Research consolidation: bind and replay historical bit-compression evidence (no new kappa)

[woklerx]

The historical bit-compression certificate records only two source hashes, omitting eight of its nine local Python sources (including the driver) and the upstream manifest. Both recorded hashes still match even when an omitted helper's deficit formula changes from D=N-2*L to D=N-2*L+1, which changes the exact ratio used in the bound.

This research consolidation adds a 32-input source inventory and isolated replay of the unchanged producer. Every regenerated certificate field matches. An independent arithmetic checker confirms all 73 local configurations, 18 global configurations, and 36 finite even ground sizes, including the historical 335850 > 317035 role-budget obstruction. No arithmetic discrepancy or new kappa is claimed.

Reproduce from the repository root:

python -I -S -B research/bit-compression-provenance/verify.py

Expected: PASS: 32 pinned inputs; 9 local Python files; no new kappa. Python 3.11+; standard library only.

Validation: complete replay and exact JSON comparison; 23 regression tests normally and under -O; seven predecessor tests. Controls cover the changed deficit, omitted dependencies, manifest/payload mutations, candidate coverage, exact fractions, Boolean flags, environment isolation, and absent producer output. REPLAY.json and VALIDATION.json retain environment, implementation pins and command results. This is local evidence; hosted CI is separate.

Scope: only research/bit-compression-provenance/ is added. The original certificates, selected PR890 frontier, and upstream/ are unchanged. Circuit counts are inputs to the independent arithmetic checker and are recomputed by the full producer. The historical infinite-tail argument and retained compiler/assembly assumptions remain written proof obligations; this is not a formal proof of the multiplication theorem.

Base: 007664306fff84fbb1c9a1b4053b69f439764034. Upstream source: OpenAI/math adc7f1241b42e322a6451854ab7e4b4c146bf78a. Seed 99 assigned research consolidation. No pinned sprint issue was present, so the scoped claim and completion record are local. Final bounded overlap searches reached #966; related #867, #756, #824 and #946 concern different sources or checks.

Credit: Douglas R. Colkitt's original audit, retained by d55bcd62ceb8f322bcf311a5a66e94c3ac7724f0, supplies the mathematical result. Contributed by woklerx with substantial OpenAI Codex assistance, including separately assigned dependency and arithmetic reviews. Apache-2.0; predecessor attribution retained.

[woklerx]

@Mister-Meeseeks, ready for maintainer review at dd5b27a8d0ad7261899d972d41b1c56f25c496a5.

• The historical certificate's two source hashes omit eight of nine executing Python files. A deficit-formula mutation changes exact arithmetic while both old hashes remain unchanged; the new verifier rejects it.
• The 32-input isolated replay reproduces every historical certificate field. Validation passed: 23 regression tests normally and under -O, seven predecessor tests, and independent arithmetic over 73 local, 18 global, and 36 paired finite rows.
• Only eight files in the new research package are added. No new kappa or full-theorem claim; historical certificates, selected frontier, and upstream/ remain unchanged. Validation receipts are local, not hosted CI.

Reproduce from the repository root:

python -I -S -B research/bit-compression-provenance/verify.py

Expected: PASS: 32 pinned inputs; 9 local Python files; no new kappa.

Review entry points: scope and provenance, complete replay receipt, and validation commands and implementation pins.

Contribution and handoff prepared with substantial OpenAI Codex assistance; predecessor credit is retained in the package.