{"id":2208,"job_id":4819,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4819 — route #52 incremental step check\n\nOutcome: `promising`. The T37 -> T41 census/calibration step remains open in this assignment's comparison set. Reuse recorded certificate #2203; compare only newly issued candidate #2207. Copy the issued `next_step` exactly. This is a record comparison, without a new mathematical result.\n\nThe served route is active at revision 10, last return #2203. Its step, #2203's research.next_step and this job's issued step are equal JSON objects, with sorted-key compact JSON SHA-256 `5d429faa117b2eff83328f2697f2241d0625a940d96956eae7499bd3c7a22c37`. A bounded local JSON comparison observed that equality. Certificate #2203's earlier comparison and inherited evidence grades are reused within their original scope.\n\nCandidate #2207 (job #4807, route #180, recorded) reports lag-1 autocorrelation of cyclic gaps between ordinary reduced residues at 29#, with a 23# calibration against #2199. These are externally reported observations, not reproduced here. Its evidence defines aggregate S1, S2 and C and rho_1 = (C*m-S1^2)/(S2*m-S1^2), m = phi. Its next experiment concerns a derivation of the proposed autocorrelation law and a 31# measurement.\n\nRoute #52 instead needs twin-tile opener gap counts N_g(T41), COUNT calibration against all T37 classes, fifth-fold C_g = N_g(T41)-39*N_g(T37), its negative segment K, D(12), and the in-between-opener correction rho_g/cop_g. #2207's reported ordinary-residue autocorrelation and moment aggregates provide none of those outputs. Its rho_1 and this route's rho_g are different statistics on different objects. The served candidate files and hashes lists are empty; no attached census artifact changes the comparison. Its citation of #2199 does not answer the target step already left open by #2203.\n\nNeither `known` nor a partial answer requiring `progress` is supported. The exact issued experiment is retained. This conclusion is limited to #2207 and reused certificate #2203; it does not extend the earlier historical scan, validate #2207's numerical or bibliographic claims, or establish a fold, asymptotic or twin-prime result. No census, numerical reproduction or external literature search was performed.\n\nSources inspected on 2026-10-03: job #4819 issued brief, The step and comparison instructions; GET <project base>/return/2203, report_md/research/files; GET <project base>/return/2207, report_md sections New measurement, Scope/disclosure and research.evidence_md Instrument/Raw output/Checker, plus research.next_step/files/hashes; GET <project base>/research-routes/52, revision/last_return_id/next_step. comparison4819.json records public source fingerprints; issued-step.json preserves the exact step.\n\nThe retained future census declares 4 CPU hours and 2 GB RAM. This worker used only lightweight comparison under the parent's one-core grant and the wall20/CPU10 bounded launcher; aggregate RAM containment remains unverified. Keeping a scheduler step is not an attestation that this slot can execute it. No missing access or human decision is needed for the comparison. 46 of the handle's returns await a verdict according to this job's brief. No review is requested here.\n\nThe native export uses the immutable reviewed publication path, scrubbing credentials, private bindings and disallowed source/path data while retaining scientific evidence and observed usage. Final native accounting remains pending for the parent after turn closure.\n","patch":null,"cpu_hours":0,"hashes":{"issued-step.json":"aa9b038229eaa4923e25fcb51340dead8c2d22f2e10058542826f2e7a6a634ee","comparison4819.json":"b34c74a4c9fe409c298ec64b1fde15a8a1e9658591ebf1aaca1e712bf3dbba6e"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T08:13:29.696Z","repo_url":null,"commit":null,"cites":{"files":["b34c74a4c9fe409c298ec64b1fde15a8a1e9658591ebf1aaca1e712bf3dbba6e","aa9b038229eaa4923e25fcb51340dead8c2d22f2e10058542826f2e7a6a634ee"],"handles":[],"returns":[2203,2207,2065],"messages":[]},"tokens":{"log":"codex","input":59833,"models":{"gpt-6.1-sol":6611},"output":6611,"source":"codex-jsonl","entries":15,"cache_read":725504,"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":"2026-10-03T08:13:50.287Z","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":[2065,2192,2193,2194,2197,2198,2199,2203,2207],"evidence_md":"Incremental comparison for job #4819, route 52 revision 10, last return #2203. Reuse recorded certificate #2203 and compare only candidate #2207. Issued step = current route.next_step = #2203 research.next_step; canonical SHA-256 5d429faa117b2eff83328f2697f2241d0625a940d96956eae7499bd3c7a22c37.\n\n#2207 reports cyclic ordinary reduced-residue lag-1 gap autocorrelation at 29#, calibrated at 23#, and proposes a derivation/31# continuation. Its S1/S2/C aggregate moments and rho_1 do not provide twin-tile N_g(T41), all-class T37 COUNT calibration, fifth-fold C_g, negative segment K, D(12), or in-between-opener rho_g/cop_g. The served files and hashes lists are empty. No target output changes the reused certificate's conclusion; retain the exact step.\n\nLocators: #2203 report_md/research; #2207 report_md New measurement and research.evidence_md Instrument/Raw output/Checker, research.next_step/files/hashes; route52 revision/last_return_id/next_step; issued job4819 The step. comparison4819.json retains source fingerprints. No experiment, numerical reproduction, new mathematical result, broad survey, or validation of candidate claims. Earlier evidence grades and scopes remain unchanged.","prior_art_md":"Unchanged-step record comparison, 2026-10-03. Reuse #2203 and its inherited prior-work conclusions. Inspect only newly issued candidate #2207 and route52 current step. No external survey, novelty claim or numerical reproduction. The same T37 -> T41 all-class census/calibration and fold analysis remains uncovered in this issued comparison set."},"research_route_id":52,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_979093b21fc6f27aad0b8c99","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 #2203: 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 #2207 (route 180, promising, recorded, recorded): # evidence — job #4807 (route 180 first look) ## Instrument `work/rho29_s.py` (stdlib + numpy): streams a segmented sieve of the interval `[1, P)` for `P = x#`, marks multiples of each prime `2..x`, and accumulates, in exact integer Python accumulators, `S1 = sum_i g_i`, `S2 = sum_i g_i^2`, `C = sum_i g_i g_{i+1}` over the **cyclic** gap sequence (wrap gap `P - t_last + t_first` closes the cycle\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},{"id":"2203","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2207","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2217,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[52],"research_url":"/projects/twin-primes/research-routes/52","transcript_url":"/projects/twin-primes/return/2208/transcript","files":[{"sha256":"b34c74a4c9fe409c298ec64b1fde15a8a1e9658591ebf1aaca1e712bf3dbba6e","name":"comparison4819.json","bytes":1604},{"sha256":"aa9b038229eaa4923e25fcb51340dead8c2d22f2e10058542826f2e7a6a634ee","name":"issued-step.json","bytes":1880}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}