Combine T37, T8 and T16: conditional κ > 0.00173009636352

[hexapode]

Combining the retained T37, T8 and T16 chronologies with the unchanged staged-width suppliers from #3605 gives a new exact allocation on 488 replicas. It improves the conditional endpoint beyond our T530 contribution #3626, from approximately 0.00173007186471 to 0.00173009636353. These are recomputed complete profiles, not sums of older headline gains.

The paid profile is {1:10826280, 2:3188592, 3:1015650, 4:447984, 5:94794, 8:35136, 48:186782}. The deterministic construction reconstructs 1,791,936 literal roles across 4,392 calls and charges 437,757 physical families. Original order, dispatch and supplier provenance is retained.

All seven source-bound full-admission stages passed, including the final strict physical/precision/outer release and actual comparison against completed T530. Five terminal receipts are authenticated with eleven rejection/optimized-mode controls. Both changed native suppliers reuse authenticated caches freshly checked earlier in this session. Portable materialization reproduces the source manifest and scientific driver exactly; a fresh end-to-end portable CLI was not run. Final finite checks and an isolated declared Git-source closure are checked separately.

An additional solver-free certificate enumerates all 2,551 packing patterns and proves the exact fractional packing optimum at a certified upper root endpoint. The candidate attains that profile. This ceiling fixes the present supplier inventory, capacities and nine-call normalization; it says nothing about different operators, geometries or recursive interfaces. The private search and optimization tooling is excluded.

The endpoint is 0.001730096363528623534230 − 10^-46 − 10^-70. All inherited all-size, compiler, analytic and other conditional premises remain. This does not change the selected result or claim an unconditional multiplication theorem.

Exact original predecessor blobs and the completed T530 comparison claim are retained in this branch's own ancestry. Source-history checks do not rely on unmerged predecessor objects. Open next questions and reproduction commands are in the package README.

Credit Ross Richardson's staged-width suppliers and T37 lineage, the retained T8 and T16 chronologies and their source-specific predecessors, and our earlier composition work. Substantial OpenAI Codex assistance is disclosed. Separate checks within one AI-assisted session are not independent human or formal-kernel acceptance.

[thakrarsagar]

Independent verification (no κ): PR3694 (research/t488-independent-audit), at your head 72c268f1. The code is standard-library only and does not import or run this PR's code.

Reproduced (no correctness defect in your finite claims in the checked scope)

• Your literal journal (payload 20662cc6…; your expander reproduced FILL byte for byte here) passes a separate owner audit:
  • template windows, derived two ways;
  • same-call physical families, capacities and chronological prefixes;
  • PR3630's active-local-pair gate, which the template windows imply;
  • the complete invoice, equal to your profile.
• A from-scratch LP gives 2,551 patterns, the same basis and dual as your CEILING.json, and a unique LP-minimum profile. Your profile is exactly 488 × that minimum.
• κ is reproduced in two enclosures.

Two non-blocking notes

1. The five reject() controls in owners/independent_literal.py, inherited from Reduce helpers 644/660 from width 8 to 7; conditional κ > 0.00173 #3605, cannot fail. Examples: lo<lo, len({f,f})==2, and re-tests of equalities the preceding gates already asserted. In a local run of your auditor with each gate, and with all five gates, replaced by need(True,…), it still printed PASS and listed the five controls. The gates themselves are fine on your data, and your admission owners stage also passed here.
2. The native pins in SOURCE-PINS.json and NATIVE-RECEIPT.json hash the .json.gz container. A fresh Linux/CPython 3.14 rebuild of both providers differs only in gzip header byte 9 (OS: 0xff here, 0x13 in your files); payloads are identical. Pinning payload hashes, as you already do for FILL, would make them portable.

Details: README findings and evidence/. Your full replay.py ran out of memory in discovery emit (> 5.1 GB) on my 7.9 GB machine, after fresh native, owners, parent-lift, rebind and bind had passed.

[hexapode]

Addressed both findings in commit 2969dce. Thank you for the independent audit and the concrete reproduction.

The literal auditor now applies the same five validation rules to the actual journal and corrupted fixtures. A separate regression test executes the actual production callsite with small fixtures and detects each disabled rule, all five disabled together, and an omitted production call. The full corrected owner replay passed all 1,791,936 roles with the same invoice and physical stock.

Fresh canonical-word authentication now checks decompressed payload hashes. Tests of the actual authentication loop accept changed gzip headers/recompression and reject changed payloads for either provider. Historical compressed-file hashes and frozen admission receipts are retained unchanged.

The registered finite package replay and committed-source/history checks pass on this commit. The small regression tests are extracted-statement tests, separate from the full owner replay. This update changes neither κ nor the scientific program and does not claim a new native or seven-stage admission run. Credit for identifying both inherited issues is included in the package README.