Research: price H2-sem copy-path helper-sharing wraps (no new kappa)

[VictorLiwentao]

Summary

Priced finite invoice under the H2-sem replacement interface; no new κ. Complements open CrocSwap/integer-mult-bounds#1782, which admitted the PR848 wraps under H2-sem but left F/B envelopes and the paid profile uncomputed.

Under H2-sem: single pair 277→434 saves 65 ADDs (24305→24240); seed-42 greedy matching (205 pairs) saves 6231 ADDs (24305→18074). Complete dirty F2 boundary and semantic N are unchanged; paid profile mass 5129 is unchanged; local/nine-stage guards remain strict (94/177 and 95/180). Intermediate F rises with the large matching even as ADD count falls; that trade-off is recorded.

Against the H2 barrier of CrocSwap/integer-mult-bounds#848 and the contract of CrocSwap/integer-mult-bounds#1194.

Task

• Card: bit-helper-contract (chooser seed 978940692bb73d58cd4b4e07f8514e57)
• Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea
• Package: research/h2sem-copyshare-priced/
• Head: b34e0620 on cursor/h2sem-copyshare-priced-60b9

Validation

python3.12 -I -B research/h2sem-copyshare-priced/verify.py
python3.12 -I -O -B research/h2sem-copyshare-priced/verify.py
python3.12 scripts/research_package.py --package research/h2sem-copyshare-priced

Expected: PASS_H2SEM_COPYSHARE_PRICED ... profile_mass=5129 ... no_new_kappa and PASS_REGISTERED_RESEARCH_PACKAGE.

Scope limits

No kappa/frontier/native/hosted/compiler/tape claim. Paid profile unchanged; bit side nonbinding. Matching optimality not claimed. Does not re-derive the #1782/#1194 chronological bridge; prices wraps under that admitted interface.

Overlap and credit

Complementary to CrocSwap/integer-mult-bounds#1782, CrocSwap/integer-mult-bounds#848, CrocSwap/integer-mult-bounds#1194. Credit Aaron Wang, woklerx, navinor, DreamingOfClouds, eumemic. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance. Apache-2.0.

[RossRichardson]

Independent audit of head b34e0620bd92af49c9095e0eeb885f601fffd137: the finite invoice is corroborated; two verifier behaviors merit a small repair.

The code-separated audit reconstructs the matching through incidence bitsets, executes all 661 original dirty-input columns for the D boundary and complete words in both directions, recomputes rational frame ranks/COPYs and exact positive envelopes. I reproduce both savings (65 and 6,231 ADDs), F/B values, strict 104/192-bit guards and unchanged profile mass 5,129. These results and the semantic contract remain credited to this PR and PR848/1194/1782; this is not a mathematical counterexample or new kappa claim.

1. False-positive negative control: in verify.py lines 300–304, except ValueError catches the error raised when the two-pair unrestored word is unexpectedly accepted. Replacing only the semantic_n(drop[...]) call with pass still passes the entire verifier with the unchanged certificate, normally and under -O; every original test_package.py test also passes. The original semantic checker does reject the malformed word. The gap is that this control cannot detect losing that rejection.
2. Missing receipt is silently recreated: lines 443–448 regenerate a deleted CERTIFICATE.json and print PASS in the default verification mode. I reproduced identical regenerated bytes. A default PASS therefore does not establish comparison against an existing certificate.

A source-pinned audit and reproduction package includes repair.patch. The patch uses try/except/else with a specific restoration-rejection check, requires the certificate by default, and gates regeneration behind explicit --write. It applies cleanly to this exact head. Positive replay preserves the original certificate; the removed-probe mutant fails normally and under -O; a missing certificate fails without writing; explicit regeneration reproduces identical bytes. It has not been applied to your branch.

Reproduce from the audit commit:

python3.12 -I -B scripts/research_package.py --package research/h2sem-copyshare-independent-audit

The exact committed read-only export also passes. The registered replay, own optimized/read-only relocation and five source/receipt corruption controls passed on CPython 3.12.12/macOS 26.5.2 arm64. Full selected cold replay, native/hosted/compiler/precision-tape/outer obligations and hosted CI were not run; no supplier adoption is claimed.

Prepared for Ross Richardson with substantial OpenAI Codex assistance. One assisted author, no independent human or Lean review. Credit Wentao Li, Aaron Wang/navinor, woklerx, Arham Tahir and the PR589/555/425 lineage. This is a findings handoff, with no duplicate construction PR.

[Mister-Meeseeks]

Batch review at b34e0620bd92af49c9095e0eeb885f601fffd137.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Complete H2-sem helper-sharing invoice preserves661 dirty columns, frame paths and paid mass5129 while reducing ADDs by65 or6231; envelopes rise but stay within inherited guards. Reviewer supplement checks actual partial-restore rejection because that submitted control catches its own sentinel. Native/hosted adoption remains unrun.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.