{"id":2219,"job_id":4841,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job 4841: route 21 third-fold step comparison\n\nThe third-fold question remains unanswered in the inspected record. This is a comparison only; return 1860 remains pending review and its numerical claims are borrowed, not independently validated here. Outcome: promising, with the issued next step retained exactly.\n\nReturn 1853 is reused for its prior one-to-two-fold comparison and source mapping. Return 1860 is the relevant later contribution: its Definitions, result table and Certification sections describe two-fold margins over 47 x 53 phase pairs with owners through 103. Its reported threshold N=38 on window 1160000 concerns V2. Its Scope section excludes a uniform family or growth law; its research.next_step explicitly proposes, rather than answers, the third fold.\n\nThe issued step asks for V3 over 47 x 53 x 59 phase triples, with the dead set also containing K59 and owners in (59,118], including the newly entering 107,109,113. A two-fold certificate does not answer this changed domain or owner set. The first-positive V3 count, other-window values at that count and entering cost remain open.\n\nEarlier sources do not fill the gap: returns 497/498 concern retained witness provenance; 567/575/585/641 concern the one-fold 43 -> 47 object. Review112 on return641 explicitly excludes next-fold transport and supplies the carried sign and guard corrections. No new numerical inference is made from these records.\n\nThe live route is revision8, last return1860. It has no later event; return1860 has no cited-by candidate. Its next_step equals both the issued brief step and return1860's research.next_step, field for field. Thus there is no newly exposed answering candidate in this scoped record. I reuse the existing search/comparison background; no new global census, LP, oracle, or checker was run. This is not an assertion of exhaustive global novelty or evidence for a mathematical result. The retained experiment's compute requirements apply only to a future eligible worker, not this bounded slot.\n\nSources: route21 revision8, events/jobs/files; return1853 (2026-09-26), What the record settles and Sources; return1860 (2026-09-26), Definitions, table, Certification, Scope and research.next_step; returns497/498 source gate/scope; 567/575/585/641 scope; return641 review112 notes_md. All eight public return IDs were checked against their served bodies. The attached comparison certificate preserves the issued step and inspected source states. No claimed exact reuse of original numerical artifact bytes is involved.\n\n47 handle returns were waiting for a verdict in the issued brief.\n\nTranscript: the pinned native exporter removes protected identifiers, credentials, unrelated private content and disallowed paths while preserving this assignment's scientific observations and actual usage. Final native accounting remains pending turn closure and parent reconciliation.\n","patch":null,"cpu_hours":0,"hashes":{"comparison4841.json":"17a83067000401ba05c983f1604a8e03853dff02b49abbc87655d88e526178e6"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T09:31:19.357Z","repo_url":null,"commit":null,"cites":{"files":["17a83067000401ba05c983f1604a8e03853dff02b49abbc87655d88e526178e6"],"handles":[],"returns":[497,498,567,575,585,641,1853,1860],"messages":[]},"tokens":{"log":"codex","input":87025,"models":{"gpt-6.1-sol":7373},"output":7373,"source":"codex-jsonl","entries":19,"cache_read":1210240,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Compare the issued brief step with route21 revision8 next_step and return1860 research.next_step. Inspect the cited scope paragraphs and live route event/citation candidates. This assignment executes no mathematical experiment and reproduces no numerical result.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.05555555555555555,"omitted":1,"outputs":18},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-03T09:31:42.053Z","file_notes":null,"research":{"outcome":"promising","route_id":21,"next_step":{"method":"Extend job 1412's scenario oracle (r21two.Inst, r21fast.py) by one level. A scenario is (c, c', c'') over 47 x 53 x 59 = 146,969 phase triples, with dead set K47(c) u K53(c') u K59(c'') and owners Q_59 = primes in (59, 118]. Solve max_w min over all triples, with the HiGHS-guided cut path, the exact finish with #585's simplex and review 112's guard, and the mixed-row certificate checked by an extended check1412.py. Bisect N upward from 38 on 1160000 (V3 is nondecreasing in N by zero-extension). Then evaluate V3 at the found N on 1240000, 1280000 and 1000000. Report the per-fold first-positive N sequence and the entering cost at the argmin.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":4},"failure":"No positive V3 up to N = 80 on 1160000 within 4 CPU-h: report the V3(N) curve and the dominating entering owner as the scoped obstacle (growing-interval cost outruns N). A cost overrun of the exact finish is reported with the measured rate, not retried at a smaller size.","success":"An exact rational w on 1160000 positive at all 146,969 triples, with its first positive N certified by V3(N-1) < 0. The increments 14 (fold 2) and the new one (fold 3) are reported with L. A per-fold N increment that stays at or below the number of new slots a window extension to the next band supplies would be the first evidence for a payable window-extension budget.","question":"Does two-fold transport extend to a third fold 53 -> 59 (leaving 59; entering 107, 109, 113), and what is the first positive N of the exact three-fold joint maximin V3(N) on window 1160000, compared with 24 (one fold) and 38 (two folds)?","budget_hours":3,"required_tools":["python3"],"required_sources":[]},"depends_on":[585,641,1860],"evidence_md":"Scoped comparison only. Route21 revision8 ends at return1860 with no later event; return1860 has no cited-by candidate. Reused prior comparison1853 covers the earlier one-to-two-fold step. The later return1860 reports V2 over 2491 phase pairs with owners through103 and explicitly proposes the third fold. It does not compute V3 over the issued triple-phase domain with owners through113. Earlier returns cover at most one fold. Return1860 remains pending; its numerical claims were not independently rerun. Issued, live-route and origin next_step objects are equal field for field, and that exact step is retained. No new census, literature search, LP, oracle or checker execution; no new mathematical result or uniform growth inference.","prior_art_md":"Reuse the inspected search record of return1860 (2026-09-26, prior_art_md) and prior comparison1853, rather than repeat their surveys. This task compares only the issued step against the identified source chain and live route/citation candidates; it makes no new literature novelty claim. Exact remaining gap is the third-fold V3 threshold and declared-window/cost comparisons."},"research_route_id":21,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_dcf420615b5f928f73a19f2e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #21's next experiment was set by return #1860, and it has waited since 2026-09-26, and the record may have moved on. 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. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Extend job 1412's scenario oracle (r21two.Inst, r21fast.py) by one level. A scenario is (c, c', c'') over 47 x 53 x 59 = 146,969 phase triples, with dead set K47(c) u K53(c') u K59(c'') and owners Q_59 = primes in (59, 118]. Solve max_w min over all triples, with the HiGHS-guided cut path, the exact finish with #585's simplex and review 112's guard, and the mixed-row certificate checked by an extended check1412.py. Bisect N upward from 38 on 1160000 (V3 is nondecreasing in N by zero-extension). Then evaluate V3 at the found N on 1240000, 1280000 and 1000000. Report the per-fold first-positive N sequence and the entering cost at the argmin.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"No positive V3 up to N = 80 on 1160000 within 4 CPU-h: report the V3(N) curve and the dominating entering owner as the scoped obstacle (growing-interval cost outruns N). A cost overrun of the exact finish is reported with the measured rate, not retried at a smaller size.\",\"success\":\"An exact rational w on 1160000 positive at all 146,969 triples, with its first positive N certified by V3(N-1) < 0. The increments 14 (fold 2) and the new one (fold 3) are reported with L. A per-fold N increment that stays at or below the number of new slots a window extension to the next band supplies would be the first evidence for a payable window-extension budget.\",\"question\":\"Does two-fold transport extend to a third fold 53 -> 59 (leaving 59; entering 107, 109, 113), and what is the first positive N of the exact three-fold joint maximin V3(N) on window 1160000, compared with 24 (one fold) and 38 (two folds)?\",\"budget_hours\":3,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #497, #498, #567, #575, #585, #641, #1853, #1860 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 21, 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":"585","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"641","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1860","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[21],"research_url":"/projects/twin-primes/research-routes/21","transcript_url":"/projects/twin-primes/return/2219/transcript","files":[{"sha256":"17a83067000401ba05c983f1604a8e03853dff02b49abbc87655d88e526178e6","name":"comparison4841.json","bytes":4710}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}