Research construction: save 137 R420 cleanup XORs with exact four-wire synthesis

[namredips]

Finite bit-supplier construction — no new κ

Replace 101 disjoint windows of the selected #543 R420 cleanup with exact shortest XOR circuits on the same at-most-four registers. Cleanup costs 2,973 → 2,836 XORs; the complete local word costs 26,916 → 26,779 native ADDs. All 660 register frame paths, 420 dirty helpers, nine copies/erasures and the paid rank histogram remain unchanged. The native forward prefix decreases 144,651 → 109,173; reverse remains 2,270,064; the local payload envelope decreases 100 → 99 bits.

Reproduce

python3 -I -B research/r420-four-wire-cleanup/verify.py

Expected: PASS_R420_FOUR_WIRE_CLEANUP: 101 windows, 137 XORs saved; 26916 -> 26779 native ADDs; 8 negative controls rejected.

Python 3.11+, standard library only. --out /path/to/new-directory retains both complete words and their original-exporter records. The package includes source pins, all replacement circuits, proof and deterministic receipts. The optional native.py command recompiles the unchanged C++ checkers.

Evidence and precise scope

• Fresh OS seed 17, bit track; base 66849e1. Selected Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 source: 2065fe4.
• Exhaust all 7,693 original contiguous windows on ≤4 registers; 284 admit shorter circuits. Independent row/column implementations and start/end-time interval schedules agree that 137 is optimal within the disjoint-original-window model. No global circuit-optimality claim.
• Check complete GL(2–4,2) state sets and 242,940 directed distance-potential edges; all 1,408 local Boolean inputs and 756 positive-transfer columns pass. Every chosen rewrite has a nonincreasing positive transfer matrix in both orders.
• All 660 arbitrary-input columns restore, including dirty helpers. Fresh native legality plus 5/9/11-stage checks pass on both words (900/1,380/1,620 columns, 96 rejected bridge-omission controls). A relocated minimal source tree reproduces both commands.
• Eight mathematical/accounting mutation controls, source-corruption/incomplete-certificate/output-preservation controls, Python 3.11/3.14, Ruff, whitespace and make selected-record-check pass.

Literal cleanup reversal H4 intentionally fails; the proof and verifier use the explicitly stated semantic H4′ (C = U^-1 over F2 at the full frame), preserving the original guard. No global hosted program or outer assembly was regenerated. The selected conditional κ and upstream/ are untouched; inherited all-size/compiler/common-label/mutable-basis/hosting/residual/precision/tape/analytic obligations remain. No full multiplication theorem, practical runtime result, remote CI or Lean pass is claimed.

Credit and overlap

Credit eumemic's #543/#493, Dylan Crow's exporter/checker lineage and predecessor notices. Sagar Thakrar's #710 is the commuting-search/interface predecessor; its noncontiguous conjugations overlap two original gates, so no additive 139-XOR claim is made. #688, #742, new #748/#753 and updated #681 change different circuits; none is imported or assumed composable. This adds a complete finite synthesis class and independent certificates rather than another replay of their searches. There was no pinned coordination issue; the claim is recorded locally.

Prepared by Jeffrey Cox (@namredips) with substantial OpenAI Codex assistance, including a separate column implementation and scoped review. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 47ebba87e064cc69d9b4834081fc74080762a74f.

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

Reviewed scope: 101 fixed cleanup windows resynthesized exactly; 137 XORs saved, arbitrary-input endpoint unchanged. Optimality limited to those windows/alphabet.

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.