Mister-Meeseeks · Oct 14, 2026 · Oct 13, 2026 · Oct 13, 2026
diff --git a/research/complex-temporal-pair-seed28/CLAIM.md b/research/complex-temporal-pair-seed28/CLAIM.md
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+# Local sprint claim
+
+- Track and seed: Complex supplier, OS seed 28 (`secrets.randbelow(60)`).
+- Base: `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`.
+- Object: compose the separately optimized dyadic temporal schedules for helpers L348 and L359 on the selected PR1094/PR1263 complex word. They share ADD event 24336.
+- Proposed method: seed 28 chooses index `28 mod 2 = 0` from the two zero-static helper pairs whose individual all-integer schedules both improve and are nonzero at a shared ADD. Compose those exact single-coordinate minima, then compare the complete exact invoice against the sum of separate deltas.
+- Expected deliverable: source-pinned finite circuit package with exact schedules, shared-ADD correction, both complete invoices, both 712-column replays and negative controls. No joint optimum or new kappa claim.
+- Expected finish: 2026-10-13 23:57 UTC.
+- Coordination: no pinned sprint coordination issue found; claim recorded locally.
+
+Candidate tasks and overlap details are in `research/seed28-complex-reroll-20261013/ASSIGNMENT.json`.
+
+## Final result and handoff
+
+Result completed on 2026-10-13. For the seed-selected pair L348/L359, both separate exact minima are improving and active together at ADD 24336. Their solo deltas total -403 real; the shared coefficient contributes a +3 real cross correction, leaving -400 real / 800 complex saved per orientation. The complete invoices, all-scale accounting, paid-profile check, 712-column replays and three controls are recorded in `RESULT.json` and `PROOF.md`. No joint optimum or new kappa is claimed.
+
+The final overlap refresh found PR #1380, which addresses the same general shared-ADD mechanism but certifies a disjoint finite pair set: all 16 pairs in its certificate contain L225, and none is L348/L359. This contribution adds the distinct PR1369 zero-static pair and composes its exact one-coordinate minima; it does not claim PR #1380's joint-optimality result. PR #1376's L248/L253 schedules have disjoint ADD supports.
+
+Submitted as [PR #1388](https://github.com/CrocSwap/integer-mult-bounds/pull/1388), an additional-pair finite certificate with no selected-result or kappa change.
diff --git a/research/complex-temporal-pair-seed28/LICENSE b/research/complex-temporal-pair-seed28/LICENSE
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diff --git a/research/complex-temporal-pair-seed28/NOTICE.md b/research/complex-temporal-pair-seed28/NOTICE.md
@@ -0,0 +1,5 @@
+New composition code and result are Apache-2.0. The selected predecessor files
+under `vendor/pr1369/` are retained from CrocSwap/integer-mult-bounds PR #1369,
+commit `f28e1c460cd910886f9b06835abd6b1c96d2992f`; its NOTICE and source pins
+are included. Nested PR1263/PR1161/PR1259 sources retain their attribution and
+notices. No upstream or frozen source file was modified.
diff --git a/research/complex-temporal-pair-seed28/PROOF.md b/research/complex-temporal-pair-seed28/PROOF.md
@@ -0,0 +1,71 @@
+# Finite paired temporal-gauge certificate
+
+## Predecessor word and domain
+
+The verifier pins and replays PR1369's zero-static temporal census on base
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`, then recovers the exact PR1263
+static word in both orientations. The eligible zero-static helpers are
+
+`[272,288,348,359,381,440,444,446,447,469,478,479,491,503,507,514,515,519,542]`.
+
+For each helper and orientation, the attributed exact integer DP optimizes its
+incident ADD sequence over the certified finite breakpoint interval. The
+verifier checks each new DP result against PR1369's frozen census. It then
+enumerates all 171 helper pairs, retaining pairs whose single-coordinate
+minima improve and are both nonzero at a shared ADD. The identical candidate
+list in both orientations is `[(348,359),(479,515)]`; seed 28 chooses its first
+pair.
+
+This search optimizes one coordinate at a time. It does not claim a joint
+minimum for the two-coordinate objective.
+
+In the final overlap refresh, PR #1376 covered a disjoint-support L248/L253
+composition. The concurrent PR #1380 covered 16 shared-ADD pairs, all with
+L225, including L225/L348 but not L348/L359. This certificate prices the
+distinct L348/L359 pair from the PR1369 zero-static domain; it does not
+duplicate PR #1380's joint-optimum claim.
+
+## Simultaneous composition
+
+At each original ADD, the composed coefficient is scaled by the product of
+the two selected dyadic gauge factors. Entry and transition scales, with a
+terminal restoration when the final gauge is nonzero, are emitted on their
+own helper lines at the original ADD frame. The full exact invoice prices
+every inserted scale and every changed coefficient;
+the complete replay checks both orientations on all 712 formal columns.
+
+For any shared ADD with original coefficient c, helper signs s1 and s2, and
+chosen exponents e1 and e2, its combined price change is
+
+`price(c * 2^(s1*e1+s2*e2)) - price(c)`.
+
+At event 24336 the exact data are:
+
+| Orientation | signs (L348,L359) | exponents | c | separate ADD deltas | combined delta | correction |
+|---|---|---|---:|---:|---:|---:|
+| Forward | (+1,-1) | (-1,3) | -8 | -1,-4 | -2 | +3 real |
+| Backward | (-1,+1) | (1,-3) | 8 | -1,-4 | -2 | +3 real |
+
+All other incident ADDs are disjoint between the two helpers. Therefore the
+joint invoice delta is `-161 - 242 + 3 = -400` real primitives, or 800 complex
+primitives. Literal lowerer invoices independently confirm 136002 to 135202
+forward and 136018 to 135218 backward.
+
+The candidate's paid profile and all non-scalar events equal the static word.
+The scale entry, transition, and any necessary terminal restoration work is
+included. Prefix ceilings remain 52 and 68
+bits under the existing 192-bit local charge. The selected exponent and
+supplier certificate do not change.
+
+## Controls and limits
+
+The verifier checks an all-zero schedule identity, rejects a candidate with a
+missing L348 transition scale, and rejects a shared-ADD coefficient mutation
+that omits the L359 exponent. These controls and the 712-column replay test the
+finite scalar map, not all-size hosting or supplier admission.
+
+The claim depends on the pinned PR1263 source word, PR1369 single-coordinate
+DP and PR1161 invoice/replay implementation. It does not show that this pair
+is optimal among all two-coordinate temporal schedules, that three or more
+gauges compose profitably, or that the operation saving changes the recursive
+profile or kappa.