Research: reproduce T185 and certify a precision-only kappa refinement

[digitalis-p]

Change and mathematical scope

This independently reproduces Dugongue's T185 construction in #2863 and certifies a tiny precision-only improvement to its explicit rational κ. The circuit, allocation, paid profile, optimal moment root and inherited assumptions are unchanged. No new circuit, larger packing optimum or measured speedup is claimed.

Pinned comparison: #2863 at 34328b1d5e5bebac62d5cabec993dfbfd7b2123f.

• Before: 0.001720100805416885927944 - 10^-46 - 10^-70.
• After: 0.0017201008054168859279440070756063355312 - 10^-62 - 10^-86.
• Exact gain: 7.07560633553120000009999999999999999000000009999999999999999e-27.

The full rational, high-precision decimal, source manifests, proof argument, generators and release receipts are in research/t185-precision-replay. This does not update the reviewed selected record.

Task and overlap

Research base: 1cdd4bf. Original supplier source: #2833 at e9307b4. Task selected-packing, scope changed after independently confirming #2863's attained fixed-inventory dual over all 1,163 patterns.

A bounded structural pivot found no candidate: 216 outside columns/provider cannot add a fifth independent cancellation direction by adjoining one column; this does not exclude redistributing existing directions. All 94 selected entry/frame tests fail retained interfaces. Other helpers/lines remain unsearched. Mason Hale's active Discussion #2612 structural investigation broadly overlaps this lane; no exclusive priority is claimed. The precision method itself is established predecessor work.

The final direct, paginated GitHub refresh found no stronger comparable published claim or matching refinement. #2464's stronger numerical target is not a built comparable construction. #2866 is our earlier, distinct superseded contribution.

Validation

POSIX, Python 3.12.14; full dependency pins and commands are in README.md and requirements-full.txt.

• Complete fresh baseline: PASS, 1364.56 s, including six native chains and retained-parent admission.
• Frozen precision candidate complete admission: PASS, 926.09 s, including a separate strict release. Native evidence is explicitly reused only from this session's fresh baseline.
• Independent rational endpoint/conservative checks, dual proof and admission-driver audit: PASS.
• Registered bounded replay: PASS; 63 strict outer inequalities, 17 outer rejecting controls, and two package source/provenance mutation controls.
• Post-release full supplier/source/native-cache inventories and commit-byte preflight: PASS. Published tree exactly matches the verified local tree.

Run:

python3.12 -B scripts/research_package.py --package research/t185-precision-replay

The README also gives the complete cold reproduce_all.py command. That combined orchestrator received syntax/help/export preflight; its complete constituent stages were run separately, not as an additional redundant combined cold run.

Reproduction defects are preserved honestly: the original published fast wrapper fails two missing manifest-listed .gitattributes files; exact separate recovery then exposes a gzip OS-header comparison. A separate adapter checks identical decoded regenerated payloads while preserving immutable container hashes. No original checker or manifest is weakened, and the original wrapper is not reported as passing unchanged.

Both requested main gates were run on untouched base: make verify fails historical singleton-target unpacking; make frontier1094-verify fails a historical proof-supplement hash. Logs are included. Frozen CRLF input bytes are intentionally retained despite git whitespace warnings.

Credit and remaining obligations

Credit Dugongue/#2863; Yiyang (Lyy-iiis)/#2857; the full vacancy-relay, replica, native and ownership lineage; and dataisfire, chafreaky, Vlado Vojdanovski, Jeremy Kothe and the retained outer-parameter contributors. NOTICE preserves attribution and licenses. Substantial OpenAI Codex assistance, including four delegated agents, is disclosed; no independent human review is claimed.

All inherited all-size/compiler, hosting, common-label/mutable-source, precision/tape, recovery, ordinary recursion, BIT H1-H5 and analytic-transfer obligations remain. Finite certificate success is not a formal proof of the full asymptotic multiplication theorem.

Open next questions

README.md and HANDOFF.md identify changed native/consumer interfaces or multi-helper relations as structural follow-ups, with complete conversion/cleanup/hosting prices required. Further decimal refinement has negligible value. Proving one exact inherited all-size or precision/tape implication is a separate useful direction.