Research: H2-sem admission of the PR848 copy-path helper-sharing wrap (no new kappa)

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Prepared by Aaron Wang, with help from opencode. Apache-2.0; no independent human review claimed. No new kappa, no selected-frontier or supplier change.

Scope

Card bit-helper-contract (scope key bfb61f829a81535adeae, chooser OS nonce df6f572bc7d7dbccbe487fe013268a12, priority revision 3), scope refined to one replacement H2/K implication, per the card's first experiment ("write one replacement H2/K implication for a single helper-mixing operation, then try to falsify it on dirty inputs"). Base main 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Claim: discussion 1166 comment 18920693.

Object: the helper-writing copy-path sharing wraps that PR848 (research/r439-copy-path-sharing-barrier) recorded as rejected by the inherited gate-local H2 (H2_D_frame0_targets_from_helpers), against the exact replacement contract H2-sem of PR1194 (research/r439-semantic-d-contract-seed10/PROOF.md). PR848 priced the D-portion sharing as an arithmetic upper bound only (best pair 277 -> 434, saving 65; seed-42 greedy disjoint matching 205 pairs / 6,231 source reads) and left it interface-blocked.

Audited implication (I). If a wrapped D section satisfies H2-sem conditions 1-3 with the semantic matrix N unchanged, and the unchanged xcheck_p.py owner checker passes every inherited H1-H5/U/J/K-C flag on the PR 1194 virtual splice, then the PR 1194 chronological substitution bridge transfers the interleaved-lemma conclusion to the wrapped word on arbitrary dirty inputs.

Evidence (package research/r439-copyshare-h2sem-admission/, no new kappa)

wrap	H2-sem 1-3	boundary operator (661 columns)	frames at D/A cut	semantic K	inherited flags failing	D source reads
single pair 277 -> 434	pass	exact	equal	N = K	exactly H2, K_equals_D	18,020 (-65)
seed-42 greedy matching (205 pairs)	pass	exact	equal	N = K	exactly H2, K_equals_D	11,854 (-6,231)
PR848 C2 target-temp control	pass	exact	equal	N = K	none	18,087 (+2)

So the PR848 obstruction is scoped to the inherited gate-local H2 only: under H2-sem the helper-sharing wraps are admissible, and the semantic K check passes exactly where the literal extractor fails. All 661 basis columns are replayed exactly; by PR 1194's F2-module argument coefficient equality on those columns is equality on every module, covering arbitrary dirty streams in the stated interpretation.

Falsification attempts (why each clause matters):

• F1 unrestored helper temp: rejected at endpoints. F2 wrong restore operand: boundary equation broken on a dirty helper column. F3 restore at a mid-body chronological cut: boundary equation broken.
• F4 target-feeding-helper wrap (span closed before the fed target's own single D gate): scalar operator exact, endpoint passes, frames equal; rejected only by H2-sem condition 2 (the retained no-target-feedback clause; the checker's H1 also fails). Any weaker replacement that drops that clause would admit it.
• F5 source-feeding-helper wrap: scalar operator exact, but the framed replay rejects the frame-0 source read outright (climb not nested: register 0 from frame 2 (dim 1) to frame 0 (dim 0)). Raw operator identity does not justify frame-sensitive execution, confirming at one instance PR 1194's and r439-abc-semantic-bridge's warning.

PR848's complete oriented-pair census (430 operands, 184,470 pairs, 41,404 positive) and seed-42 greedy matching are recomputed deterministically and checked against the recorded constants.

Reproduce

From the repository root (standard library only):

python3 -B scripts/research_package.py --package research/r439-copyshare-h2sem-admission

Expected PASS_R439_COPYSHARE_H2SEM_ADMISSION pair=277->434 saving=65 matching_pairs=205 matching_saving=6231 columns=661 controls=7 no_new_kappa and PASS_REGISTERED_RESEARCH_PACKAGE research/r439-copyshare-h2sem-admission outcome=completed (observed on Windows/CPython 3.12; --check-only gives PASS_PACKAGE_METADATA_AND_PINS). test_package.py replays at a fresh path and rejects a mutated source pin, a mutated certificate and a missing pin block. python3 -B -m unittest discover -s tests -p 'test_research_*.py' passes (42 tests, 2 skipped).

Remaining obligations (explicitly not claimed)

• No priced construction: the 6,231 figure remains a source-read arithmetic bound. F/B envelopes, the 104/192-bit expressions, COPY/ERASE accounting and the paid profile were not recomputed; intermediate integer envelopes can differ at an identical binary endpoint, so the precision guards remain open. No word is proposed as a supplier.
• No kappa, frontier, native/hosted admission; all-size compiler, realization, hosting, precision/tape, recovery and analytic obligations untouched.
• The bridge is PR1194's, applied. Whether H2-sem condition 2 is necessary at a framed level is open (F4 is the recorded boundary probe); greedy-matching optimality is not claimed.

Overlap and credit

Submission-time find_overlap.py (446 open PRs incl. drafts, 418 discussion records, complete pagination, 2026-10-14 09:50 UTC) matches only this package, its claim and PR848's own record; not a novelty certificate. Credit: Aaron Wang, PR848 (pair census, greedy matching, C1-C3 controls reused here), woklerx, PR1194 (H2-sem contract and chronological substitution bridge), Arham Tahir (research/r439-abc-semantic-bridge, the bridge-application pattern), eumemic PR555 and DreamingOfClouds PR589 (the R439 word), and the retained scalar-interface/xcheck lineage. Word and checker are consumed as pinned sources; no predecessor package is vendored or modified. Overlap with concurrent register-model work (discussion 1317) is disjoint in object.

[Mister-Meeseeks]

Batch review at 1cfe5e10ce38b04209699c1a6b0e62b87e21833f.

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

Reviewed scope: Selected R439 helper-sharing pair and205-pair matching satisfy the credited H2-sem substitution premises: all661 dirty columns, semantic K and exact continuation frames verified. Literal gate-local H2/K failures are explicitly distinguished. Unpriced6231 source-read reduction is not native/hosted or precision admission.

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.