Finite R480 construction: 252 shortest quad12 circuits, 24 fewer ADDs (no new kappa)

[bbMisk]

The historical R480 quad12 uses 23 ADDs. This finite construction admits an 11-ADD replacement through complete local precision accounting, then rebuilds literal cleanup: 33,958 → 33,934 ADDs. No new kappa. Only research/r480-quad12-exact-seed12/ is added.

Prior result credited: PR1002's R439 frame272 is the same ordered circuit after relabeling. It already establishes the unconstrained 11-ADD and guarded 12-ADD minima. This submission adds the complete census of 252 shortest programs, their four reverse-transfer classes, and native admission in the historical PR503/510 R480 word. It does not claim a new minimum or combine other PRs' savings.

Every shortest program violates the local entrywise reverse guard in three entries, yet every class fits the complete 104-bit local envelope. All have forward bound 176,135; reverse bounds range from 3,723,720 to 3,729,576. The chosen class minimizes the reverse bound among these 252 programs and reduces the original 3,751,204 bound while retaining a 102-bit payload. The paid histogram, rank mass 5,592, all 720 register frame paths, 480 dirty helpers and nine COPY/ERASE pairs are preserved.

The row-subtraction DAG completes 868,423 states and 5,005,248 edges. A separate breadth-first implementation independently certifies minimum 11 and count 252. This fixes six wires and one positive integer transfer; it does not establish unrestricted XOR optimality.

Reproduce from the repository root with Python 3.10+ and its standard library:

python3 -I -B research/r480-quad12-exact-seed12/verify.py --replay-search

Expected: minimum 11, 252 shortest programs, four reverse classes, 33,934 ADDs, 720 columns, 20 rejected controls and no new kappa. The README includes the C++17/Boost native command and package tests.

Completed checks include all local Boolean inputs, exact signed inverses, both complete dirty-input orientations, all 672 frame Grams, source-bound mutable-source interfaces, independent/native record equality, native five/nine/eleven-stage replay on both words (960/1,440/1,680 formal columns and 96 rejected bridge controls), and optimized minimal offline replay with corruption controls. The selected-record check and its 25 tests pass. A single repository-wide make verify attempt in an untouched detached base was stopped at its 180-second limit in historical endpoint-gauge generation; no full-suite pass is claimed.

Base: 2921874911956718fcaaaf9396fe8267b3cfa9f0. OS assignment seed: 12, bit-supplier track. No pinned coordination issue exists; the local claim and overlap records are included. Source pins, exact receipts, proof and inherited obligations are packaged. Selected PR942/PR589 and upstream/ remain unchanged. Full hosted emission/invoice, supplier binding, outer assembly, all-size/compiler, realization, precision/tape and analytic obligations remain separate or inherited. No full multiplication-theorem formalization or remote CI pass is claimed.

Credit DreamingOfClouds, eumemic, Ross Richardson's PR925 search/checker, woklerx's PR1002 minimum, Ali Romman's native harness, Dylan Crow, DaysSky, Zhihao Chen, Jacob Sussman, mtpsl and Gareth Davidson. Related R480 work #823/#1003 and full-prefix admission precedents #857/#906/#980 are explicitly credited. Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance; one AI agent, no independent human review. Apache-2.0. Do not merge automatically.