[RossRichardson]

Finite bit-supplier construction; no new kappa. Replace the selected PR589 R439 word's phase-B frame-519 block B[163:205] with two exact integer-map schedules using 16 + 16 rather than 19 + 23 ADDs. Rebuilding its required literal reverse cleanup saves another ten ADDs: the complete local stream falls 24,305 → 24,285.

The twelve source registers and all 661 frame paths are preserved. No helper, COPY, MOVE or recursive child is added; nine COPY ranks, paid profile and rank mass 5,129 are unchanged. Forward positive bound stays 49,347; reverse bound falls 1,113,070 → 1,031,082; payload remains 93 bits under the inherited 104-bit cap. The local reverse positive matrix is entrywise dominated (22 strict entries).

search.py exhausts each fixed factor's destination-once, distinct-positive-donor class. A separately written integer subset-sum/backward Bellman verifier imports no search code and independently confirms the 16+16 class minima over 8,192 states / 49,152 state-destination pairs. The class does not cover unrestricted XOR synthesis or arbitrary cuts/factorizations.

Reproduce with standard-library Python 3.11+:

python3 -I -B research/r439-frame519-seed02/verify.py

Expected: PASS_R439_FRAME519, adds=42->32, local_ADDs=24305->24285, minima=16+16, columns=661, boolean_inputs=4096, controls=11, reverse_bound=1031082, payload_bits=93, no_new_kappa.

Executed validation: exact integer factor/product maps, all 4,096 Boolean block inputs, full 661 dirty-input columns, the owning H1–H5 interface, complete exporter invoice, normal/optimized Python, byte-identical candidate regeneration, and source/certificate corruption rejections. Unchanged native legality and five/nine/eleven-stage checkers pass for both words on 883 / 1,327 / 1,549 columns, including 96 omitted-bridge controls and three record-corruption controls. native.py reproduces the retained native certificate with C++17 and Boost headers. Source pins, exact certificates, proof of the finite search class, attribution and executed validation are included.

Base f567884aeb8851b6e794af1184119a3bfbe1e631, assignment seed 02, bit-supplier track. Reviewed source heads: PR589 a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46, PR799 80e6463157cfc80b85af09e7e2f14748fe2dac60. Only research/r439-frame519-seed02/ is added; selected inputs and upstream/ are unchanged. No pinned coordination issue exists, so the claim/result are recorded locally.

Overlap refreshed immediately before submission. Aaron Wang's PR891 reports a whole-block single-write obstruction at frame 519; this construction permits realization in each of two fixed factors and supplies a witness outside that class. Gareth Davidson's concurrent PR904, inspected at 883a0bdf7792693e57c16be660824b57aacfbe05, saves one forward ADD in overlapping B[200:204]; this result saves ten across the whole block and adds exact factor minima. No combined saving or import of pending code is claimed. Gautam Gupta's PR844 and Aaron Wang's PR873 provide related scheduling methods on distinct frames and are credited.

Credit eumemic (PR543/PR555), DreamingOfClouds (PR545/PR589), Dylan Crow, DaysSky, Zhihao Chen, Jeremy Kothe, Chafik Boukhalfa and the retained construction/checker lineage. Prepared by Ross Richardson (@RossRichardson) with substantial OpenAI Codex assistance, Apache-2.0. No independent human review is claimed.

The rank moments and selected conditional kappa 0.001661634653669567 are unchanged. Full repository/global hosting/outer assembly/selected cold replay and Lean theorem checks were not rerun; no fresh global bound is claimed. The inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic assumptions remain. Remote CI is separate from the completed local checks.