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

research/r439-block8-integer-factor/CLAIM.md

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+# Local sprint claim
+
+- Track: bit supplier. OS randomness assignment seed: **18**.
+- Base: `f567884aeb8851b6e794af1184119a3bfbe1e631`.
+- Started: 2026-10-13; expected finish within 45 minutes of scope selection.
+- No pinned coordination issue exists (GitHub GraphQL checked); the only open
+  issue is #650 about Discussions. Claim recorded locally as instructed.
+- Candidates considered: (1) whole positive-integer factorization of tuned R439
+  B block 8, (2) phase-A quad 18 resynthesis, (3) cleanup frame reduction.
+  Choose (1): (2) closely repeats existing quad work and (3) is excluded by
+  #827's fixed-prefix result. Seed 18 selects block 18 modulo 10 = 8.
+- Exact object: PR589 tuned R439 B[404:449], frame 523, twelve wires.
+  Search full-block nonnegative integer row-subtraction factorizations, without
+  preserving the predecessor's two-factor boundary. Require the same forward
+  integer matrix and entrywise nonincreasing reverse positive matrix.
+- Deliverable: one literal circuit witness, exact verifier, paid restoration
+  and source/access/frame accounting, mutation controls, and a scoped note.
+- Overlap checked through PR854, all open PR titles and relevant bodies.
+  #844 changes R439 block 4 with fixed-factor destination-once optimization;
+  #810 changes historical R420 block 8; #728/#792 change R439 A mini-nodes;
+  #827 concerns cleanup frames, not scalar factorization. This investigates a
+  different whole-block search class on the punctured word, imports none of
+  those pending implementations, and will not add their savings to ours.
+- Selected result: #799 with #589, conditional kappa 0.001661634653669567.
+  This experiment claims no new kappa and will not edit the selection.
+
+## Result update
+
+The 5,000-trial strict search produced no shorter reverse-dominated circuit
+among its 333 identity factorizations. One pivot kept exactly the same sampled
+trajectories and allowed a larger reverse positive bound subject to the full
+existing 104-bit native cap. The resulting 40-gate block saves ten ADDs with
+cleanup; the native envelope grows from 93 to 94 bits. No moment/kappa change.
+The full search coverage, witness, exact controls and replay are packaged here.
+
+Final overlap refresh: all open PR metadata through #856 on 2026-10-13;
+#843 (head c99f4478156906c323b1a041f0443f76139d6b6c) changes frame 509,
+#844 (dee2c7d506312d2e555a59fb0916c161b4e64028) changes frame 520, and
+#848 (510441077c17ad775003b22fca03a519f5330453) is a sharing barrier.
+No block-8/frame-523 substitution found. No pinned coordination issue exists
+on the final check either. Main remains the exact experimental base.
+
+Submitted result: [PR #857](https://github.com/CrocSwap/integer-mult-bounds/pull/857).
+Local and native verification passed; detailed evidence and limitations are in
+`VALIDATION.md`. One focused PR submitted; no selected-frontier change or merge.