Instantiate the P112 integral retraction certificate in Lean

[an664]

Instantiates the conditional PR1610 bridge with the exact P112 integer matrices from PR1497. The closed Lean certificate proves MP=0, QP=I_33 and I_104-PQ=WM for M288x104, P104x33, Q33x104 and W104x288, without assuming those identities. A proved sparse adapter connects the literal computations to the unchanged ordinary integer matrix operations. The existing kernel/image, quotient, saturation and monomial consequences are then instantiated with their actual remaining hypotheses.

Local isolated Lean 4.30.0 core/Std accepts 40 positive units and 636 named axiom reports (159 inherited, 477 new). The observed union is propext and Quot.sound; no positive errors, warnings, sorryAx or added axioms were accepted. The damaged-W fixture fails specifically where ordinary decide rejects 1=-1, with no compiled object. The successor took 47.591 seconds within the unchanged 120 seconds/unit and 600 seconds/successor caps. The three Pro-authored elaboration repairs are recorded; matrices, statements, dependency and theorem inventory remain unchanged.

All 65 original source/metadata members are authenticated. Complete-manifest/source binding, all 21,409 exact scalar comparisons and 14 tooling tests pass under normal and optimized CPython 3.12.14. The generic package hook checks source/numeric/tooling evidence; dedicated Lean replay is separate and uses an already installed exact compiler. A separate GPT-6 Pro review of the original source found no additional mathematical, orientation, binding or coverage flaw; it did not run Lean or certify the complete manifest. Its reviewer execution claims remain separate from these local receipts. No hosted-CI or independent human approval is claimed.

All six final repository commands pass: python3.12 -I -B scripts/research_package.py --package research/p112-integral-retraction-instance. The advertised dedicated Lean runner also passes on the complete package in 53.657 seconds (50.120 seconds charged to the successor), with a separate process-session watchdog.

This closes one finite numerical hypothesis of the existing bridge. rankMetadata=71 remains metadata, with no numeric rank theorem. Geometric generator-to-relation coverage, zero exclusion, local Lemma 5, a nonzero-field-element adapter, P120, decoder construction and physical supplier budgets remain outside scope. Monomial consequences retain lawful commutative-group and individual-row relation hypotheses. No kappa or selected-frontier change.

Revision-3 formal-interface-lemma; scoped claim1527. Source heads are unchanged: PR1497 7a1309f18f56d04c2db33bf1607e0332d19f72b3 and PR1610 985fd79ffea7ae7375fe6aa3ce9940b125c7dca2. Complete reads of four relevant Discussion threads and the newest 100 open PRs at 06:57:59 UTC supplement the older complete 533-PR/305-Discussion cache. No matching concrete P112 instance was identified in this bounded coverage; PR1309/1365 and the newer cold-specialization claim concern distinct interfaces. This is not a novelty certificate.

Andrey Mas with substantial GPT-6 Pro mathematical/source development, diagnostic repair and separate original-source review through ChatGPT. Codex handled source preparation, execution audit, local kernel replay and mechanical packaging, with no mathematical repair. Retain PR1497/1610 and predecessor credit: Brett Halligan / @burntout76 and Ninefold (PR1212), DreamingOfClouds (PR717), and themilkman216 (PR968). Apache-2.0.

[Mister-Meeseeks]

Batch review at 830a94bf25479adf0694407e88cc5d15a9359d69.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Lean 4.30 replays the concrete P112 integral retraction identities MP=0, QP=I and I-PQ=WM, with 40 positive units and 636 axiom reports plus the damaged-W control. The 71-rank metadata is not itself a rank theorem; geometric and field-interface applications remain separate.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.