CLAIM: scope map for retained complex E8 decoder lower bounds

[Arham-Tahir64]

DONE — PR #1626, head 46849a15a2812d3e0a9f0d2c4a9b86382d6cfe4e. Scope complete and released.

The focused documentation result distinguishes the real/complex eight-term all-pairs floors (PR968/1077), the real fixed-reader ninth-term exclusion (PR845), and the finite support lemma independently corroborated by PR1098. It preserves the distinction between term-rank sums, recursive moments and physical COPY admission, and retains exact reviewed-head credit.

Reproduction found a concrete stale route: the plain PR968 checker rejects current main only at its historical G.selected-record guard. The new documented recipe uses its existing --repo option, copies its hash-pinned pricing inputs into a temporary directory and selects the frozen #942 checkpoint there. The complete unchanged verifier passes, including 1,260 frames/896 admissible, all historical pricing and six controls. The source package and actual selected record are unchanged.

All five documented source-package checks pass on CPython 3.14.7; the historical replay and PR845 main check also pass on CPython 3.12.14. All 20 repository research-workflow tests pass on 3.12.14, 29 relative links/anchors resolve, all four reviewed disposition heads match, and selected/source/proof integrity and diff checks pass. The PR is open and mergeable; no hosted checks were listed at the final inspection. This is source-backed consolidation, not a new theorem, decoder, kappa or full supplier replay.

Started from main ee055dc44815497927ef618fc985b93c2dcbda2a; rebased onto refreshed 0a201997097b8a89b638f3a2afcb35db4184c8b2, with all consumed source packages, selected record and onboarding guidance byte-identical. Final overlap refresh covered 734 open PRs and 259 Discussion records with complete pagination and no warnings; every diff/nested source was not searched. Outside-map classes must still be checked against pending work.

Next action: a researcher can use the map to identify one exact changed hypothesis and a source-pinned identity/full paid budget before synthesis. No extra search inside the already excluded fixed-reader ninth-term or eight-term all-pairs domains is proposed. Physical centre/frame/restoration, compiler/hosting/precision and analytic obligations remain separate.

Credit Mihir Srivastava/PR845, themilkman216/PR968, woklerx/PR1077, Adam Gall/PR1098, DreamingOfClouds/PR717/446/595, Joel Pulikkan/PR620 and the retained lineage. Prepared by Arham Tahir with substantial OpenAI Codex assistance; no subagents or independent human review. Apache-2.0.

Original scoped claim

CLAIM — scope-navigation: retained complex E8 decoder bounds

Question: which changes to term count, reader factors, coefficient field, puncture size or exactness actually leave the hypotheses of retained PR845/968/1077, and what does PR1098 independently corroborate?
Base: main ee055dc. Chooser nonce 2f5e17a27f7174806a1785a7c24a478f; priority revision 3; scope key b18e0e173a4430a9564b. Scope refined to one bounded family index, following the scope-navigation card.
Method/domain: compare the four retained proofs/READMEs with their exact-head maintainer dispositions, then replay their existing finite evidence. Expected artifact: one concise source-linked decoder scope map and an onboarding link. No new theorem, decoder, supplier, kappa, frontier selection or adoption claim.
Credit: Mihir Srivastava/PR845, themilkman216/PR968, woklerx/PR1077, Adam Gall/PR1098, and DreamingOfClouds/PR717 with the retained model lineage.
Overlap: entry scan completely paginated 732 open PRs and 253 discussion records at 2026-10-14 04:09 UTC. PR1232 and PR1285 repair historical status/current-review routing; PR1133 concerns a fixed-reader support-descent theorem. This scope is their distinct coefficient/term/mask boundary map. Literal index searches found no matches; this is not proof of novelty and every diff was not searched. Pending decoder research will not be represented as adopted results.
Success evidence: every statement traced to the retained proof and reviewed head; reproducible existing finite checks and resolved local links. Falsification: any claimed exclusion broader than its source hypotheses, or a claim that PR1098 certifies the full single-lift argument. Stop after this map and checking; at most the repository's default 60-minute session.
Claim expires: 2026-10-14T06:20:00Z.
Prepared by Arham Tahir with substantial OpenAI Codex assistance; no subagents or independent human review. Apache-2.0.

[starship-s]

DONE / RELEASED: retained masked-rigidity navigation

Status: DONE, 2026-10-15, priority revision 4. PR #2430, exact commit bb436aa50cf989702f56a950af50df6990628ec9, updates the existing decoder map without changing the selected frontier.

Established: a source-backed route to PR1212/1389/1399/1788, distinguishing eight costly terms from rank-eight sums, real cost floors from characteristic-zero rigidity, and P104 frame complements from arbitrary punctures. Evidence: five unchanged source replays with their controls, 65 workflow tests, link/fragment checks and a separate Astra source-fidelity review. Author-checked; no independent human or new theorem verification is claimed. The review's citation-label correction is included.

Next useful step: identify a candidate's exact field, geometry and term-count hypothesis, then check live overlap before searching outside the cited chain. Higher-term cases and physical supplier admission are not settled by this update. Claim completed and released; public evidence and predecessor credit are in the PR.

Original scoped claim

CLAIM: connect the retained decoder map to the rank-eight masked rigidity results

Status: CLAIM, 2026-10-15 09:10 UTC, priority revision 4. Scope-navigation consolidation; no new theorem, supplier or κ.

Question: the existing map correctly excludes masked identities from its all-pairs theorems, but it does not link the subsequently retained E-graph rigidity results. Can a short addition distinguish the covered eight-costly-term cases from higher-term factorizations, without implying that a rank-eight sum forces eight terms?

Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Task scope-navigation, nonce b354c3f7c6a0345880a54f10bfa849bf, scope key fff26335d457e528d9c4, refined to the existing map's masked-exactness boundary. Exact retained heads: #1212 57099cb5684f38877f31d149d598801671a633db; #1389 5480912a95c3edd0a9ef7532dcc7fc7060d12380; #1399 4e1ba3a1ded94772cce5f8c0ad667a92afd6c493; #1788 c7d75c1dd348ed4312b095ca467ce966493cf9e8.

Method/domain: inspect the written hypotheses and maintainer dispositions for P120, P112, P111 and the three P104 frame-complement orbits; replay the relevant unchanged finite checks and validate the new links. Keep real COPY-cost conclusions separate from characteristic-zero rigidity. No search, repricing, pending-result adoption or edits to frozen packages.

Expected artifact: a focused update to docs/research/complex-decoder-scope-map.md. Success is a source-backed route to the retained obstructions, with explicit limits and predecessor credit. Stop if a source does not support the proposed summary. About 45 minutes including verification; claim expires 2026-10-15T11:10:00Z.

Overlap: complete cached pagination of 626 open PRs and 1,159 Discussion records, fetched 09:06–09:08 UTC, plus local notes and ledger. #2133 maps P104 side-correction costs, #2183 bootstrap obligations, and #2376 QQ16 observations; this adds only the missing masked-rigidity route to the existing #1626 map. These searches do not cover every diff.

Evidence is currently source inspection only; artifact LOCAL-ONLY until published. Credit Arham Tahir's original map, Brett Halligan/burntout76's #1212, Josie Elliston's #1389/#1399/#1788, themilkman216's #968 and DreamingOfClouds' E-graph model. Substantial Hermes AI assistance; no independent human review.

[starship-s]

Published PR #2430 at bb436aa50cf989702f56a950af50df6990628ec9, linking the retained masked-rigidity results and their scope limits from the existing decoder map.

Five source replays, 65 workflow tests, and link/fragment checks passed locally. This is documentation only: no new theorem or κ, and no change to the selected frontier. Verification details and predecessor credit are in the PR. The scoped claim is complete and released.