Research: save 108 R420 XORs with restored frame-zero sharing (no new kappa)

[mikhailramalho]

This finite bit-circuit contribution factors helpers 552 and 521 in PR543's frame-zero dirt compensation. It saves 108 binary XORs, including both preparation and restoration: 26,916 -> 26,808 native ADDs. Both dirty helpers are restored before phase A. Status: research contribution / finite circuit improvement; no new kappa.

The complete MOVE/COPY/ERASE subsequence, 420 helpers, nine copies, rank mass 5,112 and both measured native positive-prefix bounds remain unchanged. The pair census covers all 87,990 helper pairs by two methods; 108 is maximal only within this specified single-pair recipe on the fixed D matrix.

The interface change is explicit: the original H2 forbids helper destinations in D. This package proves and checks the sufficient replacement that D has the same aggregate (x,s,y) -> (x,s,y+Ns) map and restores every helper before A. The stock H2 and literal K check reject the compressed representation as expected; exact normalization and actual candidate replay validate the stated finite extension. No predecessor checker is patched.

python3 -B research/r420-frame-zero-pair/verify.py

Expected: PASS_R420_FRAME_ZERO_PAIR D=19922->19814 native_adds=26916->26808 columns=660 kappa=unchanged.

Requires Python 3.11+, C++17 and Boost headers; Python dependencies are standard library only. Passed locally with Python 3.13.7, GCC 15.2 and Boost 1.88:

• Exact E8/frame audit, all 660 dirty-input columns, independent set-valued D and raw-record interpreters.
• Unmodified C++ legality and nine-stage replay: 1,380 columns and 18 omitted-bridge controls per word.
• Six D rejection controls, a positive control, and an F2-neutral record control rejected specifically by the positive-prefix guard.
• Normal and optimized Python, complete exact-certificate comparison, output-overwrite protection, and make selected-record-check.
• Isolated reproduction from a Git archive containing only this contribution and its nine declared source files.

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Reviewed PR543 source: 2065fe4f72a914d907f1046603f5a36f17018535. Source pins, circuit recipe, exact certificate, proof, search scope, validation and local seed-1 claim are included under research/r420-frame-zero-pair/. No existing file, upstream/ content or selected-frontier pointer changes.

Final overlap refresh through #685: #670 and #674 change separate phase-B blocks; #661 fixes D and excludes circuit changes; #673 and #677 concern different dirty primitives. Their work is credited and not imported. No pinned coordination issue exists.

The hosted-parent reconstruction, invoice and changed-word outer assembly remain integration obligations, together with review of generalized D under the retained all-size/common-label interface. The selected composition is complex-limited. Repository-wide make verify, Lean and remote CI are not claimed. This is not a proof of the full multiplication theorem.

Credit: eumemic's PR543/493 construction and checker; Dylan Crow, DaysSky, Chafik Boukhalfa, Zhihao Chen, DreamingOfClouds and the cumulative predecessor lineage detailed in the README. Prepared by Mikhail R. Gadelha (@mikhailramalho) with substantial OpenAI Codex assistance, under Apache-2.0. No independent human review claimed.

[Mister-Meeseeks]

The 20-PR pilot triaged 23dcb610c2b156b76b9d599ea296c3cbde224b2d and is leaving this PR open for focused follow-up.

Remaining maintainer review: Replay unchanged command in existing Linux/Boost-capable environment; then review generalized D interface and C++ controls. Local failed compilation is an environment limitation.

This is a bounded-review disposition, not a rejection or a request to repeat unrelated full-suite checks. Pilot record. Your contribution and original attribution remain in the queue ledger.