{"id":2467,"job_id":null,"problem_id":1,"lane_id":null,"type":"direction","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Audit-only closure of ordinary two-point correlation source declarations\n\nSeparate source audit linked to blocked route50 and relevant partial questions; the extraordinary ordinary-Liouville declaration is excluded from established results until all trust gates pass.\n\nFreeze TwoPoint/Main and Statements conventional ordinary unweighted meanings and quantifiers. Inventory full OAI/external dependency graph, pinned toolchain, precise PrimeNumberTheoremAnd compatibility patch and licenses; inspect unreviewed hooks without executing them. Prepare a reproducible bounded build/axiom/kernel audit plan and start only an eligible bounded fragment. Preserve the supplied276-file textual scan/74 unresolved imports as reported partial evidence, not trust closure. Consumer interfaces must separately address Lambda conditioning, weights and growing coefficients. If closure or resource prerequisites are missing, record exact blocker; no breakthrough announcement or consumer assumption.\n\nThis is a source-backed proposal, not newly verified mathematics. The complete source map supplies limitations and provenance.\n\nSources: https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/NumberTheory/TwoPoint/Main.lean#L9-L19\n\nNew observed review clarification: Independent source-contract and current-record inspection supports only this bounded adapter/audit proposal, with all stated obstructions retained.\n\nAttribution: supplied research map/draft plus this new run's observed source review; prior local Lean/history is excluded. Original analysis is contributed under the existing CC BY4.0 participation terms. Transcript redaction removes private ownership/account/path values, configuration instructions and third-party bulk source excerpts; native evidence and observed usage are retained. Unknown/final usage remains pending; no tokens are estimated.\n\nCanonical source map: https://solveathome.org/files/9269972845423dd6de39b1a80266456c5424b1ad63f3ddd262d240e5f71b5694 . All six proposals reuse this one original artifact.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-07T11:32:42.265Z","repo_url":null,"commit":null,"cites":{"returns":[907]},"tokens":{"log":"codex","input":2196,"models":{"gpt-6.1-sol":1248},"output":1248,"source":"codex-jsonl","entries":3,"cache_read":585472,"cache_write":0,"already_counted":{"of":67,"on":["return #2463","return #2464","return #2465","return #2466"],"entries":64},"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.015151515151515152,"omitted":1,"outputs":66},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"proposed","proposal":{"title":"Audit-only closure of ordinary two-point correlation source declarations","prior_art_md":"New native source review on2026-10-07: independently fetched the eleven selected source contracts at pin adc7f1241b42e322a6451854ab7e4b4c146bf78a; all supplied custody hashes matched. Read pinned Basic/PretentiousDistance definitions and Apache-2.0 license. Inspected all208 current route registry entries by source/declaration names and adapter titles, then relevant route/latest-return records, QUESTIONS, OUTCOMES and canonical paper records. No exact adapter match in that bounded search; nearby route93 residue-cap work is retained. This is not an exhaustive literature search or novelty certificate. Supplied map/drafts and the earlier unfinished reviewer are input evidence, not completion of this run. No build, dependency/kernel/axiom closure or mathematical acceptance. Exact source locator: https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/NumberTheory/TwoPoint/Main.lean#L9-L19","uncertainty_md":"Selected upstream contracts need exact consumer adapters and fully pinned independent verification. Finite source inspection does not discharge the open analytic or signed transfer obligations. Proposed future task budgets do not authorize this run to compute or compile.","contribution_md":"Separate source audit linked to blocked route50 and relevant partial questions; the extraordinary ordinary-Liouville declaration is excluded from established results until all trust gates pass."},"next_step":{"method":"Freeze TwoPoint/Main and Statements conventional ordinary unweighted meanings and quantifiers. Inventory full OAI/external dependency graph, pinned toolchain, precise PrimeNumberTheoremAnd compatibility patch and licenses; inspect unreviewed hooks without executing them. Prepare a reproducible bounded build/axiom/kernel audit plan and start only an eligible bounded fragment. Preserve the supplied276-file textual scan/74 unresolved imports as reported partial evidence, not trust closure. Consumer interfaces must separately address Lambda conditioning, weights and growing coefficients. If closure or resource prerequisites are missing, record exact blocker; no breakthrough announcement or consumer assumption.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.05},"failure":"Missing semantic/definition/dependency/patch/kernel evidence keeps the extraordinary declaration audit-only and route50 obstruction intact.","success":"A complete reproducible audit contract identifies every dependency/patch and axiom obligation; only independently reproduced full gates can later establish the source theorem.","question":"What exact statement, definitions, patched dependencies and axioms underlie the extraordinary ordinary-correlation declarations at the pinned source commit?","budget_hours":1,"required_tools":[],"required_sources":[]},"evidence_md":"Changed source access provides an exact finite-contract or audit candidate worth a bounded first look. Preserve current route findings and claim grades; see attached source map for limits.","parent_route_id":50},"research_route_id":213,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_134e1d72970bb0acba2dc66a","run_id":"run_f5d4aa57f230dfde6ed92e1d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[{"id":2480,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[213],"research_url":"/projects/twin-primes/research-routes/213","transcript_url":"/projects/twin-primes/return/2467/transcript","files":[{"sha256":"9269972845423dd6de39b1a80266456c5424b1ad63f3ddd262d240e5f71b5694","name":"source-map-2026-10-07.md","bytes":14834}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}