Research: factor center quarters and certify the adapter-cost limit (no kappa)

research/complex-center-quarter/CLAIM.md

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+# Local sprint claim
+
+- Contributor: @ssteeper, with substantial OpenAI Codex assistance.
+- Track: complex supplier. OS-random assignment seed: **35** (one cryptographic
+  random byte, rejection sampling above 199, then reduction modulo 100).
+- Exact base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+- Selected result: #626, `660de893d27bb7abd1d5b01b1640207528a5c851`, on
+  #622/#623 and #543; selected kappa `51110230636731/31250000000000000`.
+- Claim: factor the common quarter coefficient in the eight copied-center
+  scatter/gather blocks of the selected CK and JP8 local programs. Scale the
+  disposable center once at frame zero and use signed unit additions. Preserve
+  the paid center child and every private clear. No new kappa is proposed.
+- Method: exact symbolic boundary maps on arbitrary persistent and private
+  inputs; explicit binary-Horner primitive recount; native frame/wrapper replay;
+  positive prefix bounds; missing-scale, sign, clear and frame controls.
+- Seed diversification: `35 % 2 = 1` selects JP8 first; `35 % 8 = 3` selects
+  center 3 for the first local witness and adverse controls. Extend only to the
+  complete eight-center template and the identical CK interface, not a new
+  repository-wide search.
+- Expected deliverable: a self-contained finite circuit research package with
+  a read-only reproduction command, exact receipt, source pins and proof.
+- Expected finish: 2026-10-13 05:56 UTC (2026-10-12 22:56 America/Los_Angeles).
+
+## Selection and coordination
+
+Three narrow candidates were considered:
+
+1. Fixed-boundary JP8 B-frame reassignment: close to #698's CK-frame census,
+   and expensive to distinguish within this session.
+2. Sharing JP8 cleanup coefficient work: active #722, #739 and #751 work
+   already covers equal magnitudes, dyadic rescaling and reverse Horner.
+3. Factoring quarter coefficients in disposable copied centers: selected.
+   This changes a center scatter/gather block across multiple scalar macros,
+   while retaining all center children and using the original macro lowering.
+
+GitHub's pinned-issue query returned no issues. The only open ordinary issue was
+#650 (Discussions), so no reservation issue or unrelated comment was created.
+The initial overlap inspection covered all open PR metadata through #751,
+including bodies mentioning centers, scalar lowering, cleanup and gathering.
+#750 relocates a live CK cleanup scale; #696/#723/#734 change within-macro
+coefficient lowering; #749 changes the compensation target basis; #745 audits
+arbitrary private-center inputs. These are related but distinct. No pending
+implementation or result is imported. The accepted review ledger ends at #626.
+
+Prior negatives inspected include #687's fixed K-triangle relocation census,
+#651's delivery/hosting rigidity and #719's fixed-middle cleanup rank-two
+obstruction. None concerns the scalar quarter factor in a private, already
+paid center stream. This experiment changes no copied-information rank cost.
+
+## Result
+
+Completed 2026-10-13 05:33 UTC (2026-10-12 22:33 America/Los_Angeles).
+Submitted as [PR #786](https://github.com/CrocSwap/integer-mult-bounds/pull/786).
+
+All eight centers of both selected providers in both orientations are covered.
+Factoring the quarter saves 864 real scalar primitives per program. The complete
+local accounting exposed a limitation: eight new scale macros add 128 generic
+adapter allowances, increasing each conservative local bound by 3,319,594,144.
+The experiment stops at this finite circuit construction and scoped cost audit;
+there is no net supplier-cost or kappa improvement claim.
+
+The complete original/candidate scalar boundaries pass on 724 arbitrary inputs.
+All 32 primitive block pairs, 32 new rejection controls, 50 inherited native
+controls, 57,600 independent integer-matrix entries, 32 clear omissions and five
+focused failure tests pass. Source/receipt corruption, portable minimal-checkout
+and gzip-repackaging controls also pass. See VALIDATION.md for execution limits.
+
+Final overlap refresh: 602 open PRs through #783. Main still equals the exact
+base. Concurrent #755 (`a1dd9f819102c40e0b5e4a75215cf69ee864f480`) is credited
+for forward JP8 center coefficient reuse. This adds reverse gathering, CK
+coverage, recursive-input equality and the extra-macro accounting limit while
+retaining per-addition work clearing; no priority or stronger saving is claimed
+for the shared forward taps. #769 concerns CK cleanup/preconditioning and #776
+fixed-order A/B frames. Neither overlaps the changed center circuit. No pending
+source was imported. No pinned coordination issue was found, so this is the
+single local claim/result update.