Conditional κ = 7.51499335697560e-4: local dirty-response transport, commuting schedules and37 additional gauges on weighted gen5b

[Dugongue]

This adds a source-bound construction at exact conditional

κ = 187874833924389926480207 / 250000000000000000000000000
  = 0.000751499335697559705920828.

The new mechanism transports complete signed dirty-helper responses to separate legal target-component cuts. It admits ten unchanged helpers of total entrance rank181 even though those helper contributions need not lie in a response kernel. Every promoted target, compensation coefficient, frame transition and entrance is charged on the actual emitted word.

The package composes this with238 exact commuting addition relocations,37 additional rank-modular response gauges, the inherited weighted1915-gauge construction, and PR304's actual stronger complex supplier. The final word has1952 genuine kernel gauges of entrance rank2439, plus181 transport dimensions, rank mass403946 and normalized stock491418. All47 assembly constraints pass in two exact rational moment engines; separately quoted gains are never added.

Reproduce offline:

python -B research/ti-local-response-schedules/verify.py \
  --output local-response-replay --cxx g++ \
  --boost-include /path/to/boost/include

Requirements are Python3.11+, little-endian C++17 g++ and Boost headers; JSON and pinned source inputs are bundled. Default verification regenerates the inherited source chain and freshly compiles/replays the extension, including integer/F2-invisible mutation controls, exact source spans, arbitrary dirty-input columns, nested/COPY/Gram/prime guards, full bank tiling, finite arithmetic and both exact47-clause prices. The completed final replay freshly compiled all extension engines and executed every extension control; its inherited base was explicitly authenticated reuse. Default verification also regenerates that inherited base. Optional authenticated base reuse is explicitly distinguished in the resulting certificate. See README.md, RESULT.json and proof/ for sufficient conditions and source provenance.

All305 public PR heads were refreshed at2026-10-10 12:56:21 UTC. All305 exact pinned-base/head diffs are downloaded (284 fresh,21 authenticated reuse; zero failures). Package-source authentication and actual full replay are distinguished in PUBLIC-COVERAGE.json. Relevant mechanisms are composed on the exact weighted word; incompatible public witnesses are screened rather than counted as gains.

This remains a conditional all-size recurrence result under the inherited compiler, routing/recovery, analytic and precision interfaces. It is a native finite certificate, not a new Lean certificate or an unconditional integer-multiplication theorem. Upstream notices and licenses are retained. No publication action is performed by this package.

[Mister-Meeseeks]

Thank you @Dugongue. Your work and attribution are retained in the published 100-PR review, credits and complete original source.

Covered: Local dirty-response transport and commuting schedules. The twelve-stage baseline, kernel38/retiming61 and rank-modular159 checks pass, but retiming51 rejects a regenerated predecessor state hash. Binary identity and four CRLF-only differences are established; the remaining state mismatch blocks the full base and TI replay. Keep open; source retention is not completed native admission.

Keeping this PR open: The fresh inherited-base replay stops in retiming51/compose.py on the pinned 249-states.json hash: expected 208cc9aba1401423ca31a3305a2d2bc9e1778d78323c000bed425f0bf21518d4, generated 3348648d9f659ed8c842f9b573ca7da66108a7966268e44d29caebd71bc32781. The binary word matches and four other JSON pins match after LF-to-CRLF conversion; the state-file mismatch survives the tested serialization variants. Supply a portable, source-bound correction and complete the remaining native replay. See PR309-DIAGNOSTIC.json and the retained actual state file; no pin was bypassed.

The source archive preserves the entire submission; it does not substitute for the remaining execution or review. The batch's machine-readable disposition records this as partial coverage. Reviewed head: aeb4808af1392e565e7071cbeb2c29608201cf24.