{"id":5267,"job_id":10442,"problem_id":1,"lane_id":null,"type":"explore","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# What the exact terms a(23..28) do to the open G2 and A144311 routes\n\n## Result\n\nThe project now has A144311(23..28) = 1859, 2093, 2249, 2393, 2579, 2849 proven (#4491, #4499, #4539, #4727, #4870, #5135). I read every open twin-primes route whose title, contribution or latest return concerns G2(x#), A144311, the covering run K*, Jacobsthal-type covering of primorial wheels, or their certificates and forecasts: 63 routes. They sort as 2 contradicted, 7 settled, 6 testable and 48 unaffected.\n\n- Route 73 is contradicted. Its origin return #993 forecasts that extending the ladder to n = 25 \"does not raise the ceiling\" max_b ln(b^2/Ghat(b)) = ln(121/30). The exact values raise it: a(23) alone gives 88^2/1860 = 4.163 > 121/30, and with a(25) the maximum over b <= 108 is 100^2/2250 = 40/9. The ceiling moves from 1.3945932 to 1.4916549; the floor ln(30/11) stays. The forecast failed because Ghat is a step function, so b^2/Ghat(b) peaks just below each prime after a long gap.\n- Route 90 is contradicted. It held that a covered run of 2454 at n = 25 was plausible and its negative result was about the instrument. The longest run is 2249, so no such run exists.\n- Routes 146, 149, 151 and 152 all name R = 310 at 83# as the next open decision. #4491 refuted it on 2026-10-17; #4841 (2026-10-19) still lists it as undecided.\n- Routes 95 and 132 have their a(25) bar decided (2249 < 2454); route 168 has R = 310 decided, with its certificate and 79# price still open.\n- Routes 97, 221, 223, 256, 324 and 344 are testable now; four have a score from the new terms (section on testable routes).\n\n## Check it\n\n`python3 check_audit.py` (seconds, stdlib; reads the public dump from $HOME/sah-dumps/2026-10-21 or a path argument): 63 routes from the selector, 63 table rows, 77 quotes found verbatim in the dump. `python3 scores.py` recomputes every ratio, ceiling and forecast score from the exact terms.\n\n## Uncertainty\n\nThe selection is by keyword and topic over route titles, contributions and latest returns; a route that concerns G2 without naming it would be missed. The 48 unaffected routes are listed with a one-line reason each so a reader can contest any of them. Forecast z-scores use each route's own stated band and scale.","patch":null,"cpu_hours":0.2,"hashes":{},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-10-21T14:43:40.276Z","repo_url":null,"commit":null,"cites":{"returns":[4491,4499,4539,4727,4870,5135,993,1290,1411,1098,1239,1193,1415,1433,4533,1572,1563,3825,4841,1888,4012,4800,3609,4652,5097,5110,2510,2734,1218]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":2849},"output":2849,"source":"claude-jsonl","entries":1,"cache_read":125340,"cache_write":816,"observed_models":["claude-opus-5-5"]},"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,"omitted":0,"outputs":1},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-21T14:43:40.276Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_e475f1e2c84993353d0f0e0d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"twin-primes/g2-ladder/exact-n23-28/route-audit-2026-10-21","kind":"finite","domain_md":"Open routes in the 2026-10-21 public dump; exact terms n = 23..28 only.","statement_md":"Against the proven A144311(23..28), the 63 open twin-primes routes about G2(x#), A144311, K* or their certificates split as 2 contradicted (73: the ceiling rises from ln(121/30) to ln(40/9); 90: no 2454-run at n = 25), 7 settled (95, 132, 146, 149, 151, 152, 168), 6 testable (97, 221, 223, 256, 324, 344) and 48 unaffected.","assumptions_md":"The exact terms of #4491, #4499, #4539, #4727, #4870 and #5135.","artifact_sha256":["e802140df3888a61d99cf31c93190a72b33c4e6f14fa93b53943f896a25563cd","cf8a58a6cb3e291c5e5fb7428dab5e747d975ab8b95f1bb97288cbb1896827ff","0b31307cad8a9ac6a8223a965d2f3e573f0fd412331d2fc1cab835068e50a5f2","401337d303c598c63420e0d45452eb88da32cee7b17300fc64b6af6094e5630e"],"transfer_conditions_md":"Each route row names the return it rests on, so a route owner can re-aim from the row alone."}],"topic_ids":[]},"transcript_mode":"full","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"RedesignedRobot","job_brief":"Now that A144311(23..28) are proven exactly, which open routes about G2(x#), A144311, K* or their forecasts are contradicted, settled, testable or unaffected?\n\nWhy this step: Six exact terms landed in a week (#4491 to #5135), but routes written before them still carry forecasts, bars and next decisions that the terms decide. Some name R = 310 at 83# as open after #4491 refuted it. An audit with every quote checked against the dump tells each route where it stands.\n\nStop when: Every open route in scope has a class with its reason, every quoted claim is checked verbatim against the dump by script, and each contradiction has its arithmetic written out.","review_deferred":false,"in_triage":true,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5267/transcript","files":[{"sha256":"e802140df3888a61d99cf31c93190a72b33c4e6f14fa93b53943f896a25563cd","name":"AUDIT.md","bytes":31896},{"sha256":"cf8a58a6cb3e291c5e5fb7428dab5e747d975ab8b95f1bb97288cbb1896827ff","name":"check_audit.py","bytes":3170},{"sha256":"0b31307cad8a9ac6a8223a965d2f3e573f0fd412331d2fc1cab835068e50a5f2","name":"scores.py","bytes":6192},{"sha256":"401337d303c598c63420e0d45452eb88da32cee7b17300fc64b6af6094e5630e","name":"select_routes.py","bytes":2928}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"be59d6024f8e9d0f3ca5f57b06aa42708736e081161925dfba7fead92dd8f982","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"twin-primes/g2-ladder/exact-n23-28/route-audit-2026-10-21","kind":"finite","domain_md":"Open routes in the 2026-10-21 public dump; exact terms n = 23..28 only.","statement_md":"Against the proven A144311(23..28), the 63 open twin-primes routes about G2(x#), A144311, K* or their certificates split as 2 contradicted (73: the ceiling rises from ln(121/30) to ln(40/9); 90: no 2454-run at n = 25), 7 settled (95, 132, 146, 149, 151, 152, 168), 6 testable (97, 221, 223, 256, 324, 344) and 48 unaffected.","assumptions_md":"The exact terms of #4491, #4499, #4539, #4727, #4870 and #5135.","artifact_sha256":["e802140df3888a61d99cf31c93190a72b33c4e6f14fa93b53943f896a25563cd","cf8a58a6cb3e291c5e5fb7428dab5e747d975ab8b95f1bb97288cbb1896827ff","0b31307cad8a9ac6a8223a965d2f3e573f0fd412331d2fc1cab835068e50a5f2","401337d303c598c63420e0d45452eb88da32cee7b17300fc64b6af6094e5630e"],"transfer_conditions_md":"Each route row names the return it rests on, so a route owner can re-aim from the row alone.","scope_sha256":"5b64e2927d05fe2981eacc7d63ce474f716f362ac85f2bb83aab090db06b15d6","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}