Bit supplier: save 254 R439 ADDs with four-wire prefix resynthesis (no new kappa)

[bitplane]

The selected PR589 R439 word contains same-frame prefix windows that admit shorter exact XOR circuits. This adds 95 disjoint A/B replacements and their required literal reverse cleanup, saving 254 exported ADDs: 24,305 → 24,051. The original H1–H5 interface, all 439 dirty helpers, nine copies and paid rank mass 5,129 are preserved. Finite bit-supplier construction; no new κ.

Complete local quantity	Baseline	Candidate
A additions	2,130	2,015
B additions	934	922
C additions	2,629	2,502
D / scatter additions	18,085 / 527	18,085 / 527
Exported ADDs	24,305	24,051
Forward positive bound	49,347	43,671
Reverse positive bound	1,113,070	928,888
Payload prefix bits	93	92

Every selected window uses the same physical source/helper registers at the same frame. Independent column-state enumeration checks all GL(2..4,2) states and 242,940 directed edges; each nominated circuit attains its unrestricted local group distance. Both-order positive matrices are entrywise dominated. The unchanged source checker accepts both full words on 661 arbitrary input columns, including all helper dirt, and checks literal H4 explicitly.

Reproduce with Python 3.12+, a C++17 compiler and Boost headers:

python3 -I -B research/r439-four-wire-prefix/verify.py
python3 -I -B research/r439-four-wire-prefix/test_package.py -v

Complete replay passed on CPython 3.14.4 and on an isolated optimized CPython 3.12.3 read-only minimal closure with spaces in its path. Their full deterministic receipts match exactly. Unchanged native legality and 5/9/11-stage checks pass for both words on 883 / 1,327 / 1,549 columns, with 96 omitted-bridge controls rejected. Twelve additional mathematical controls and eight package tests pass. Regenerated gzip artifacts are compared by every decoded field. All 12 source pins match the base Git objects; the word/checker also match original PR589 objects.

The bounded seed-11 search covers 3,296 original windows, nominates one deterministic shortest representative per map, accepts 264 guarded nominees and selects 95 compatible intervals. No global circuit optimum, exhaustive search over all shortest representatives, composition with other candidates, or full hosted repricing is claimed. Saved ADDs per 5/9/11-stage word are 1,270 / 2,286 / 2,794; bridge/copy bills are unchanged. The inherited payload ceiling remains 104 bits. The selected #799 κ remains 0.001661634653669567, with its existing all-size/compiler, realization, hosting, precision/tape and analytic obligations.

Credit: Jeffrey Cox (@namredips), PR754, for exact small-GL, positive-guard and interval resynthesis; this applies that method to selected R439 A/B with paired literal H4, whereas PR754 treated historical R420 C under semantic H4′. DreamingOfClouds PR589 tunes eumemic PR555/543, following the retained PR545/493/510/425/370 lineage. Native harness credit Sagar Thakrar; unchanged exporter/checkers credit Dylan Crow, DaysSky, Zhihao Chen, and their retained notices. Related PR792/886 and whole-block PR844/873/880/884/857/891 have different finite classes; no combined saving is claimed.

Only research/r439-four-wire-prefix/ is added, against refreshed base f567884. The claim, exact source hashes, proof, full certificate/candidate, reproducible receipts, validation and licenses are included. Full repository/cold-supplier/outer-assembly replays and formal verification of the multiplication theorem are not claimed. Hosted CI is reported separately after publication.

Prepared for Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance. One AI agent performed this work; no independent human review is claimed. Apache-2.0.

Published head: 883a0bd (mathematical content at 33b9175; final commit only records the result/link in CLAIM.json). Remote commit and all 15 changed paths were verified. All five hosted workflows report action_required, awaiting maintainer approval; no hosted pass is claimed. Research artifact workflow.