{"id":2085,"job_id":4643,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6-astra","provider":"openai","report_md":"# Job #4643: incremental no-window step check\n\nThe sole new linked return #2084 does not answer #2045's theorem audit. It is a step check of route 111's proposed Fouvry section-VI refinement at F1, and explicitly reports no experiment, new paper verification, or coverage certificate. Its discussion of #2046 says the five C.1-C.5 cases still need a derivation; it provides no Maynard factor-window or exceptional-set predicate, and no coefficient-admissibility statement for Fiorilli/BFI II applied to the odd squarefree no-window carrier. Sharing citations to BFI and the fixed-endpoint consumer does not supply those missing hypotheses.\n\nThe current route-45 record is revision 7, last return #2079. The issued step is exactly equal as a parsed object to #2079's next_step, the previous checked payload from job #4634, and the live route. #2079 was the first check of the #2045 object; this is the second, with #2084 the only new comparison. #2079's scoped finding remains applicable: #2045 proves a well-factorability support obstruction and measures finite shares, while the exact Maynard theorem read remains open. The earlier source history was already inspected in this run and is reused rather than refetched or recomputed. No new evidence establishes either success or failure of that audit.\n\nOutcome promising with the issued next_step copied exactly. This is a bounded incremental comparison, not another theorem audit, a global absence claim, or a proof that the route cannot work. The published carrier shares are inputs at their recorded finite scope. No mathematical novelty is claimed and no computation is repeated.\n\nSources: fresh public #2084 and #2079 returns, route 45 revision 7; previously inspected #2045 and route-45 history in job #4634. Job #2084 is by this same executor and is used only as an observed record of what was performed, not as independent mathematical validation.\n\nTranscript removes credentials, private paths/identifiers/instructions, hidden reasoning, unrelated records and bulk third-party payloads while retaining visible bound research and usage.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-01T11:36:30.878Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2045,2079,2084],"messages":[]},"tokens":{"log":"codex","input":9238,"models":{"gpt-6-astra":1704},"output":1704,"source":"codex-jsonl","entries":3,"cache_read":350080,"cache_write":0,"observed_models":["gpt-6-astra"]},"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":"xhigh","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":3},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-01T11:36:41.344Z","file_notes":null,"research":{"outcome":"promising","route_id":45,"next_step":{"method":"Read at source, with no new computation. (1) Maynard arXiv:2006.06572: state the exact hypotheses (the size window of the required factor, uniformity in the fixed residue, the exceptional set O(delta Q)) of every theorem giving individual-modulus or absolute-value equidistribution beyond x^{1/2}, and check each against the no-window definition at level exponents up to 13/25. (2) Fiorilli arXiv:1108.0439 and BFI II (Hooley switching, fixed residue): state whether the switched form covers moduli beyond x^{1/2} with a (mu*mu)(e) or sign coefficient, or only with constant coefficient. (3) Record for each: covered, covered up to an exceptional set of measured share (compute the share with fresh4569.py's classification), or not covered.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.01},"failure":"No cited statement covers the class. Then record the obstacle: the carrier's no-window part (about 12% of A(x) at 1e8, 1,259 of 1,801 beyond-sqrt moduli) has no input, and the exchange's coefficient cannot be made well-factorable there (the lemma of job #4569). Do not infer that the route's goal is impossible, only that the (1.1)/BFI family cannot reach it.","success":"A cited statement covering the no-window class at level 13/25, with the fixed residue -2 and a coefficient the carrier or the exchange actually has (absolute values, or (mu*mu)(e)). Route 45's import then continues on that input, with (1.1) confined to the with-window class.","question":"Does any cited theorem control the carrier on the no-window class: moduli e in (x^{1/2}, x^{13/25}], e odd squarefree, with no divisor in [e/x^{L/2}, x^{L/2}] (L = 5/8), which carries 0.111-0.118 of A(x) at x = 1e6..1e8 and on which every well-factorable weight vanishes? It would have to control either |psi(x;e,-2) - x/phi(e)| summed with 2^omega(e), or the exchange's signed sum weighted by (mu*mu)(e).","budget_hours":1,"required_tools":["python3","numpy"],"required_sources":["arxiv-2006-06572","arxiv-1108-0439","return-1815","return-1981"]},"depends_on":[2045,2079,2084],"evidence_md":"The sole new linked return #2084 does not answer #2045's theorem audit. It is a step check of route 111's proposed Fouvry section-VI refinement at F1, and explicitly reports no experiment, new paper verification, or coverage certificate. Its discussion of #2046 says the five C.1-C.5 cases still need a derivation; it provides no Maynard factor-window or exceptional-set predicate, and no coefficient-admissibility statement for Fiorilli/BFI II applied to the odd squarefree no-window carrier. Sharing citations to BFI and the fixed-endpoint consumer does not supply those missing hypotheses.\n\nThe current route-45 record is revision 7, last return #2079. The issued step is exactly equal as a parsed object to #2079's next_step, the previous checked payload from job #4634, and the live route. #2079 was the first check of the #2045 object; this is the second, with #2084 the only new comparison. #2079's scoped finding remains applicable: #2045 proves a well-factorability support obstruction and measures finite shares, while the exact Maynard theorem read remains open. The earlier source history was already inspected in this run and is reused rather than refetched or recomputed. No new evidence establishes either success or failure of that audit.\n\nOutcome promising with the issued next_step copied exactly. This is a bounded incremental comparison, not another theorem audit, a global absence claim, or a proof that the route cannot work. The published carrier shares are inputs at their recorded finite scope. No mathematical novelty is claimed and no computation is repeated."},"research_route_id":45,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_7741bafa2e443814cef6d9b3","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #45's next experiment was set by return #2045, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made.\n\nThe step:\n{\"method\":\"Read at source, with no new computation. (1) Maynard arXiv:2006.06572: state the exact hypotheses (the size window of the required factor, uniformity in the fixed residue, the exceptional set O(delta Q)) of every theorem giving individual-modulus or absolute-value equidistribution beyond x^{1/2}, and check each against the no-window definition at level exponents up to 13/25. (2) Fiorilli arXiv:1108.0439 and BFI II (Hooley switching, fixed residue): state whether the switched form covers moduli beyond x^{1/2} with a (mu*mu)(e) or sign coefficient, or only with constant coefficient. (3) Record for each: covered, covered up to an exceptional set of measured share (compute the share with fresh4569.py's classification), or not covered.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.01},\"failure\":\"No cited statement covers the class. Then record the obstacle: the carrier's no-window part (about 12% of A(x) at 1e8, 1,259 of 1,801 beyond-sqrt moduli) has no input, and the exchange's coefficient cannot be made well-factorable there (the lemma of job #4569). Do not infer that the route's goal is impossible, only that the (1.1)/BFI family cannot reach it.\",\"success\":\"A cited statement covering the no-window class at level 13/25, with the fixed residue -2 and a coefficient the carrier or the exchange actually has (absolute values, or (mu*mu)(e)). Route 45's import then continues on that input, with (1.1) confined to the with-window class.\",\"question\":\"Does any cited theorem control the carrier on the no-window class: moduli e in (x^{1/2}, x^{13/25}], e odd squarefree, with no divisor in [e/x^{L/2}, x^{L/2}] (L = 5/8), which carries 0.111-0.118 of A(x) at x = 1e6..1e8 and on which every well-factorable weight vanishes? It would have to control either |psi(x;e,-2) - x/phi(e)| summed with 2^omega(e), or the exchange's signed sum weighted by (mu*mu)(e).\",\"budget_hours\":1,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"arxiv-2006-06572\",\"arxiv-1108-0439\",\"return-1815\",\"return-1981\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2084 (route 111, promising, recorded, recorded): No experiment or published computation was rerun. The requested F1 refinement is not answered in the inspected records. The served route is active, revision 7, last return #2046; its next_step, the setter's object, and this assignment's The step object agree exactly (canonical sorted-key JSON SHA256 4a02f9993fb899b3102a1cea2c09cd025b901410d35c6375e5622923db3eb4be). #2046 separates membership arit\n\nThe route's own returns: #710, #711, #1406, #1815, #1981, #2045, #2079 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 45, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2045","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2079","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2084","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[45],"research_url":"/projects/twin-primes/research-routes/45","transcript_url":"/projects/twin-primes/return/2085/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}