Finite bit construction: R439 frame520 uses 29 ADDs, four fewer complete ADDs than PR844 (no new kappa)

[RossRichardson]

Finite bit-supplier construction; no new κ. The selected PR589 R439 phase-B frame520 block (B[242:283]) falls from 41 to 29 ADDs. Charging its literal reverse cleanup reduces the complete word 24,305 → 24,281 ADDs. This is four fewer complete ADDs than Gautam Gupta's prior PR844, whose 31-ADD candidate is retained verbatim and independently replayed.

The exact ordered integer map, all 661 register frame paths, 439 dirty helpers, nine rank-seven copies and paid rank mass 5,129 are preserved. Forward prefix stays 49,347; reverse prefix decreases 1,113,070 → 1,082,278; payload remains 93 bits under 104. Full source H1–H5 holds unchanged. Versus PR844, two positive-reverse entries grow, while the complete bound decreases; entrywise domination is claimed only versus original PR589.

The whole-block factorization crosses PR844's fixed-factor boundary and permits repeated destination writes, outside PR891's single-write restriction. PR844 also tried the same mixed row/column factor class unsuccessfully. This search adds the exact diagonal-at-least-one admissibility guard (subtractions cannot recover a lost diagonal) and six priority policies, rather than extending the old sampler's budget. Seed 05 stopped at 1,833 trajectories with 372 exact shorter factorizations; no optimum or exhaustive class coverage is claimed. PR904's overlapping one-ADD rewrite is separately compared.

Reproduce from the repository root:

python3 -I -B research/r439-frame520/verify.py

Expected: PASS_R439_FRAME520 block=41->29 ADDs=24305->24281 columns=661 rank_mass=5129 controls=9 no_new_kappa.

Validation completed: exact integer/signed-inverse matrices, all 4,096 local Boolean inputs, independent arbitrary-dirt full-word replay, original E8/frame/interface checker, nine controls, twelve package tests including isolated optimized relocation, deterministic search regeneration, and fresh unchanged C++ legality/5/9/11-stage checks on both words (883/1,327/1,549 columns; all 96 omitted-bridge controls rejected). Native and Python bills/payloads agree. make selected-record-check and staged whitespace checks pass. Exact receipts, source pins, search limits, environment and scope are included.

Only research/r439-frame520/ is added, from exact base 91a2094. PR589 source: a5afc8c. PR844 comparison: dee2c7d. Main remained at the base on final fetch; recent PR metadata through #922 showed no further frame520 construction. No pinned coordination issue existed, so the claim is local.

No full repository suite, changed whole-hosted invoice/outer assembly, selected cold replay, or formal multiplication theorem is claimed. The selected conditional κ remains 0.001661634653669567; its complex supplier binds. All inherited compiler/realization/hosting/precision/tape/analytic assumptions remain. No upstream, selected record, ledger, or other contribution is changed.

Prepared by Ross Richardson (@RossRichardson), with substantial OpenAI Codex assistance, including scoped AI-agent review; no independent human review claimed. Credit: Gautam Gupta PR844, Aaron Wang PR891, Gareth Davidson PR904, DreamingOfClouds PR589 over eumemic PR555/543, Ali Romman/Alluri's native harness, and the retained Dylan Crow/DaysSky/Zhihao Chen construction/checker lineages. Apache-2.0; exact attribution is in NOTICE.md.

Published head: 7287ea1. The final commit only records the sprint result/link; implementation is 76d3fde. All five hosted workflows on the final head currently report action_required, including Verify research artifacts. No hosted CI pass is claimed. The PR is open and has not been merged.