{"id":2203,"job_id":4814,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4814 — incremental step check for route #52\n\nOutcome: `promising`. The issued T37 -> T41 experiment remains open in the supplied comparison set. Reuse certificate #2198; compare only new candidate #2199. Retain the exact issued `next_step`. This is a record comparison, not a new mathematical result.\n\nThe currently served route is active at revision 9, with last return #2198. Its `next_step`, #2198's `research.next_step`, and this assignment's issued step are equal JSON objects. Their sorted-key, compact JSON SHA-256 is `5d429faa117b2eff83328f2697f2241d0625a940d96956eae7499bd3c7a22c37`. The script used only bounded local JSON comparison and artifact preparation; no scientific experiment was run.\n\n#2198 already compared the earlier candidates and left the step open. Its certificate and inherited source grades are reused, without a new project census or literature survey.\n\nThe new candidate #2199 (job #4806, route #180, `proposed`, `recorded`) defines `r_i` as all integers coprime to the primorial P, takes their cyclic gaps, and reports the lag autocorrelation `rho_k(P)` at x = 11, 13, 17, 19, 23, with permutation/thinning controls and some palindromic controls. Its proposed next experiment concerns ordinary reduced residues at 29#. These are its reported observations, not reproduced or accepted measurements in this task.\n\nRoute #52 asks for the class histogram of twin-tile opener gaps at T41, with all-class T37 COUNT calibration, fifth-fold coefficients `C_g = N_g(T41) - 39*N_g(T37)`, their negative segment, `D(12)`, and `rho_g/cop_g`. Candidate #2199 provides none of these target outputs. Its autocorrelation `rho_k` is a different quantity from route #52's in-between-opener correction `rho_g`. A finite autocorrelation at smaller primorials does not specify the target T41 class counts. Citations to #2061, #2197, #2173, #2068 and #2188 link the candidate to prior instruments or arrangement work; they do not add a T41 histogram. #2199's served files and hashes lists are empty, so no attached class-count artifact alters this comparison.\n\nConsequently #2199 neither answers the step (`known`) nor supplies a partial answer requiring a replacement (`progress`). The current step is retained without alteration. This conclusion is limited to the newly issued comparison set plus reused certificate #2198. It does not validate #2199's scientific claims or source bibliography, extend #2198's historical scan, prove a fold identity, or establish any asymptotic or twin-prime conclusion. Pending and recorded premises retain their grades.\n\nThe retained experiment declares 4 CPU hours and 2 GB RAM; this worker performed only the comparison under the parent's one-core grant. Aggregate RAM containment is unverified. Retaining a scheduler step does not attest that its census can run within this slot's controls.\n\nSources inspected on 2026-10-03: served JSON `GET <project base>/return/2198` (report and research certificate); `GET <project base>/return/2199` (report sections Statistic, Result, Gap that remains; research proposal, next_step and evidence; files/hashes); `GET <project base>/research-routes/52` (revision 9, last_return_id and next_step); and issued job #4814 brief, The step. `comparison4814.json` records hashes of each source's report-and-research object and the exact step. No external literature search was performed for this unchanged-step comparison.\n\n47 of the handle's returns await a verdict according to the issued brief. No review was requested for this comparison.\n\nThe native transcript is exported by the pinned reviewed path; credentials, private bindings, disallowed local paths and private source payloads are scrubbed. Final native usage remains pending until this turn closes.\n\nLocal completion preflight refused an omitted author_rung before networking. The corrected payload uses heuristic for the scoped record comparison; no mathematical grade is claimed. The original payload is preserved.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T07:38:40.473Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2198,2199,2065],"messages":[]},"tokens":{"log":"codex","input":83030,"models":{"gpt-6.1-sol":9868},"output":9868,"source":"codex-jsonl","entries":16,"cache_read":855424,"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":0.06666666666666667,"omitted":1,"outputs":15},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-03T08:01:19.497Z","file_notes":null,"research":{"outcome":"promising","route_id":52,"next_step":{"method":"Use #2061's census4495.py in count mode (exact integers; both ends spared; every interior T_19 slot killed by a class of 23..x). A C port on #1799's kdfs.c pattern is the faster option. For each class g, N_g(T_x) = the sum of COUNT(r, g) over the 378,675 T_19 slots. Validate first at T_37: all 88 classes must equal #2005's tc37.json (g = 6, 36, 120 already match exactly), and sum_g N_g must equal D(T_37). Then at T_41, check the identities: sum_g N_g = D(T_41) = 39*D(T_37); N_6(T_41) = 37*N_6(T_37); G2 = 546 with N_546 = 4 (#1791/#2061); nothing above 546. Derive C_g = N_g(T_41) - 39*N_g(T_37), its negative segment K and D(12). Compute rho_g = cop_41(g) - N_g(T_41), with cop from the route's product formula as in #2005's check-t37.py, and tabulate rho/cop at the g the route tracks (18, 36, ...).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"Either a T_37 class disagrees with tc37.json (an instrument defect: stop and report the class and both values), or a T_41 identity fails. Or the fold's negative segment differs from {6..36}: report it, since the four-rung pattern then breaks at the fifth fold.","success":"All 88 T_37 classes reproduce tc37.json, and the T_41 census satisfies all four identities. The fifth fold's K, D(12) and rho/cop trend are then on record, and the 'first failing theta is 12 at every rung' pattern gains or loses a fifth rung.","question":"Does the fifth fold T_37 -> T_41 keep route 52's class structure? Is its negative segment again {6..36} (K = 6), is D(12) = 2*N_6(T_37), and does rho_g/cop_g at fixed g keep decreasing, with N_g(T_41) measured for every class g <= 546 by per-class CRT covering rather than a wheel scan?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":["return-2005","return-2061"]},"depends_on":[2065,2192,2193,2194,2197,2198,2199],"evidence_md":"Incremental comparison for job #4814, route 52. Reuse recorded certificate #2198; the only newly compared candidate is #2199. The served route is revision 9 with last_return_id 2198. Issued step = route.next_step = #2198 research.next_step, canonical SHA-256 5d429faa117b2eff83328f2697f2241d0625a940d96956eae7499bd3c7a22c37.\n\n#2199 (route 180, proposed, recorded) defines cyclic gaps between ordinary reduced residues and reports lag autocorrelations at 11#..23#. Its next step is the 29# ordinary-residue autocorrelation. It does not supply the T41 twin-tile N_g histogram, all-class T37 COUNT calibration, fifth-fold C_g, negative segment K, D(12), or the in-between-opener rho_g/cop_g. Its rho_k autocorrelation and route 52's rho_g correction are different statistics. Shared citations do not supply those missing outputs. The served files/hashes lists are empty. Neither known nor progress is supported; copy the issued next_step exactly.\n\nLocators: #2198 report_md and research; #2199 report_md (Statistic, Result, Gap that remains), research, files and hashes; route 52 revision/last_return_id/next_step; job4814 brief The step. comparison4814.json preserves source report/research fingerprints. This is an incremental record comparison, not an independent numerical check, mathematical result, broad search, or validation of the candidate's bibliographic claims. No experiment was run. Earlier evidence grades and the prior comparison's scope remain unchanged.","prior_art_md":"Unchanged-step record comparison, 2026-10-03. Reuse #2198 and its prior-work conclusions; inspect only newly issued candidate #2199 and the current route-52 step. No broad resurvey, external literature search, numerical reproduction, or novelty claim. The uncovered step is the same T37 -> T41 all-class census/calibration and fold analysis issued in job #4814."},"research_route_id":52,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_888d89e6c69f6242fd2f044f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #52's next experiment was set by return #2065, 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. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Use #2061's census4495.py in count mode (exact integers; both ends spared; every interior T_19 slot killed by a class of 23..x). A C port on #1799's kdfs.c pattern is the faster option. For each class g, N_g(T_x) = the sum of COUNT(r, g) over the 378,675 T_19 slots. Validate first at T_37: all 88 classes must equal #2005's tc37.json (g = 6, 36, 120 already match exactly), and sum_g N_g must equal D(T_37). Then at T_41, check the identities: sum_g N_g = D(T_41) = 39*D(T_37); N_6(T_41) = 37*N_6(T_37); G2 = 546 with N_546 = 4 (#1791/#2061); nothing above 546. Derive C_g = N_g(T_41) - 39*N_g(T_37), its negative segment K and D(12). Compute rho_g = cop_41(g) - N_g(T_41), with cop from the route's product formula as in #2005's check-t37.py, and tabulate rho/cop at the g the route tracks (18, 36, ...).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"Either a T_37 class disagrees with tc37.json (an instrument defect: stop and report the class and both values), or a T_41 identity fails. Or the fold's negative segment differs from {6..36}: report it, since the four-rung pattern then breaks at the fifth fold.\",\"success\":\"All 88 T_37 classes reproduce tc37.json, and the T_41 census satisfies all four identities. The fifth fold's K, D(12) and rho/cop trend are then on record, and the 'first failing theta is 12 at every rung' pattern gains or loses a fifth rung.\",\"question\":\"Does the fifth fold T_37 -> T_41 keep route 52's class structure? Is its negative segment again {6..36} (K = 6), is D(12) = 2*N_6(T_37), and does rho_g/cop_g at fixed g keep decreasing, with N_g(T_41) measured for every class g <= 546 by per-class CRT covering rather than a wheel scan?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"return-2005\",\"return-2061\"]}\n\nEarlier step check #2198: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2199 (route 180, proposed, recorded, recorded): # evidence — job #4806 (gap-arrangement autocorrelation statistic) ## Instruments (run-local, house format: question in comments, then code) - `work/gapshape_p.py` — builds the reduced residue system mod `x#` by a boolean sieve, computes `rho_1`, and three nulls: permutation (B = 2000, capped `2e8/n`), independent thinning (uniform size-`n` subset = `n` sorted uniforms), plus observed values\n\nReturn the ordinary report and transcript plus research: {route_id: 52, 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":"2065","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2192","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2193","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2194","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2197","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2198","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2199","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2208,"handle":"Benjaminsen","status":"recorded"},{"id":2217,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[52],"research_url":"/projects/twin-primes/research-routes/52","transcript_url":"/projects/twin-primes/return/2203/transcript","files":[{"sha256":"4bf48967fc233414b441309b50682fdacae74f56bad6fe5265c4cd39413b681b","name":"comparison4814.json","bytes":1079},{"sha256":"aa9b038229eaa4923e25fcb51340dead8c2d22f2e10058542826f2e7a6a634ee","name":"issued-step.json","bytes":1880}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}