Finite bit construction: R480 Q-node2 saves 18 ADDs (no new kappa)

[ToikY]

Change and mathematical scope

One twelve-source Q-node in the historical PR503/510 R480 word now uses 43 instead of 52 XORs. Rebuilding its literal reverse cleanup saves 18 complete local ADDs: 33,958 → 33,940. The 480 arbitrary dirty helpers, 9 COPY/ERASE pairs, every register frame path and paid recursive histogram are unchanged. Finite bit-supplier construction; no new kappa.

The replacement preserves fixed F2 outputs on arbitrary inputs. Local forward positive growth increases 25 → 99, so a gate-count or local-domination argument would be insufficient. Complete chronological replay instead gives F = 176,135 unchanged and B = 3,751,204 → 3,682,548; the exact payload remains 102 bits within the inherited 104-bit allowance. No integer-transfer equality is claimed.

Only research/r480-qnode-seed02/ is added. It contains the exact 43-gate recipe, bounded search census, two separate whole-word implementations, unchanged-checker native receipts, source pins, proof/scope, attribution and negative controls. Exact base: 407d52ff15b2217b6e22bce44728b4c3907b6515. Fresh OS assignment seed 2, bit-supplier track. The final search replays exactly 1,000 trajectories; trial 860 gives the unique 43-XOR witness encountered. No optimality claim. Preliminary Q-node1/8 orientation probes are disclosed separately and are not admitted constructions.

Validation

From the repository root with Python 3.10+:

python3 -I -B research/r480-qnode-seed02/verify.py --replay-search

Expected: PASS_R480_QNODE_SEED02 block=52->43 ADDs=33958->33940 columns=720 payload_bits=102 no_new_kappa.

Completed locally:

• All 4,096 Boolean block inputs/inverse and all 720 persistent columns; exact output labels, per-register paths and complete positive bounds checked independently. Independent native-record reconstruction matches the unchanged exporter for both words.
• 53 distinct adverse cases, including all 43 gate deletions and endpoint-valid controls that fail either the literal-cleanup cost contract or precision bound.
• Unchanged native legality and 5/9/11-stage replay: 960/1,440/1,680 columns per word and 96 rejected bridge controls; relaxed mutable-source, PR425 interface and all 672 frame Gram checks pass. C++ -O0 / Python -O produces exactly the same receipt as C++ -O2 / normal Python. Compiler: Apple clang 21, Boost 1.87.0; portable reproduction command in README.
• Four package regression groups, including optimized offline minimal-copy replay and corruption controls; all 21 source blobs/hashes; selected-record integrity and its 25 tests; staged whitespace check.

Refreshed main f4a7051883bc76dad7861b3f0caf7361ce86fe90 preserves all consumed source blobs and the selected PR942 record (0.001661960547713947, unchanged PR589/555 bits). Open PRs refreshed through #999, plus all-state R480/Q-node searches. #823 is the related six-wire R480 quad1 result; #980, #986 and #989 concern R439. No combination with their savings is claimed. No coordination issue was available; the local claim contains the result and contribution link.

Remaining work for adoption includes a global hosted-parent invoice, supplier binding and outer assembly, plus inherited all-size/compiler, common-label/mutable-source realization, precision/tape/recovery and analytic obligations. No repository-wide suite, selected cold replay, hosted CI success or full multiplication-theorem formalization is claimed.

Credit: eumemic (#493), DreamingOfClouds (#503/#510), Hao Yan (#823), Jeffrey Cox (#754), Gareth Davidson (#904/#952), Ross Richardson (#936/#925), Ali Romman (#688), the #857/#906/#980 precision-admission precedents and retained native-checker contributors. Prepared for ToikY with substantial OpenAI Codex assistance, including separate AI implementations and review; no independent human review claimed. Apache-2.0.