Research: decoder source cosets save 244 R420 XORs (no new kappa)

[cxnmai]

Finite circuit research construction — no new κ

Change one decoder-total source representation in the accepted #543 R420 bit word, then recompute its dirty-input compensation and literal cleanup. 244 fewer binary XORs per local invocation: 26,916 → 26,672.

The total itself grows from 25 to 43 XORs; A and C together cost 36 more, but D saves 280. This is a distinct mechanism from #708: its full dirty operator stays fixed, whereas this candidate changes 93 helper-dirt columns and compensates them. No new helpers/copies/frame paths; all 660 register paths and local rank mass 5,112 are unchanged.

Reproduce

python3 -B research/r420-decoder-cosets/verify.py

Expected: PASS_R420_DECODER_COSET total=26916->26672 saved=244 columns=660 controls=6 no_new_kappa.

Standard-library Python 3.11+. Recipe, complete cost certificate, source pins, proof, attribution and validation receipt are included. --word /tmp/candidate.json.gz emits the complete candidate.

Evidence

• Seed 3, bit-supplier track; exact base 66849e1475c930fd7732b1a0067ffee7e1e95f60.
• Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 source pin 2065fe4f72a914d907f1046603f5a36f17018535.
• Original 80-operand pool has source rank 80; expanded 171 dead-register pool has rank 90/nullity 81. Bounded 32-trial descent scores 2,997 candidates and accepts five moves. No optimality claimed.
• Independent set-valued replay of all 660 dirty columns; original Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 checker verifies all 672 frames and H1–H5. Six meaningful negative controls.
• Original exporter emits 29,874 → 29,630 records. Forward positive bound unchanged at 144,651; reverse increases 2,270,064 → 2,301,524. Local payload envelope remains 100 bits below the 104-bit cap.
• Clean minimal archive replay, source-corruption rejection, optimized-mode refusal and whitespace checks passed on Linux/Python 3.14.7. Final static AI review found no issues; no independent human review claimed.

Scope and overlap

Only research/r420-decoder-cosets/ is added. No pinned coordination issue existed; claim is local. Final overlap check through #747 distinguishes #708 sharing, #731's fixed compensation-matrix kernel audit, #733's two-sided basis composition and #742's shared target donors. None is imported, composed, or claimed as our work. Savings from changed K must not be added to those constructions without another audit.

C++ multistage replay, hosted-parent/global invoice, changed outer assembly, repository-wide make verify, selected cold replay, Lean and remote CI were not run. Inherited all-size/compiler/common-label/mutable-basis/hosting/residual/precision/tape/analytic obligations remain. No stronger κ or practical runtime speedup is asserted; selected frontier and upstream/ are untouched.

Prepared by Chinmay Khaladkar (@cxnmai) with substantial OpenAI AI assistance, under Apache-2.0. Credit remains with eumemic's #543/#493, Dylan Crow's exporter/checker lineage, Zhihao Chen's #425 interface, #472's realization and the predecessor notices.

[Mister-Meeseeks]

100-PR batch review at 0ccc0b425d2b9667108d3a0918a5cfa0aa7a5861.

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

Reviewed scope: R420 decoder coset rewrite compensates the changed dirty-helper columns; 244 native XORs saved with unchanged frame profile.

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.