Research: reduce R420 block 5 from 46 to 34 XOR gates (no new kappa)

[x0hu]

This finite bit-circuit contribution reduces block 5 of eumemic's PR543 R420 word from 46 to 34 XOR gates. Regenerating literal cleanup saves another twelve gates, reducing the full native word from 26,916 to 26,892 scalar ADDs. It is a research contribution / finite circuit improvement, with no new kappa claim.

Five explicit sum-sharing rewrites preserve the exact integer forward map on the same twelve registers. The reverse cancellation-free matrix is entrywise no larger for every nonnegative starting-bound vector. Full native replay preserves all 660 symbolic input columns, arbitrary helper dirt, every register's frame path, 420 helpers, nine copies and rank mass 5112. The reverse prefix bound falls from 2,270,064 to 2,229,592; the rounded prefix charges are unchanged.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. PR543 source: 2065fe4f72a914d907f1046603f5a36f17018535. Only research/r420-block5-resynthesis/ is added. Exact source pins, matrices, operation recipe, certificate, scope and attribution are included.

python3 -B research/r420-block5-resynthesis/verify.py

Expected: PASS_R420_BLOCK5_RESYNTHESIS block=46->34 native_adds=26916->26892 rank_mass=5112 kappa=unchanged.

Validation passed with the standard library on macOS using Python 3.12.13, 3.13.12 and 3.14.3. Checks include the pinned predecessor E8/frame/dirty-column/interface audit, an independent record interpreter in both directions, six circuit/interface controls and four record controls on each word. Optimized Python is refused. The selected-record binding and whitespace checks pass. A separate Codex reviewer found no mathematical or accounting blocker and independently checked all 4096 block inputs.

This package stops at the block and complete native word. Full C++ multistage replay, hosted invoices, outer assembly, repository-wide make verify, Lean and remote platform execution were not run. The inherited all-size/compiler/physical/hosting/precision/tape/analytic assumptions remain. Integration into a supplier still requires its normal complete replay.

The final overlap refresh found concurrent #670 at 2e31fcad7f9ecc8b97039ecb2333e581fd725fa1. That work changes the separate 50-gate block 3. This PR contributes a distinct block-5 replacement; their composition is not claimed here. #661 fixes the gate stream and explicitly excludes resynthesis. No pinned coordination issue existed, so the seed-5 claim and completed result link are recorded locally.

Credit remains with eumemic, Dylan Crow, DreamingOfClouds and the inherited supplier/accounting authors named in the README. Prepared for x0hu with substantial OpenAI Codex assistance, including separate verification and review workers. Apache-2.0; no independent human review or full multiplication proof is claimed.

[Mister-Meeseeks]

Integrated at ee055dc44815497927ef618fc985b93c2dcbda2a in the 20-PR pilot, retaining your original commit, source notices and contributor credit.

Block 5: 46→34 XORs, 24 saved including cleanup. Integer forward equality, reverse majorant domination, frame paths and all dirty columns checked. No hosted supplier or composition with #670 claimed.

The scoped package check passed at 1b01fd8b135fb2c458554fbbbab4338336bf366d. This is research integration; the selected κ and inherited theorem assumptions are unchanged. Review, evidence and attribution. Thank you for the contribution.