{"id":2465,"job_id":null,"problem_id":1,"lane_id":null,"type":"direction","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Exact two-root Selberg remainder adapter for the rough-pair upper census\n\nAddresses partial Q-X-upper-0829n using a separate source-based proof adapter. The existing loose upper-sieve result is prior work; a port is not a better census ratio.\n\nInspect Q-X-upper-0829n and existing finite bound. Freeze interval, root sets with the collision at2, modulus, normalizer and exact lcm remainder. Derive the stated envelope by CRT and compare resulting denominator/error to the existing result. Inventory selected dependency closure and adapter defects before any full compilation. Keep weighted FundamentalBlockEstimate support/cost requirements explicit; no positive twin count, improved DHR threshold or quadratic gap conclusion.\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/EgyptianFractions/OptimizedSelbergError.lean#L62-L69\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":"2026-10-07T11:31:33.515Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"codex","input":3680,"models":{"gpt-6.1-sol":1646},"output":1646,"source":"codex-jsonl","entries":4,"cache_read":766720,"cache_write":0,"already_counted":{"of":61,"on":["return #2463","return #2464"],"entries":57},"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":0.016666666666666666,"omitted":1,"outputs":60},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"proposed","proposal":{"title":"Exact two-root Selberg remainder adapter for the rough-pair upper census","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/EgyptianFractions/OptimizedSelbergError.lean#L62-L69","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":"Addresses partial Q-X-upper-0829n using a separate source-based proof adapter. The existing loose upper-sieve result is prior work; a port is not a better census ratio."},"next_step":{"method":"Inspect Q-X-upper-0829n and existing finite bound. Freeze interval, root sets with the collision at2, modulus, normalizer and exact lcm remainder. Derive the stated envelope by CRT and compare resulting denominator/error to the existing result. Inventory selected dependency closure and adapter defects before any full compilation. Keep weighted FundamentalBlockEstimate support/cost requirements explicit; no positive twin count, improved DHR threshold or quadratic gap conclusion.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.05},"failure":"Missing remainder pricing or normalizer mismatch leaves the bound conditional; record insufficiency without converting it into a theorem.","success":"A source-to-actual-model remainder contract is exact and the denominator/error comparison identifies whether it improves anything.","question":"Can the actual interval n(n+2) BoundingSieve prove the explicit 2^omega(a)2^omega(b) lcm-remainder envelope used by the pinned logarithmic-error theorem?","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."},"research_route_id":211,"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":2477,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[211],"research_url":"/projects/twin-primes/research-routes/211","transcript_url":"/projects/twin-primes/return/2465/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":[]}