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Paired-cube and shared-core reproduction

This extension inherits PR #130 at 6a9970a530119174507904e23592fd59ede19a5d and gives the conditional saving 4609169/10000000000 = 4.609169e-4.

From the repository root with Python 3.11+:

make paired-cube-verify

The selected incremental target uses only the Python standard library. CI runs it in its own paired-cube matrix group. The checks are:

  • Rebuild the selected signed H-channel graph from exact zero restrictions of the pinned PR #117 positive DAG. Replay the frozen 6,074 carrier arcs, coordinate frames, full backward intersections, signed physical mixer, center closure and 4,840 rank-20 partial gauges. Independent checks cover every scalar coefficient of H+K+B=I, the original-source K involution and inverse, actual frame containment and reverse target chains.
  • Reconstruct the bit subset from the existing PR #97 witness and readout order. Check the retained 9,543 and omitted 2,022 slots, moved zero-frame dirty reads, changed first transitions and target subsequences. Unchanged complete-basis and rational-frame suites remain inherited checks.
  • Rebuild both shared-core child lists and certify strict moments, full rare-class fallback, stopped bit saving, actual finite group/router charge, semantic guard, row stock, 47 strict inequalities and seven assembly margins.

For arithmetic and the selected bit reconstruction alone:

make paired-cube-certificate

The new proof supplies the original-source schedule, complete dirty cores, orthogonal sharing and paid final corrections. The completed core excludes the old independent-bank exterior tail; replacing that tail is justified by the exact core operator, not by subtracting a rank histogram term. The general Clifford, uniform weighted bit and restored-row proofs from PR #130 are retained.

The complex cover is specified mathematically and not materialized by the verifier. Its full group order and finite routing allowance remain in the certificate. The new signed dirty-response matrix is charged by a numerator bitlength bound and binary expansion, without a positivity assumption. Finite checks do not formalize the all-size analytic/tape theorem.

To save a compact report and retain generated local files outside the repo:

python3 scripts/paired_cube_producer.py --output /tmp/paired-cube-verification.json --work-dir /tmp/paired-cube-work

The compatible matching is frozen because different maximum-matching implementations may choose different optima. No SciPy dependency or matching optimality claim is needed. Only compact arcs, source pins and generators are submitted; raw graph/frame dumps and unselected research are excluded.

The contribution map in SOURCES.json and NOTICE explicitly credits an664's PR #128 sharing principle, eumemic's PR #117 DAG and the PR #97 / Swapnil word. Their source-specific legal and assistance notices remain unchanged. Proof sources are included without a PDF.

Shared source bindings

The inherited joint-dual manifest no longer binds Makefile, README.md or NOTICE, so editing them does not touch it. Earlier round notes describe the time when it did. If a bound producer, certificate or finite input changes, explicitly refresh its hashes, regenerate joint arithmetic and update the validation receipt's certificate digest. Its mathematical fields and previous complete replay payload must remain equal when their producer/verifier inputs are unchanged. The complete affected replay command, when needed, is make verify-joint.

Stage the final artifacts before the deterministic certificate regeneration and require git diff --exit-code to remain clean. CI checks the committed hashes and never silently refreshes source pins.