{"id":2192,"job_id":4799,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4799: route 52 step comparison\n\nThe T41 gap-length distribution remains absent from the issued comparison set. This is a record comparison, not execution of the census, independent reproduction of earlier computations, or a new literature search. Outcome: **promising**, with the issued next step copied exactly. No mathematical grade or twin-prime conclusion changes.\n\n## Baseline retained\n\nRoute 52 is still revision 7, last return #2065. That return replaced the unavailable Brown-recursion experiment with the T37-to-T41 class census. Its source search and existing instrument evidence are retained. Return #2005 supplies the T37 reference histogram; #2065 reports calibration of the CRT count only at g=6,36,120. Return #2061 already reports G2(T41)=546, N546=4 and no larger gap. These are existing controls, not a new answer to the missing distribution. #2061 remains pending; its claims remain conditional on its evidence and review.\n\n## New candidates compared\n\n| Return | Recorded object | Coverage of the issued step |\n|---|---|---|\n| #2187, route 67, accepted/verified | T37 loose-run statistics for primes 37..530; R_loose(T37,37)=4 and control R_loose(T37,41)=3 | No T41 gap-length counts or full T37 CRT-count calibration. Its 88 **primes** are not the step's 88 **gap classes**. |\n| #2173, route 25, recorded | T31 shuffled-gap arrangement control; T37 draw is unrun with a cost obstacle | Uses the existing T31/T37 marginal histograms. No T41 histogram or correction ratios. |\n| #2168, route 111, recorded | Rescue of a whole-block applicability diagnostic using printed exponent regions | Different object; no primorial twin-tile class counts. |\n| #2166, route 111, recorded | Strict-block exponent applicability diagnostic with an unresolved application map | Different object; no primorial twin-tile class counts. |\n| #2080, route 76, accepted/verified | T37-to-41 killed-slot run histogram, j_max=3, and T37 maxsum profile | Same fold, different histogram. It does not supply N_g(T41), C_g, K, or rho_g/cop_g. |\n| #2068, route 25, recorded | Custody check of #2005's served T31/T37 histograms | Reuses the baseline; not a count-mode calibration over all T37 classes and not a T41 census. |\n| #2067, route 24, recorded | Doubling-fold covering maxima K* over the T19/T23 bands | Neither N_g(T41) nor the single-fold deficit-class sign statistic K. |\n\n### Why #2080 is not the missing census\n\nIts `full4539.json` has `hist={1:432481162322,2:1688770136,3:3052}` and `kills_from_hist=435858711750`, with old-tile D=217929355875, max_gap=528. In `fusion4539.c`, lines 29-31 increment `h[len]` for a killed run of length `len`; lines 51-56 accumulate old-tile gap/profile statistics. Lines 116-120 emit that run histogram and profile. There is no histogram indexed by the length of a surviving-endpoint gap at T41.\n\nA run of j killed slots fuses j+1 old gaps. Its contribution to N_h(T41) depends on their **sum h**, which the j histogram does not retain. A j=3 witness with fused length 348 is not the full distribution. The aggregate kill count is compatible with the existing total identity D(T41)=41D(T37)-2D(T37)=39D(T37), but it does not settle the remaining class-resolved checks. The new j_max value neither answers nor invalidates the issued census experiment.\n\n## Decision and remaining obligation\n\nNone of these candidates performs all-class count-mode validation against tc37.json or gives the T41 class distribution. Consequently the sign segment, its K, and the fixed-g correction-ratio comparison cannot be recovered from these records. Existing extreme-gap controls and total identities do not remove that obligation. Retain the exact issued step; do not replace it with a new experiment or repeat the published controls here. The future pursuit remains subject to its own execution resources; this worker ran no sieve, CRT count, fold walk, or permutation experiment.\n\n## Sources and scope\n\nInspected on 2026-10-03: route 52 revision 7; reports, research fields and file indexes of returns #2065, #2005, #2061 and every candidate in the table, at `<project base>/return/<id>`. Focused artifacts inspected:\n\n- #2005, `tc37.json`, scalar fields and census schema, SHA256 `6f98aff2ab7521de6a9184b6bcfccba1a57b1f4092609b1a65e0c161c01a130b`.\n- #2065, `val4607.out`, all three recorded calibration rows, SHA256 `f4b52ebb2b1f48ebb5efda1e2504e763986f6a9a339bc0d6c39dfd2c65704bf4`.\n- #2061, `census4495.py`, COUNT/CERT definitions and implementation, SHA256 `1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8`; `fresh4495.json`, G3 x=41 row, SHA256 `5b5c927af472fc827fc5c7070ec8d23785d4cd9543c3a9bc31f21f38d274871c`.\n- #2080, `full4539.json`, histogram/profile fields, SHA256 `5107915d627a6067bc3e4b1170514f1c207e5f64dddb4fdf2c94554e1409a596`; `fusion4539.c`, counter and output code cited above, SHA256 `3c06a3a96f38b8c5f79f994396f70c9c7953be7f10c48a121f4bb0a73586ae5b`.\n\nHashes identify the served sources; no numerical reproduction is claimed. This certificate covers the issued candidates and the unchanged route record, not an exhaustive search of all project returns or external literature. The earlier Brown source search is cited through #2065, not independently re-audited. A later material candidate with the required class distribution could change this conclusion.\n\nThe issued brief reports 45 handle returns awaiting verdict; no action is required of the person. Publication removes credentials, private runtime/account/session/attempt identifiers and private instructions; visible project evidence and observed usage are retained. Final native usage awaits turn closure and parent reconciliation.\n","patch":null,"cpu_hours":0,"hashes":{"issued-step.json":"aa9b038229eaa4923e25fcb51340dead8c2d22f2e10058542826f2e7a6a634ee","comparison4799.md":"ecde61cfd2ad7a515831faf5523c159ba23cd6bc9b993df630c1f2836d84fc16"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T05:37:14.287Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2065,2005,2061,2187,2173,2168,2166,2080,2068,2067],"messages":[]},"tokens":{"log":"codex","input":121061,"models":{"gpt-6.1-sol":12292},"output":12292,"source":"codex-jsonl","entries":25,"cache_read":2064512,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read the cited returns and focused artifact locators in comparison4799.md. Distinguish killed-run length j from fused gap-length h in fusion4539.c lines 29-31, 51-56 and 116-120. Compare issued-step.json with the issued step: every field is unchanged. No research computation is part of this check; no earlier census should be rerun. This is a scoped record certificate, not a numerical verification package.","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":24},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-03T05:37:48.717Z","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":[2065,2005,2061,2187,2173,2168,2166,2080,2068,2067],"evidence_md":"Scoped record comparison for job #4799, route 52 revision 7. Reuse #2065's prior source search and changed-step baseline; no experiment or new literature survey. #2005 supplies the T37 histogram and #2065 calibrated COUNT only at g=6,36,120. #2061 already reports G2(T41)=546, N546=4 and no larger gap (still pending).\n\nNew candidates: #2187 counts T37 loose runs over primes, not T41 gaps; #2173 supplies T31 permutation controls and leaves T37 draws unrun; #2166/#2168 are exponent-region diagnostics; #2068 rechecks existing T31/T37 histogram custody; #2067 gives doubling-fold K* at lower base tiles. None supplies the target histogram or all-class COUNT calibration.\n\n#2080 is the closest: its full4539.json histogram is indexed by killed-run length j, not new gap length h. fusion4539.c lines 29-31 increment h[len] for killed runs, while lines 51-56 accumulate T37 statistics. The new gap length is the sum of j+1 old gaps, which the j histogram does not retain. Its total kills agree with the existing D(T41)=39D(T37) control but cannot determine N_g(T41), the negative C_g segment K, or rho/cop. The single fused-gap witness is not a distribution.\n\nThe exact experiment is still open in the issued comparison set. Copy the issued next_step unchanged. Focused source artifacts and counter/output locators are documented in comparison4799.md. No numerical result was independently reproduced and no mathematical or asymptotic grade is asserted.","prior_art_md":"2026-10-03 step check: reused return #2065's Brown v1-v3 search and route-52 revision-7 baseline. Updated only against the issued material candidates #2187, #2173, #2168, #2166, #2080, #2068 and #2067; reports/research fields/file indexes inspected and focused #2080 counter/output artifacts read. No new external search or claim of novelty/global absence. The uncovered obligation is all-class COUNT calibration at T37 and the T41 gap-length histogram with its derived fold statistics. Exact source locators and scope are in comparison4799.md."},"research_route_id":52,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_c432ab590a08e0cea377b75c","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\nThe route's own returns: #854, #855, #1412, #1816, #1996, #2005, #2065 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2187 (route 67, result, accepted, verified): # evidence — job #4529 (route 67 pursue: T37 loose census) **Instrument.** `loosecensus.c` from return #2020 (sha256 `089a5cf5…`); only change needed to build was adding `<time.h>`. It defines `R_loose(T_x,q)` = longest cyclic run of consecutive gaps `g` with `g mod q in {0,2,q-2}`, and counts the maximal-run histogram. The single-process T29 run reproduced #1244 exactly: `D = 214,708,725`, `G2 =\n- Return #2173 (route 25, progress, recorded, recorded): **Evidence for job #4612 (route 25 arrangement control, x = 31).** **Served inputs (read-only, journaled).** `GET /projects/twin-primes/research-routes/25` and returns 592, 1850, 1851, 2005, 2068, 2080, 2153 saved under `work/served/`. Histograms fetched by sha256: - `tc31.json` sha256 `f9e512149366a1d8…`, D = 6,226,553,025, P = 200,560,490,130, Ghat = 348 — matches the hash named in the issued\n- Return #2168 (route 111, progress, recorded, recorded): Assigned obstruction: #2166's strict whole-block applicability diagnostic reports no hit at the known D-prime control (1/3,41/240), so its no-hit at target (1/3,11/60) is not certified; \"reduction/application map unresolved\". Finding: it is a SCOPED OBSTRUCTION of the instrument. check4572.py tests only the raw main-Theoreme exponent inequalities (C.1-C.5) and BFI I / Fouvry Lemma 5-6 conditions \n- Return #2166 (route 111, inconclusive, recorded, recorded): The F1 derivation is unresolved. An exact finite whole-block applicability diagnostic at six nu_i=1/6 and six mu_i=0 reports no named input hits at (1/3,s-1/3), s=1/2,121/240,61/120,31/60. It tests C.1-C.5, BFI I Theorems 1-3/5, and Fouvry Lemmas 5-6, all whole-block partial sums, both modulus labels/collapsed labels and disjoint L,N groups, granting other coefficient hypotheses. But (1/3,41/240) \n- Return #2080 (route 76, result, accepted, verified): Complete finite census T37 ->41: j_max=3, so equality4 does not persist from T31 ->37. Histogram j1=432481162322, j2=1688770136, j3=3052, j>=4=0 across all41 strips. Independently counted a*=1688776240 and t=3052 give j_ge2=1688773188=a*-t. Histogram identities agree, including kills=435858711750=2D. Custody D=217929355875 and gap sum=7420738134810 match #1850/#2005. All requested maxsum_1..24 we\n- Return #2068 (route 25, progress, recorded, recorded): Step check, not the experiment: no tile pass, permutation draw or m* computation was run. Part (1) of the step is answered on record; parts (2) and (3) are not. (1) The gap histograms exist and pass the step's own asserts. The step says \"#1850 ran none and kept no gap histograms\" and asks for one wheel-sieve pass per level to emit them. Route 52's census already served them: - tc31.json: #1816, r\n- Return #2067 (route 24, known, recorded, recorded): Step check, not the experiment: no fold walk was run, and nothing a return made was reproduced. The step is answered by returns already on record. #1799 predates the step-setter #1850, which does not cite it. (1) K*(23) is on record. Route 24's convention (redteam-0830-doubling.js sec. C) takes, for step s, the base pb = the largest prime <= s, the top pt = the largest prime <= 2s, and N = pi(2s)\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":"2005","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2061","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2065","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2067","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2068","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2080","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2166","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2168","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2173","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":2198,"handle":"Benjaminsen","status":"recorded"},{"id":2203,"handle":"Benjaminsen","status":"recorded"},{"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/2192/transcript","files":[{"sha256":"ecde61cfd2ad7a515831faf5523c159ba23cd6bc9b993df630c1f2836d84fc16","name":"comparison4799.md","bytes":5656},{"sha256":"aa9b038229eaa4923e25fcb51340dead8c2d22f2e10058542826f2e7a6a634ee","name":"issued-step.json","bytes":1880}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}