Research construction: R439 block 8 saves ten ADDs within the existing payload cap (no new kappa)

[zeusinsight]

Finite bit-supplier construction; no new κ. Whole-block nonnegative integer factorization shortens PR589's tuned R439 phase-B block 8 (B[404:449], frame 523) from 45 to 40 additions. Rebuilding its literal reverse cleanup reduces the complete native word from 24,305 to 24,295 ADDs.

This deliberately trades precision headroom for a smaller circuit: the forward bound remains 49,347, the reverse bound grows 1,113,070 → 1,228,514, and the complete native payload envelope grows 93 → 94 bits, strictly within the unchanged 104-bit cap. The exact forward integer map, all 661 register frame paths, 439 helpers, nine retained copies, paid histogram and rank mass 5,129 are preserved. No improved recursive moment or multiplication exponent is claimed.

Reproduce with:

python3 -I -B research/r439-block8-integer-factor/verify.py
python3 -I -B research/r439-block8-integer-factor/native.py

The second command needs C++17 and Boost. Completed validation includes all 4,096 local Boolean inputs, 661 arbitrary-input columns, the original H1–H5 interface, independently interpreted exported records, ten corruption controls, and fresh unchanged native legality and 5/9/11-stage checks on both words: 883 / 1,327 / 1,549 columns, with 96 bridge-omission controls rejected. Python/C++ prefix bounds and paid profiles agree. Optimized Python, minimal-source relocation, source/certificate mutation checks, deterministic search regeneration and selected-record integrity pass. Exact certificates and environment details are included.

OS assignment seed 18, bit track. A bounded 5,000-trial search completed 333 identity factorizations and found no shorter reverse-dominated candidate. One pivot reused exactly those trajectories and allowed reverse growth subject to the complete native cap, yielding the frozen 40-gate witness. This is sampled coverage, not an optimality or impossibility theorem.

Base f567884aeb8851b6e794af1184119a3bfbe1e631, selected PR799/PR589 conditional κ 0.001661634653669567. Supplier head a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46 and all consumed files are pinned. Only research/r439-block8-integer-factor/ is added; upstream and selected inputs remain unchanged. No full hosted invoice, global assembly, broad regenerating suite, selected cold replay, Lean or remote CI success is claimed. Inherited realization/compiler/hosting/precision/tape/analytic obligations remain.

Overlap refreshed through #856. #844 changes R439 block 4 using a fixed-factor class; #843 changes frame 509; #810 changes historical R420 block 8; #728/#792 change A mini-nodes. This changes the full positive factorization of the distinct punctured block without preserving its two-factor boundary. Their implementations and savings are not imported. No pinned coordination issue exists, so the scope claim and result are recorded locally.

Credit eumemic, DreamingOfClouds, Dylan Crow, mtpsl (whose PR691 verifier structure is adapted with attribution), and the retained supplier lineage. Prepared for @zeusinsight with substantial OpenAI Codex assistance, under Apache-2.0. No independent human or subagent review is claimed.