7e8d98e351ac153d81943218bf168dc8548b1cea.

Validation uses Python 3.12 and the standard library:

python3.12 -Werror -B scripts/research_package.py --package research/p112-common24-graph-audit

Both registered optimized commands pass: complete graph/root-space audit, and adversarial triangle/color/small-space controls plus actual CLI corruption checks for Boolean-for-integer receipt changes, deleted graph edges, and changed source bytes. The source manifest binds only canonical-main inputs. REVIEWED.json retains exact target proof/result/code hashes as review provenance without requiring pending PR history at runtime. Final head b71bb48a96acb2a010a8552e85a52411339263d0 (scientific commit 9edc051dbf0036678c475b9dda92fc2b35a5edf8) passes the exact 11-file committed-byte/source-history check and official committed export integrity check. Both actual registered commands pass from a read-only Git-free export under -I -O -Werror -B; all 12 files remain unchanged. Single-run times were 4.182 seconds and 13.558 seconds on CPython 3.12.3/Linux. The exported archive SHA256 is 979f9cbd8ce39addf88e6fbee72fb26fd4c1058fb592fd7881d8d443bbdf66ae. The follow-up commit only corrects the coordinated Discussion snapshot timestamp from 07:27 to 07:24 UTC; scientific bytes are unchanged.

This is independent implementation and written checking in the same donor/assistant context, not independent human acceptance or formal-kernel verification. No full C5 theorem, whole-cell closure, cut-threshold sharpness, decoder floor, supplier admission, full multiplication theorem or new kappa is claimed. No merge or selected-frontier change is requested.

Credit Nick Petalas for capacities, root geometry, shortening and shared-cut predecessors; DreamingOfClouds for PR3154/TWOSIDE/C5; David Arias for the quadratic model; joaqcoo and the retained E8/P112 lineage. The same donor's #3931, #3951 and #3960 retain their earlier results. New audit: Chris R / Clear1nsight, substantial OpenAI Codex assistance, Apache-2.0. Open next questions and the inherited rank-five obligation are explicit in PROOF.md and TASK.json.

Hosted CI39216828226 passed on exact final head b71bb48a96acb2a010a8552e85a52411339263d0, completing 2026-10-19 07:38:13 UTC. Planning and replay jobs both succeeded; logs include the graph, control and registered-package PASS markers, and the committed-inputs-unchanged step passed. No comments, submitted reviews or inline review threads were present at the completion check.

Task complex-rank-shape-decoder, changed scope to the independent common-cut acceptance audit. Parallel scoped work is #3972 (historical caller inventory) and #3973 (new common30 span theorem). This audit also supplied bounded read-only cross-review and a direct witness check of #3973, with no objection found; it did not independently rerun that complete geometry census.