Finite bit construction: R439 frame 524 saves 28 complete local ADDs (no new kappa)

[RossRichardson]

Finite bit-supplier construction; no new kappa. Replace PR589's frame-524 phase-B block B[449:490] with 27 rather than 41 ADDs. Rebuild its required literal reverse cleanup: the complete local word falls 24,305 → 24,277 ADDs. The two original LU factors retain their exact integer maps and attain independently checked minima 12 + 15 in the destination-once positive-donor class.

All 661 register frame paths, 439 dirty helpers, nine COPY/ERASE pairs, H1–H5, paid profile and rank mass 5,129 are preserved. The forward positive bound stays 49,347; the reverse bound falls 1,113,070 → 1,057,838. Payload stays 93 bits under the inherited 104-bit cap. Every preparation, source read, frame transition and literal restoration is included; no helper or recursive child is added.

Reproduce with standard-library Python 3.11+:

python3 -I -B research/r439-frame524-seed13/verify.py

Expected: PASS_R439_FRAME524 block=41->27 ADDs=24305->24277 columns=661 inputs=4096 controls=6 no_new_kappa.

Executed validation includes exact integer identities, all 4,096 local Boolean inputs, all 661 dirty-input columns, the owning E8/frame/interface checker, full exporter invoice and byte-for-byte agreement with a separate record interpreter. A separately written nonnegative donor exact-cover/backward Bellman implementation imports no optimizer code and checks all 4,096 subsets / 24,576 transitions per factor, coverage/order counts and every witness metadata field. Nine factor and six word/invoice mutation controls reject. Normal/optimized Python, seven minimal-relocation/package tests, source/certificate corruption and output preservation pass.

Unchanged native C++17/Boost legality and 5/9/11-stage checkers pass on both words on 883 / 1,327 / 1,549 formal columns, with 96 omitted-bridge controls rejected. Exact deterministic certificates, source pins, proof, executed validation and toolchain details are included. make selected-record-check and staged whitespace checks pass. Regenerated gzip containers are compared by canonical decoded content and exact exported records.

Research/publication base f567884aeb8851b6e794af1184119a3bfbe1e631 selects #799/#589 at conditional κ 0.001661634653669567. Supplier #589 head: a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46. All 16 source/context pins match base Git objects; the word and three supplier source files also match original PR589 objects. Only research/r439-frame524-seed13/ is added. Assignment seed 13, OS randomness, bit-supplier track. No pinned coordination issue was visible; the narrow claim and result are recorded locally.

Final overlap refreshed through #912. Aaron Wang's #891 gives a whole-block single-write obstruction at frame 524; this witness permits one destination write in each of two fixed factors and lies outside that class. Related Gautam Gupta #844, Krishnendu Purohit #880, and Ross Richardson #908 cover distinct frames. Gareth Davidson #904 covers small prefix windows; this adds a full-factor witness and exact factor minima. Their code and savings are not imported or combined; no mechanism-priority claim is made.

Credit eumemic (#543/#555), DreamingOfClouds (#545/#589/#510), Dylan Crow, DaysSky, Zhihao Chen, Jeremy Kothe, Chafik Boukhalfa, Rohan Arun and retained predecessors. Prepared by Ross Richardson (@RossRichardson) with substantial OpenAI Codex assistance, including three scoped AI workers for search, independent arithmetic and package review. Apache-2.0; no independent human review claimed.

This is a finite circuit construction and restricted-class minimum, not unrestricted XOR optimality or a full multiplication theorem. The paid recursive profile and selected κ are unchanged. No repository-wide regenerating suite, selected cold rebuild, new hosted/global invoice, outer assembly, Lean or remote-CI pass is claimed. All-size/compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic obligations remain inherited. Hosted CI is separate from completed local verification. No merge or frontier change is requested by this contribution.

Published head: dba9199e8cbb0136bcba6b769c36753a61092190. Mathematical implementation/certificates are at 0da7010a11e59911f5386cbc61f35393532d072a; the final commit only records the sprint result and PR link. Final local replay passes. A clean binary patch applies to the exact base in an alternate index and reconstructs the published tree d5d5a1f61a8c72aa801b05cb445a7b605972512a.

All five hosted workflows at the published head report action_required, so no hosted CI pass is claimed. Research artifacts workflow.