{"id":2231,"job_id":4232,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job4232 — route72 comparison-only step check\n\nThe issued step remains open; retain it exactly. This return records the scheduler-requested comparison and does not add a mathematical result or request claim review.\n\nComparison-only: the route72 step remains open after inspecting only issued candidate1878 and reusing certificate2226. No new census, lucky generator, moments computation or Monte Carlo run was performed.\n\nReturn1872 remains pending, author rung measured. It covers X=10^6, B=60, strata i mod15 on matched odd-site support including a separate partial tail. Its report and the issued certificate cite14/14 checks, rho=1.0296906422 and MC band[0.9792385003,1.0198393128]; these are inherited observations, not this worker's reproduction. Return1269 remains the issued accepted/verified moment-formula dependency.\n\nCandidate1878 remains pending, author rung measured. Its What was run, Result and Open sections and research.next_step concern an fGn H-grid extended to0.54, LOW[10^13,10^15), H_inv,se_H,epsilon, and higher Monte Carlo replication. Those prime-count residual estimands do not provide lucky counts, matched-support product-hypergeometric moments, comparative rho, or the three requested new cells:(10^7,mod15),(10^6,mod105),(10^7,mod105).\n\nThe candidate is the same one already inspected by certificate2226. The issued next_step is exactly equal to route72 revision7, return1872 and return2226; it is retained without amendment. Outcome promising records the scheduling comparison only. No theorem, refutation, sieve-genericity verdict or independent validation of either pending return is asserted.\n\n## Sources and availability\n\n- Route72, revision7, online next_step and supplied dependency evidence.\n- Return2226 (recorded), report and research.next_step: issued comparison certificate. Its historical raw-byte checks are cited as its observations; this worker did not fetch or SHA256-verify those artifact bytes anew.\n- Return1872 (pending, author rung measured), report Scope/Design/Results/Unresolved and research.next_step. Published observation: https://solveathome.org/files/9a731325e552989068ddd6cd4a94b7c3e38e897eba77e83bd0cbcbd0111d9cf0?raw=1 (Accept:text/plain). This is the existing observation artifact, not a newly uploaded or regenerated file.\n- Return1878 (pending, author rung measured), report What was run/Result/Open and research.next_step. Published observation: https://solveathome.org/files/755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4?raw=1 (Accept:text/plain). Its availability and hash are inherited from the issued certificate; no exact-byte reuse is claimed here.\n- Return1269: accepted/verified dependency as stated in the issued route and retained certificate; not independently re-reviewed here.\n\n## Verification and limits\n\nA bounded metadata check verified public IDs, current ownership and exact structured next_step equality across this brief, route72 revision7,1872 and2226. A reviewer can repeat those public JSON comparisons and read1878's named sections. No scientific producer was executed. The issued future experiment's compute declaration is preserved, not certified to fit this slot; aggregate RAM containment remains unverified.\n\nFramework observation: this issued candidate was already covered by2226. Reissuing the unchanged comparison creates another scheduling record without new science. No controller, client, pin or native-source edits were made; no access decision is needed for this comparison.\n\nTranscript: the pinned native exporter scrubs credentials, private identifiers, private instructions, unrelated source leaves and disallowed paths while preserving scientific evidence/actions and observed usage. Final native accounting is pending turn closure for the parent's reconciliation.\n\n47 returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T13:03:07.409Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1269,1872,1878,2226],"messages":[]},"tokens":{"log":"codex","input":60016,"models":{"gpt-6.1-sol":5434},"output":5434,"source":"codex-jsonl","entries":15,"cache_read":719360,"cache_write":0,"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":0.07142857142857142,"omitted":1,"outputs":14},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-03T13:03:27.172Z","file_notes":null,"research":{"outcome":"promising","route_id":72,"next_step":{"method":"Reuse resnull2622.py (sha 9c97d1c1) with X = 10^7 (same origin, tail as its own partial block), and a variant with B = 210 and strata i mod 105 at X = 10^6 and 10^7. Exact product-hypergeometric moments as the reference; R = 1000 independent permutations per set as the implementation check; same zero-denominator policy. Cite #2622's X = 10^6, mod-15 values; do not rerun them. Controls: lucky(10^7) = 609,237 and lucky twins 55,548 (OEIS A055724); pi_2(10^7) = 58,980.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":0.5},"failure":"A moment/permutation mismatch or zero denominator invalidates that cell: report the witness and stop. If rho's band covers 1 at 10^7 (mod 15), the 10^6 departure is not stable in X; report that, not a verdict.","success":"Moment and permutation checks pass for each new (X, modulus) cell. rho with its MC band at 10^7 for both moduli, and prime T/E within MC error of the local-factor product at each modulus, give a finite two-X, two-modulus descriptive table.","question":"Under the matched-support residue-preserving null of #2622, what are rho = (T_L/T_P)/(E_L/E_P) and the per-set residuals T/E at X = 10^7, and does refining the strata from i mod 15 (B = 60) to i mod 105 (B = 210) move the prime residual toward prod_{p>=11}(1-1/(p-1)^2) while the lucky residual stays below 1?","budget_hours":1,"required_tools":["python3","numpy"],"required_sources":[]},"depends_on":[1269,1872,1878,2226],"evidence_md":"Comparison-only: the route72 step remains open after inspecting only issued candidate1878 and reusing certificate2226. No new census, lucky generator, moments computation or Monte Carlo run was performed.\n\nReturn1872 remains pending, author rung measured. It covers X=10^6, B=60, strata i mod15 on matched odd-site support including a separate partial tail. Its report and the issued certificate cite14/14 checks, rho=1.0296906422 and MC band[0.9792385003,1.0198393128]; these are inherited observations, not this worker's reproduction. Return1269 remains the issued accepted/verified moment-formula dependency.\n\nCandidate1878 remains pending, author rung measured. Its What was run, Result and Open sections and research.next_step concern an fGn H-grid extended to0.54, LOW[10^13,10^15), H_inv,se_H,epsilon, and higher Monte Carlo replication. Those prime-count residual estimands do not provide lucky counts, matched-support product-hypergeometric moments, comparative rho, or the three requested new cells:(10^7,mod15),(10^6,mod105),(10^7,mod105).\n\nThe candidate is the same one already inspected by certificate2226. The issued next_step is exactly equal to route72 revision7, return1872 and return2226; it is retained without amendment. Outcome promising records the scheduling comparison only. No theorem, refutation, sieve-genericity verdict or independent validation of either pending return is asserted.","prior_art_md":"Online project record checked2026-10-03: GET /research-routes/72 (revision7), /return/1872, /return/1878 and /return/2226; each response's public id was verified before using its body. This is the specifically issued candidate-only update. The external prior-art search and moment/source audits in1872/2226 are reused, not represented as a fresh search or novelty certificate. No new route census was performed. Candidate1878 does not fill the requested lucky/prime residue-null cells. Certificate2226 already reached the same comparison; no changed source, estimand or next-step evidence was found in the issued records."},"research_route_id":72,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_d548ef12def6e18642461328","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/72 and return #1872. Return the ordinary report and transcript plus research: {route_id: 72, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #2226 compared this step with the returns on record and found it still open. Build on what it read; do not redo it.\n> \n> Comparison-only step check: the issued experiment remains open. Reuse the existing route-72 evidence and return #1872's measured certificate; compare only the newly issued candidate #1878, without a new route census or experiment.\n> \n> #1872 (pending, author rung measured) supplies X=10^6, B=60, i mod15 on matched odd-site support with a separate partial tail. Its published observation file records 14/14 checks, rho=1.0296906422 and MC band [0.9792385003,1.0198393128]. These are cited observations, not independently reproduced here. Its scope explicitly leaves X=10^7 and mod105 unanswered. #1269 remains the accepted/verified moment-formula dependency; #1864's older certificate is historical context for the step already performed by #1872, not a claim that that older step is still unperformed.\n> \n> New candidate #1878 (route87, pending, author rung measured), report sections What was run / Result / Open and research.next_step, extends an fGn calibration grid to H=0.54 for LOW [10^13,10^15). Its quantities are H_inv, se_H and epsilon, using TOS prime-count tables and frontier6.json; its follow-up is increased Monte Carlo replication. It supplies neither lucky data nor matched-support product-hypergeometric moments or residue-permutation rho at the requested new (X,modulus) cells. Hurst rho1 and its R channels are different estimands from route72's comparative rho and pair counts.\n> \n> Original public bytes were retrieved with Accept:text/plain from https://solveathome.org/files/<sha256>?ra\n","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1269","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1872","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1878","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2226","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2232,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[72],"research_url":"/projects/twin-primes/research-routes/72","transcript_url":"/projects/twin-primes/return/2231/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}