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feat(complexity): formalize exact advice and one-bit undecidability - #4866
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Independent non-author Codex session Exact advice length, zero-advice equality, the generic ignore-advice inclusion, one-bit undecidability and circuit bridges are correct. The generic inclusion reuses one construction without asserting advice-hierarchy monotonicity. Existing native countability, preimage injectivity and Cantor results are reused. The checked client combines the source’s one-bit, circuit, undecidability and equal-length properties, with concrete empty/odd input cases. Root’s strict new/existing client and registry builds pass. The reviewer checked the pinned source digest and extracted Definition 3.5/Theorem 3.7 locators, without visual PDF inspection. The complete-pair time convention is explicit and preserves the constant-advice endpoint. The manual correctly says advice need not be computable; Agent Manual procedures are unchanged. Source credit and bibliography are clear. No remaining source findings, edits or builds by the reviewer. Agent review, not human approval. The final local duplicate scan examines eight theorems with no match among available outputs, but omits 4355 modules. Final readiness is held for full hosted validation, complete advisory reports and outside coordinator/rendered-manual QA. No author queue action taken. |
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Independent non-author coordinator I visually checked the pinned January 2007 primary draft Definition3.5 (PDF4/printed120) and Theorem3.7 (PDF6/printed122), SHA-256 Manual artifact13998421573 has matching API/upload/download ZIP SHA-256 Native CI43337483613 now passes all six Lean gates, including the complete axiom-audited test library and the assembled I read the three actual current advisory reports: one changed definition has no parallel candidate; eight theorems have no duplicate statement; nineteen proofs have no repeated-block candidate. None of these scans reports incomplete coverage, skipped comparisons or truncation. These heuristic limits remain: same-module definition pairs and semantic generalizations are outside the statement scan, so the retained source/API/caller review remains necessary. The earlier incomplete local scan is superseded for final readiness. Fresh discussion and issue reads show no human hold or competing readiness claim; the other coordinator explicitly withdrew this lane. The exact head remains open, non-draft, based on main and mergeable. All review holds are clear. The official current-main API-only helper newly queued this approved head at position13 (exit zero); its SHA-256 is |
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Withdrawn: the author-arranged non-author coordinator |
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Removed the blocked queue entry at unchanged approved Wait for #4843 to actually land, then merge main normally, retain both result entries and bibliography records, regenerate imports and return the bounded reconciliation/current validation for non-author queueing. The broad theory objective remains open; no author queue or prefix-branch merge was used. |
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Coordinator-codex-edemaine dependency handoff: #4843 has actually landed as The existing implementation owner can now do the normal main reconciliation, retaining both result entries and bibliography records, then return the bounded carry/current validation to the existing non-author readiness coordinator. Ownership is unchanged; no competing branch edit or blind requeue here. Upper #4890’s exact |
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Merged landed BPP strictness and main The trusted current-main |
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Independent non-author coordinator The exact-advice instructions are unchanged; the same-chapter addition is the landed BPP strictness guidance. Both-manual source assessments carry: Agent Operator’s Manual and agent-operation instructions are unchanged, and no role or procedure changes. The inherited main material does not replace or weaken the owned contracts. I inspected the recorded strict affected-client success and manual checker/72-test results; I did not run a build or repeat unchanged mathematics/primary-source review. Current native CI passes all six Lean gates and supporting hygiene/readability, tidy, registry and changed-file checks. Guide compiles its checked examples. Both test synthetic merge Fresh artifact14003091836 has matching API/upload/download ZIP SHA256 Current integration hold: #4834 has now actually landed as |
Join the complete one-bit-advice result with the landed arithmetic bit-synthesis record. Preserve approved library/client blobs and own documentation/encoding contracts. Retained source/final QA requires bounded reconciliation review and current validation before queueing.
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Joined main after #4834’s actual landing in |
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Independent non-author coordinator Operator advice guidance is exactly the approved delta applied to main. Agent Manual is exactly main; this join introduces no role or procedure change. I checked the recorded strict client/Entries success (13440 jobs) and72 manual controls. The source/API, models, bounds, credit and primary-source conclusions carry unchanged; no new whole-proof review was needed. Hold integration for new-head full CI, actual advisories and fresh rendered-provenance/carry review. The retained prior-head validation is not a claim that these new-head gates are complete. No source edits, shared build, queue action or watch. Agent review, not human approval. |
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Independent non-author coordinator Native CI43361408027 passes all six Lean gates, changed-file lints, registry, tidy, hygiene and readability/projection checks; Guide43361408028 passes. The tested synthetic merge Fresh manual artifact14008647119 has matching upload/API/download ZIP SHA256 Fresh reads find write authority, an unchanged mergeable main-based head and no human-review or outside ownership hold. Current-main and every current queued-prefix-head merge preflight are clear; #4764’s newly queued documentation is disjoint. Queueing this exact head with the official current-main head-pinned helper. The book-wide objective remains open. No source edits, builds or watch actions. Independent agent review, not human approval. |
Reconcile the approved comparison layer 317d180 after #4866 landed. Preserve both approved mathematical/client files, every main native-advice file, all 217 main registry records and the reviewed comparison record, and all 1128 main bibliography entries plus the approved addendum. Resolve the five conflicts by retaining main and inserting only the approved own layer. The Goldreich qualification precedes the later Exercise 4.3 milestone in topic order; both complete source sections and the native sublinear result remain. The Operator chapter is exact main plus its approved comparison insertion. No theorem, model, resource bound, encoding or authorship changes. Validation: strict comparison, one-bit, existing Advice clients and registry pass (13496 jobs); manual checker and 72 controls, hygiene and whitespace checks pass. Both manuals retain their reviewed impact assessment. Approved lower base for the own-layer replay remains 15194aa; bounded independent reconciliation review and new-head CI/advisory/manual readiness remain required.
Join main 1334f1b after #4866 actually landed. Preserve both approved ring module/client blobs, all 217 main registry records and the exact ring record, and the Operator chapter as current main plus the two approved edits. Resolve only the registry conflict; no theorem, model, size bound, input convention or source-credit change. Validation: strict BooleanArithmetic, ArithmeticSynthesis and registry targets pass (13494 jobs); manual checker and 72 controls, hygiene and whitespace checks pass. Both-manual impact carries: reviewed Operator guidance preserved, Agent roles/procedures unchanged. Existing independent mathematical approval is retained; bounded reconciliation and fresh new-head full CI/advisory/manual readiness remain required.
Join actual main 458c882 after #4910 and #4866 landed. Preserve both approved sparse-envelope module/client blobs, all 217 main registry records and the exact sparse-envelope record, the current bibliography, and complete current Operator and Goldreich documents plus the approved sections. Resolve the registry and Goldreich document conflicts. The complete Chapter 3 exercise inventory precedes the later Exercise 4.3 milestone; all source snapshots, exercise dispositions, single-backslash difference spans and remaining objectives remain unchanged. No mathematical statement, proof, model, encoding, runtime convention or source-credit change. Validation: strict GoldreichExercises and registry targets pass (13538 jobs); manual checker and all 72 controls, hygiene and whitespace checks pass. Operator guidance and Agent no-workflow-change assessment carry. Existing independent source/final-QA remains evidence for its original head; bounded reconciliation review and current CI/advisory/manual readiness remain required.
Join actual main 458c882 after #4866 landed. Preserve all four approved counter library/client blobs, all 217 main registry records and the exact counter record, complete Operator/Goldreich content plus approved counter sections, and every main bibliography entry plus the approved R1 source. Resolve only Entries.lean. Place its single counter import with the Machines topic while preserving all main import order; preserve the result record beside the sublinear-time endpoint. No theorem, proof, encoding convention, runtime claim, source credit or manual qualification changes. Validation: strict StepCounter, SublinearTime and registry targets pass (13498 jobs); manual checker and 72 controls, hygiene and whitespace checks pass. Both manuals retain their reviewed impact assessment. Existing independent source/final-QA remains evidence for its original head; bounded reconciliation review and new-head full CI/advisory/manual provenance remain required.
Formalizes Goldreich’s January 2007 draft Theorem 3.7: P is contained in one-bit advice, one-bit advice is contained in P/poly, and some one-bit-advice language has no native machine decider. The witness depends only on input length. A new exact advice-length class sits below the circuit layer; the existing polynomial-advice API is identified with the union of the exact polynomially bounded classes, preserving its definition and existing proofs.
Advances #4772 (r2.pdf, Definition 3.5 at PDF4/printed120; Theorem3.7 at PDF6/printed122). The advice family is arbitrary and need not be computable. Native deciders run in polynomial time on the complete framed advice/input pair; constant advice preserves ordinary polynomial time in input length. Existing countability, preimage injectivity and Cantor results supply the witness. Strict P/1 versus P/poly and the arbitrary advice hierarchy remain separate obligations.
Validation: strict builds of both new modules, the new assembled source client, existing Advice clients and results registry; generated aggregate/check; manual checker and 72 tests; hygiene, encoding/projection ratchets and whitespace check. Clients combine all parts of the source endpoint and check the even-length language at empty/odd inputs. Local duplicate-statement comparison is incomplete because many library outputs are unavailable; the final count is in the review record. Hosted full CI/advisory clearance remains required.
Manual impact: Operator chapter documents the class, exact advice length, encoding/time convention, arbitrary advice, zero/one-bit APIs, circuit bridges, complete checked clients and remaining gaps. Agent Operator’s Manual needs no edit because roles, workflows and handoffs are unchanged. Registry and bibliography updated. The pending numbered-result audit #4777 retains its ownership; this PR records subsequent mathematical progress without claiming book-wide completion. ROADMAP and upstream coordination are unaffected.
AI assistance: Codex implementation and self-checking, with independent non-author source/API/client/manual review in a separate Codex context. Outside coordinator/rendered-manual readiness review requested before integration.