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Mister-Meeseeks merged 2 commits into from
Oct 14, 2026
Merged

Research construction: cyclic output frames reduce restoration (no new kappa) #1287

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ecbc47c
Research: cyclic output frames reduce fixed-reader restoration
Oct 13, 2026
8606df0
Document verification, overlap and completed sprint claim
Oct 13, 2026
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304 changes: 304 additions & 0 deletions research/cyclic-output-restoration/CERTIFICATE.json
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{
"admission": {
"admitted": 27,
"matrices": 19683,
"rejected": 19656
},
"base": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8",
"boundary": {
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"k": 1,
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{
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"k": 4,
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"schedules": 59049
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"price_comparisons": 100,
"scaled_price_checks": 150
},
"controls": [
"missing_source_uncopy",
"forward_instead_of_inverse_batch",
"missing_dirty_cancellation_pass",
"omitted_output_three_cycle",
"omitted_workspace_exit",
"missing_cycle_ADD",
"non_equivariant_reader_rejected",
"unchecked_non_equivariance_changes_map",
"premature_canonical_observer",
"nonlinear_dirty_echo"
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"depth_three": {
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"inverse_arbitrary_input_l1_peak": 80,
"invoice": {
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"status": "PASS_CYCLIC_OUTPUT_RESTORATION"
}
66 changes: 66 additions & 0 deletions research/cyclic-output-restoration/CLAIM.md
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# Local sprint claim — recursive interfaces, seed 56

Claim recorded 2026-10-13T21:28:50Z; expected finish 22:04:30Z.
Exact base: `dadfea6e8a78ff6ba901705f87532a71c6f5bbb8`.
OS assignment seed: **56**. Scope: cyclic-output-restoration/order-three/fixed-readers.

Three candidates were considered:

1. Nonzero-reader restoration coalescing: covered by PR1199, PR1203 and PR1205.
2. Higher-arity dirty connectors: PR1164, PR1185 and PR1215 already cover close alphabets.
3. **Selected:** replace paid workspace three-cycles by output three-cycles for fixed readers with `R P = Q R`. Unlike sign drift (PR1227), non-scalar drift imposes a substantive admission condition. Verify that gate and solve the complete-register boundary problem, then include both echo passes and recursive children.

Method/domain: exact integer block-circulant readers, `N=3m`, `d=3n`;
all nine reduced boundary choices per gap through four children;
all 19,683 ternary 3x3 reader matrices for admission; exact emitted forward/inverse maps and priced recurrence over bounded trees. The seed selects `m=2+56%5=3`, `n=1`, `k=4+56%5=5` and deterministic matrix coefficients. No broad circuit or selected-supplier search.

Optimistic complete boundary bill at the fixture: eager 30 SWAPs per batch,
shortest order-three frame path 16 SWAPs. Both echo passes are required,
so at most 28 SWAPs saved with all readers and source copy/uncopy unchanged.
The source permutation inside every child remains charged. Fail if literal
all-dirty-state replay or full pricing negates that saving.

Expected artifact: one scoped research construction, written interface proof,
exact deterministic certificate, separately represented boundary/admission
checks, scalar/tape invoices, negative controls and reproducible package.
No selected kappa change or physical supplier admission is proposed.

Coordination: no pinned sprint issue exists (live GraphQL check). Per the
user's fallback, the claim is local. Complete overlap snapshot at
21:27 UTC covered 859 open PRs and 24 discussion records including comments;
queries for cyclic restoration/output rotation/equivariant/intertwiner/
permutation frame had only unrelated PR508/325 hits. Read discussion1163,
1166,1167 and relevant current claims. This is bounded overlap evidence,
not a proof of novelty. Relevant PR1227/1203/1205 full descriptions were read;
PR1227's complete README was read. No delegated workers.

Predecessors: Sagar Thakrar PR1227 and PR1199, Aaron Wang/Navinor PR1155,
mightyOil/Philipp PR1203, Adam Gall PR1205, Ross Richardson/CubeJerry PR889.
Prepared by Ross Richardson with substantial OpenAI Codex assistance.

## DONE — 2026-10-13T21:45:03.216502+00:00

[Completed construction and replay artifact](https://github.com/RossRichardson/integer-mult-bounds/blob/ecbc47ccde755dfc4571a3d60da1eb334aa070cd/research/cyclic-output-restoration/README.md).
Implementation commit: `ecbc47ccde755dfc4571a3d60da1eb334aa070cd`; refreshed submission base
`b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c`.

The admitted order-three output-frame word reduces the complete five-child
echo from **588 to 504 signed ADDs**, restoring all incoming dirt. Final
pricing uses the known PR1145 six-ADD three-cycle in both words, replacing
the initial valid but nonminimal two-SWAP upper budget. The complete boundary
minimum is 15->8 triple rotations per batch; both passes save 84 ADDs.

All 66,420 gap words, 19,683 admission matrices, 192 recursive cases and
3,744 basis columns pass. Both direct and arbitrary-input inverse maps,
recurrences, access invoices, source pins, ten mathematical controls, seven
package test groups and five corruptions pass. Python3.12 registered replay
and Python3.9 agree; Python3.14 export is byte-identical. No new kappa,
physical supplier, full cold replay, total runtime or human review claim.
The deeper word increases travel and coefficient bounds; see VALIDATION.md.

Final complete overlap refresh at21:43 UTC covered871 open PRs and32
discussion records. PR1246 (`5ed1ce17a9df4c853a93f9758ba903d2620c3443`)
prices additive defect repair at canonical cuts, a different mechanism;
Hanson Sun is credited. PR1227's head remains pinned and has no comments.
No pinned coordination issue exists, so this updates the original local
claim once under the user's fallback. Claim released.
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