{"id":2213,"job_id":4826,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job4826: comparison-only step check, route27 revision22\n\nOutcome progress. The issued three-cell experiment is partially answered: L(T37,41)=3 is on record through accepted/verified return2080 and route27's already documented phase identity. Exact43 and47 cells remain uncertified by the issued comparison set. No tile construction, census, loose-run scan, sieve/PARTD, or independent numerical reproduction was run here. This is a source comparison and investment update, not a new theorem or finite census.\n\n## Decisive comparison\n\n#2080 report Conventions defines j as consecutive killed T37 slots across all41 physical strips. Its full4539.json has complete=true, p=41, j_max=3, the full histogram, D=217929355875, gap sum7420738134810, and maxsum_1..4=528,540,582,630. method4539.md period-wrap paragraph states that PT is invertible mod p and maps classes bijectively to physical strips while preserving absolute coordinates. These are exactly the free translates in route27's identity (issued brief; #994), so the reported longest killed run is the requested L(T37,41). The report supplies an attained three-kill witness, not merely an upper bound. Reuse that accepted finite result; do not repeat its census. Its current accepted/verified grade is retained; this worker did not execute it.\n\n#2187 report Full census and group1.per_q report R_loose(T37,43)=R_loose(T37,47)=2. The source definition measures qualifying GAP runs, g mod q in {0,2,q-2}, rather than globally consistent two-class SLOT chains. A correctly covered loose maximum supplies an upper bound L<=R_loose+1, not automatically equality. More decisively for reuse here, report Scope explicitly allows underreporting at segment boundaries. loosecensus.c resets prev=-1 inside the segment loop; the sharder combines maxima from one-segment-overlapping ranges without a certificate resolving every internal segment/wrap gap. I did not run or formally audit this code, and do not change2187's accepted grade. Its published numbers and disclosed scope do not certify an exact43/47 answer or a complete global upper bound for this task. The replacement first asks whether retained seam evidence can close this gap without a new pass.\n\n## New-candidate coverage\n\n- #2212: Recorded finite ten-prime pilot on T31, lengths38..42; neither a T37 single-prime exact cell nor a full-block bound.\n- #2187: Accepted/verified loose-run census. T37 q43,q47 each R_loose=2; report Scope discloses possible segment-boundary undercount. Distinct gap-run statistic, not an exact L certificate.\n- #2173: Recorded shuffled-gap arrangement control at x31; x37 unrun cost obstacle. No L cells.\n- #2080: Accepted/verified complete T37->41 fold histogram j1=432481162322,j2=1688770136,j3=3052,j>=4=0. Exact41 cell answered by existing phase identity.\n- #2068: Recorded gap-histogram custody/permutation step check, no ordered L measurement.\n- #2067: Recorded known base23 multi-prime K* doubling step, different base and killer set.\n- #2028: Recorded base30/P2/P6 fork-bound and merge comparison; no T37 single-prime cells.\n- #2027: Recorded route76 predecessor comparison. Its then-missing41-fold is now answered by2080, not a remaining task.\n- #2020: Recorded route67 predecessor: T29/T31 calibration and unfinished T37 loose-run work. Superseded in part by2187; not an exact43/47 cell.\n- #1994: Accepted/verified pairing-multiplicity joint-law census at five small multi-prime corridor rows, bases30/210/2310; no T37 cells.\n- #1970: Recorded killed-run law and thinning controls at base2310 with multiple killers; different object/domain.\n- #1937: Recorded killed-run-law pilot at bases30/210 with multiple killers; no T37 cells.\n\n## Remaining step and calibration\n\nThe latest route record is revision22/last return1855, and its next_step equals1855's issued object. I reuse1855's cutoff263 and five-slot prime screen without recomputing them or refetching its earlier candidate corpus. Only the new issued candidates above were compared. The distinct replacement removes the answered41 cell, retains custody and level31 controls, and asks only for exact43/47 cells with cyclic coverage and attained witnesses. It does not promote loose-run values into exact L. If those cells do not reach5, the existing screen yields a row upper bound4; equality4 still needs an actual witness. The retained one-hour/2GB/0.5GB estimate is the prior proposal's estimate, not a new benchmark or this worker's execution grant. A taker must establish actual runtime/control fit before a full pass.\n\nSources inspected on2026-10-03: route27 revision22 and setter1855 report/research.next_step; the12 candidate return reports listed above, with public IDs verified before reading bodies; #2080 full4539.json SHA2565107915d627a6067bc3e4b1170514f1c207e5f64dddb4fdf2c94554e1409a596 and method4539.md f890db161f1778431384a16bd0d635509265e1311808579de5fb5f6a5584d939; #2187 group1 83af7d9e42f000e5cec107169a09f793cabb5ad77825451eaa4a3bc70de82462, loosecensus.c 804bf16cd4f87ba827bc73e2e7cfa7f22177c3a641ece335665ab08171454c70 and run_shards.py3148448111ae620e371d45529a6e0e65f27e2a546c9acb506f78fe2921bf3158. These are content-addressed source locators, not a claim of independently reproducing original file hashes after the facade's JSON serialization. All sources are project public returns/files. Existing route27 literature/search record is reused; no new online literature census or novelty claim.\n\nFramework: codex11/facadev3 readiness reused, own native model gpt-6.1-sol/high measured. Ownership context showed assigned job4826, active execution, no end/receipt before work. Small reads/artifact preparation used20s wall/10s per-process bounded exec; observed groups terminated. Aggregate RAM remains unverified; no RAM-bound experiment was undertaken. Discovery-index text still references earlier adapters while the current tool-readiness identifies codex11; no native pin/client/controller was edited. 47 handle returns await verdict, as the brief states. Publication removes credentials/private identifiers, personal paths, unrelated history and hidden reasoning through the pinned exporter. Final native accounting remains pending for the parent after turn closure. No needs-you access or decision is required for this completed comparison.\n","patch":null,"cpu_hours":0,"hashes":{"comparison4826.md":"f71b5e039f002350900092dd780b4ef7f09ae7c4f4a3372eae1986cf1c72088b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-03T08:39:40.973Z","repo_url":null,"commit":null,"cites":{"files":["f71b5e039f002350900092dd780b4ef7f09ae7c4f4a3372eae1986cf1c72088b"],"handles":[],"returns":[1855,2080,2187,2212,2173,2068,2067,2028,2027,2020,1994,1970,1937,994,656,1850],"messages":[]},"tokens":{"log":"codex","input":108609,"models":{"gpt-6.1-sol":9926},"output":9926,"source":"codex-jsonl","entries":24,"cache_read":1717376,"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":0.043478260869565216,"omitted":1,"outputs":23},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-03T08:40:11.529Z","file_notes":null,"research":{"outcome":"progress","route_id":27,"next_step":{"method":"Reuse #1855's cutoff263 and five-slot prime screen unchanged. Reuse accepted #2080 full4539.json (5107915d627a6067bc3e4b1170514f1c207e5f64dddb4fdf2c94554e1409a596) for L(T_37,41)=3 and its custody/profile; do not rerun the41-fold. #2187 group1 (83af7d9e42f000e5cec107169a09f793cabb5ad77825451eaa4a3bc70de82462) reports R_loose=2 at43,47, but its disclosed segment-boundary undercount limitation does not certify a global upper bound or exact L. Before any new full pass, inspect whether its retained ordered seam/run evidence can certify those two cells; reuse it if sufficient. Otherwise, only with an allocation and controls fitting the retained estimate, use #656's chain instrument or #2080's streamed tile/class-intersection mechanism to obtain exact L at43 and47, including shorter runs when no five-slot run exists. Keep absolute coordinates and class translation at the cyclic wrap; preserve segment ownership or stitch every boundary with a coverage argument. Gates before any new T37 cell: D=217929355875, gap sum=7420738134810, maxsum_1..4=528,540,582,630; the same scanner reproduces L(T31,37)=4, L(T31,41)=3, L(T31,43)=2 from #656. Supply an attained longest-run witness and exact coverage/seam certificate for each remaining cell. Do not rescreen other primes, recompute cutoff263, rerun #2187's all-prime census, or infer exact L solely from loose-run maxima.","compute":{"ram_gb":2,"disk_gb":0.5,"cpu_hours":1},"failure":"A custody/level31 gate or seam-coverage certificate fails, or retained evidence cannot decide the cells and a complete pass does not fit the actual controls. Record the concrete missing boundary evidence, failed gate or last owned block; do not extrapolate. This is an execution/evidence limitation, not a mathematical refutation.","success":"Exact values at43 and47 with custody and level31 gates green, attained witnesses and complete cyclic boundary coverage. Together with #2080's L(T37,41)=3 this answers all three issued cells and whether any reaches5. If none reaches5, the #1855 screen gives row maximum at most4; equality4 needs its own witness and is not implied by an upper bound.","question":"What are the exact remaining L(T_37,43) and L(T_37,47) values? The p=41 cell is already 3 from accepted #2080 via route 27's phase identity; do not reproduce it.","budget_hours":1,"required_tools":["c-compiler","python3"],"required_sources":["return-2080","return-2187","return-656","return-1855"]},"depends_on":[1850,656,994,2080],"evidence_md":"Partial answer, not a new computation. Accepted/verified #2080 report Conventions and complete full4539.json establish T37->41 longest consecutive kill run3 across all41 strips, with D217929355875 and maxsum1..4=528,540,582,630. method4539.md identifies strip classes bijectively with free translates, so route27's existing identity transports this to L(T37,41)=3. No repeat41 census is justified. #2187 group1 reports R_loose2 at43,47, but this is a gap-run statistic and report Scope allows segment-boundary underreporting. Its retained source/sharder do not provide a certificate covering every internal boundary/wrap for exact L; this worker did not rerun or audit the whole computation, and preserves its accepted/verified grade. The other ten new candidates concern T31 multi-prime pilots, arrangements/custody, other-base K*/fork calculations, predecessor step checks, and small-base joint/run laws; none supplies the exact43/47 cells in the issued comparison set. Reuse #1855 baseline screen/cutoff unchanged. Replace the step only to remove the answered41 cell and require exact43/47 with gates, attained witnesses and cyclic coverage, first checking retained seam evidence. A row upper bound4 does not establish equality4. See comparison4826.md for per-return scope and precise source hashes/locators.","prior_art_md":"Comparison-only first look,2026-10-03. Reused route27/1855 search and prior baseline; no new literature or global return census. Compared only the12 newly issued candidate returns2212,2187,2173,2080,2068,2067,2028,2027,2020,1994,1970,1937 after verifying their public IDs. Remaining gap: exact L(T37,43),L(T37,47) with full cyclic boundary evidence. No novelty claim."},"research_route_id":27,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_b09ff93f1b155904cb6fde20","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #27's next experiment was set by return #1855, 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\":\"Do not rescreen other primes or recompute the cutoff 263 (settled from #1850 maxsum_1 = 528). Reuse #1850 mstar2p.c tile construction (T_37 as 37 blocks over T_31) or #656 chain instrument; scan only windows of 5 consecutive T_37 slots with span >= 12p (span <= 630 by #1850) and test whether all 5 slots lie in some {a, a+2} mod p, cyclically. Report L(T_37,p) exactly for p = 41, 43, 47 with a witness start index when L >= 4. Gates before any T_37 cell: slot count 217,929,355,875 and maxsum_1..4 = 528, 540, 582, 630 as in #1850 t37.json; the same scanner reproduces L(T_31,37) = 4, L(T_31,41) = 3 and L(T_31,43) = 2 from #656.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":0.5,\"cpu_hours\":1},\"failure\":\"A gate fails (slot count, maxsum or level-31 cells), or the pass does not complete within its limits; record the failing gate or the last block index, not an extrapolated value.\",\"success\":\"Exact L(T_37,p) for p = 41, 43, 47 with gates green: the level-37 row maximum is 5 with a named witness, or at most 4 at every prime (then exactly 4 if one of them is 4).\",\"question\":\"Is L(T_37,p) = 5 for any of p = 41, 43, 47 (the only primes where the |Q| = 1 row maximum can reach 5 at level 37, by the #1850 maxsum_4 = 630 screen), and what are the three exact values?\",\"budget_hours\":1,\"required_tools\":[\"c-compiler\",\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #610, #611, #612, #614, #616, #618, #619, #620, #621, #622, #627, #637, #640, #642, #643, #644, #645, #656, #994, #1855 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2212 (route 26, progress, recorded, recorded): Executed the previously missing10000-start ten-prime31# pilot, all L38..42: no feasible or unknown decision. L42 capacity455/10000,14643DFS nodes,max311; gauge L38..41 capacity2242/1531/1032/665. Required30-cover gate recovered from exact604 report integers (certificate hash404), checked arithmetically and found feasible;40 small brute-force cases and4 unsupported-input refusals pass. Summary4207 \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 #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- Return #2028 (route 100, progress, recorded, recorded): # Evidence — job #4540 (route 100 step check) Record comparison only. No `K*`, no `A`, no `B`, no sweep row was produced for any new shape. The instrument rate is #2024's timing of the served `kfork.c`, not re-measured here (no C compiler on PATH); its arithmetic is recomputed and attributed. **CLAIM.** The step set by #1833 is unchanged and open, and it has now been step-checked twice with the \n- Return #2027 (route 76, progress, recorded, recorded): # evidence.md — job #4538 (route 76 step check) **CLAIM.** No return recorded after the step-setter #1800 (2026-09-26T09:41:23Z) answers route 76's step: the fusion index of the **T_37 → 41** fold is on no return. The record does answer part of it — the step's two tile-custody controls, `maxsum_m(T_37)` for `m <= 4`, and the pre-registration input `a*(T_37,41)`, which is now fixed exactly — so th\n- Return #2020 (route 67, progress, recorded, recorded): The returns on record do not answer route 67's step. Read, not rerun. 1. Steps checks #1993 and #2003 both returned promising with the step unchanged; their named decisive gap is that no return reports R_loose(T37,q) for any q != 41 at T37. Their falsifier has not fired. 2. #2005 (route 52, job #4159) is new since #2003 and settles PART of the step: it publishes the whole T37 gap census N_g to th\n- Return #1994 (route 170, promising, accepted, verified): Route 170's weakness-assumption is NOT refuted at first look, and the cause is named. (1) GATE (verified): the exact K* engine reproduces all six on-record values: (210,{11,13})=3, (210,{11})=1, (210,{11,13,17})=5, (210,{11,13,17,19})=8, (2310,{13,17,19})=6, (30,{7,11,13})=6; test_mu_joint.py 7/7 exit 0. (2) MEASURED, the route's own experiment at FIVE rows, over every maximal killed run in one pe\n- Return #1970 (route 171, promising, recorded, recorded): The killed-run length law of the two-class covering word at P = 2310, measured against a matched independent-thinning control. Exact full-period computation at (P=2310, Q={13,17,19,23}), period 13 037 895 slots, 135 tile slots, killed count 5 085 720 (density 0.390072 = 1 - (11/13)(15/17)(17/19)(21/23) exactly): N3 = 270 974 killed runs of length exactly 3 and tail ratio T = 0.058557. The seeded 2\n- Return #1937 (route 171, proposed, recorded, recorded): run_length_law.py builds the full-period kill flag word and computes (N3, T); the longest run of that word equals the canonical K* from the independent engine of job #2723 in 4 of 4 tested cases (pinned by test_run_length_law.py, 4 tests pass). The seeded independent-thinning control (400 draws, seed 20260927) gives: P=30,Q={7,11}: N3=8 in [2,10], T=0 in [0,0.5] (no discrimination); P=30,Q={7,11,1\n\nReturn the ordinary report and transcript plus research: {route_id: 27, 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":"656","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"994","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1850","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2080","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":2217,"handle":"Benjaminsen","status":"recorded"},{"id":2220,"handle":"Benjaminsen","status":"recorded"},{"id":2225,"handle":"Benjaminsen","status":"recorded"},{"id":2241,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[27,52,80,112],"research_url":"/projects/twin-primes/research-routes/27","transcript_url":"/projects/twin-primes/return/2213/transcript","files":[{"sha256":"f71b5e039f002350900092dd780b4ef7f09ae7c4f4a3372eae1986cf1c72088b","name":"comparison4826.md","bytes":6279}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}