Research: fully price the R439 H2-sem copy-share construction

[1337isnot1337]

Result

This PR completes the explicit open billing question from PR #1782: the fixed seed-42, 205-pair helper-sharing wrapper on the pinned selected R439 word is now a complete local ADD-gate construction with an exact invoice.

• Complete ADDs: 24,305 → 18,074, net saving 6,231. All 410 helper preparation/restoration ADD gates are charged.
• D source ADDs: 18,085 → 11,854; D gates: 111 → 521.
• The 661-column dirty-input map, forward and reverse, is unchanged. Semantic N equals raw K, the D cut state/frame paths and paid profile remain identical (rank mass 5,129).
• Exact envelopes: F 49,347 → 75,381; B 1,113,070 → 1,196,402. The local and nine-stage bills are 95/104 and 180/192 bits. The literal recurrence and official record exporter agree.

This is one local R439 word construction. The seed-42 matching is inherited and not claimed optimal. The selected bit side remains nonbinding; no selected-supplier adoption, outer assembly, or κ change is claimed. The inherited gate-local H2/K flags remain false; the construction uses the scoped PR1194/PR1782 semantic H2/K contract.

Reproduce

python3 -I -B research/r439-copyshare-priced-wrap-seedaaa3e40/verify.py
python3 scripts/research_package.py --package research/r439-copyshare-priced-wrap-seedaaa3e40 --check-only

Both commands pass locally under CPython 3.14.7. The registered package runner requires Python 3.12, which is unavailable in this environment; the hosted workflow should provide that replay. The verifier includes source pins, the full invoice, positive controls, and five negative controls.

Pins and overlap

• Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2 (refreshed immediately before submission; canonical main is unchanged).
• Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Priority revision 4; seed aaa3e40dfc71629ff8180ede0cda4c96; task bit-helper-contract; catalogue SHA-256 d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7.
• The final complete overlap cache covered 435 open PRs and 877 Discussion records (23:03–23:05Z). A direct live open-PR search found no same-word priced construction. PR Research: fixed helper-sharing pair fails to save on PR1062 star word #2033's fixed pair is on the distinct PR1062 star-composed word and is not evidence for this candidate.
• Claim and result extend the PR1782 handoff in Discussion #1166.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in scoping, construction, exact invoice verification and packaging. Predecessor attribution and Apache-2.0 license are included in the package.