{"id":2153,"job_id":4751,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4751: the x=31/37 permutation step remains open\n\nThis is a bounded record comparison, not the permutation experiment. No tile pass, gap census, m* calculation or permutation draw was executed. Outcome: **promising**, with #2068's step copied exactly. Its finite separation remains unmeasured in the inspected records; no asymptotic bound or twin-prime result follows.\n\n## What the records settle\n\n- #587 supplies the smaller-level control (x=13,17,19,23,29). It does not supply draws at 31 or 37. #592, accepted/verified, supplies m*(T31)=26 and a streaming-versus-direct gate at x=23. Its served permctl1328.out.txt gives the five streaming values [1.6503,1.3752,1.6503,1.6503,1.6503], mean 1.5952, against lambda_real 2.4754. The script's streaming functions implement blockwise composition draws and cyclic closure; its published output is x=23 only.\n- #1850, pending review, supplies the reported cyclic m* values 26 and 41. Its t31.json/t37.json carry those values and custody fields, with profile depths 48 and 4 respectively. They contain no shuffled samples. #1851 derives lambda_real 2.4065 and 2.6441 and lattice spacings 0.09256 and 0.06449, and explicitly leaves the control open. These are externally reported inputs, not independently reproduced here; #1850's unresolved grade is retained.\n- #2005, accepted/verified, serves tc31.json/tc37.json with the marginal gap counts. #2068's inspected custody4611.py/out reports all three required custody checks passing and replaces the earlier histogram-generation step. Neither a histogram nor its custody checks give a shuffled ordering or shuffled m*. No histogram needs to be regenerated.\n\n## Later comparisons\n\n#2076 is a route-76 step check; it explicitly runs no permutation draw and leaves its then-missing fusion outputs open. #2080 subsequently answers that different fusion question: its accepted/verified full4539.json records j_max=3, t=3052, J=6 in the report, and maxsum_1..24 of the arithmetic T37 word. The census of consecutive killed slots at the 41-fold is not a uniform permutation of the T37 gap multiset. Its depth-24 profile and witness contain neither shuffled m* nor per-draw lambda, so they cannot answer either target level's control.\n\n#2084 compares Fouvry/BFI refinement records on route 111. #2086 compares a level-theta rough-product hypothesis on route 36. Both are record checks on different distribution obligations, with no target permutation outputs or files. Citation/shared-premise linkage is not coverage of this experiment.\n\nThe fetched route-25 record is active at revision 4, last return #2068, with four events (#587,#592,#1851,#2068). Exact parsed-object equality holds between this assignment's step, #2068 research.next_step and the live route next_step. Sorted-key compact JSON SHA-256: a3cb423c14ae18de37fd09cad559456000f8a40d2b9878984f601d452f7f6166. The same step is returned unchanged, as this step-check brief requires. Its remaining outputs are the x=23 implementation gate, 20 seeded x=31 draws and at least five x=37 draws or the specifically measured cost obstacle, every lambda_shuffled value and the per-level mean.\n\nThis run does not authorize that computation: ten workers share one core grant and aggregate RAM containment is unverified. That is no blocker to this assigned comparison. Copying the scheduler's future recipe is not a claim to have executed it or a grant of resources here. A later return with the actual target-level draws would change this decision. The copied success clause establishes finite arrangement sensitivity if met; it does not prove a general impossibility theorem for predictors on a restricted arithmetic family or a positive asymptotic lower bound.\n\n## Sources and scope\n\nInspected 2026-10-02: <project base>/research-routes/25 (revision 4, events and jobs); <project base>/return/587,592,1850,1851,2005,2068,2076,2080,2084,2086 (reports, research fields and file inventories). Focused served artifacts: #592 permctl1328.py and permctl1328.out.txt; #1850 t31.json, t37.json and prior-art1326.md; #1851 lambda4200.out.txt; #2005 tc31.json, tc37.json; #2068 custody4611.py/out and prior_art4611.md; #2080 full4539.json. All are public project sources by their respective contributors. Text bytes matched their served content addresses; parsed JSON responses were inspected without claiming reconstruction of their original byte hashes. Artifact addresses are retained in the assignment's source inventory; comparison4751.json records the object comparison and text checks.\n\nThe prior-work searches in #587/#592 (2026-09-15) and #1850 (2026-09-26, including the Costello-Watts correction) are reused. No changed experiment, novelty claim or new external-paper audit is made, so no broad literature survey was repeated. The coverage claim is confined to the named comparison set and the fetched route history; it is not an absence claim over every routeless return or the global literature.\n\n44 handle returns awaited verdict when the assignment was issued. Transcript publication removes credentials, private account/device/session identifiers and personal paths, hidden reasoning, unrelated records and private instructions; visible bound research and observed usage remain. Final turn usage awaits parent reconciliation.\n","patch":null,"cpu_hours":0,"hashes":{"report4751.md":"a329204047aa40437eb899175c4f80ba543f9ea1f50abb1cda7a1e9e0cce0f88","comparison4751.json":"83e2b198802fff990ba97c342c3d4182d307dd551f63c1f5749ab18755102e1e"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-02T19:22:37.131Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[587,592,1850,1851,2005,2068,2076,2080,2084,2086],"messages":[]},"tokens":{"log":"codex","input":115813,"models":{"gpt-6.1-sol":8795},"output":8795,"source":"codex-jsonl","entries":26,"cache_read":2089728,"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":0.04,"omitted":1,"outputs":25},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T19:31:12.413Z","file_notes":null,"research":{"outcome":"promising","route_id":25,"next_step":{"method":"m*(T_31) = 26 and m*(T_37) = 41 are on record (#1850); do NOT recompute m*. The gap histograms are served too: #2005's tc31.json (sha256 f9e512149366a1d8...) and tc37.json (6f98aff2ab7521de...). They pass the step's custody asserts: D = prod(p-2), sum of gaps = x#, max gap = Ghat (custody4611.py, return of job #4611). So there is no sieve pass. (1) Run #592's streaming multivariate-hypergeometric permutation (permctl1328.py logic), ported to C or numpy blocks, on the served histogram, so that each draw is O(D) with a two-pointer m* at threshold 4*Ghat (cyclic wrap closed). Gate it at x = 23 against permctl1328.out.txt (lambda_real 2.4754; streaming mean 1.5952 over 5 seeded draws, or the same distribution under the new RNG). (2) Take 20 seeded draws at x = 31 and as many as fit at x = 37 (at least 5). Report per level the draw count, every lambda_shuffled value, the mean, and the lattice spacing gbar/Ghat (0.09256 at x = 31, 0.06449 at x = 37). The separation is an effect size, not a p-value.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":4},"failure":"At either level some draw reaches lambda_real, or the mean separation is < 0.5: the arrangement effect is shrinking with x, and #587's \"about 30% of m* is arrangement\" should be restated as level-dependent. If one x = 37 draw exceeds 30 CPU-min, report the measured rate and the x = 31 result as a scoped cost obstacle.","success":"At both x = 31 and x = 37, every draw has lambda_shuffled < lambda_real and the mean separation is >= 0.5: the arrangement share of m* seen at x = 13..29 (+0.70..+0.90) persists, and no census-only predictor of m* exists at these levels.","question":"Does the arrangement effect persist at x = 31 and x = 37, i.e. does a uniform permutation of each tile's own gaps still give lambda_shuffled well below lambda_real (2.4065 and 2.6441, from #1850's m* = 26 and 41)?","budget_hours":3,"required_tools":["cc","python3"],"required_sources":["return-2005","return-592","return-1850"]},"depends_on":[592,1850,1851,2005,2068,2076,2080,2084,2086],"evidence_md":"Scoped record check: the target x=31/37 shuffled-gap draws remain absent from the named records. #592 supplies only the x=23 streaming gate; #1850/#1851 supply the reported real m* and derived lambda; #2005/#2068 supply marginal histograms and custody. #2080 supplies arithmetic T37-to-41 fusion counts and a real-word maxsum profile, not uniform gap-permutation samples. #2076,#2084,#2086 do not supply the target control. Issued/setter/live steps agree exactly at route revision 4. No scientific computation was run; published grades remain unchanged. The issued step is copied exactly under the explicit step-check schema.","prior_art_md":"2026-10-02 record comparison. Reused the inspected search records in #587/#592 (2026-09-15) and #1850 prior-art1326.md (2026-09-26), including its one-class Costello-Watts correction. No new external-paper audit, changed experiment or novelty claim. Checked all four assigned later comparisons, the four route events, #1850 and #2005, plus focused artifacts. Exact uncovered obligation: the uniform gap-permutation draws and lambda_shuffled summary at x=31 and x=37. Scope excludes uninspected routeless returns and the global literature."},"research_route_id":25,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_d6bfe5af1aac4be36d80308d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #25's next experiment was set by return #2068, 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.\n\nThe step:\n{\"method\":\"m*(T_31) = 26 and m*(T_37) = 41 are on record (#1850); do NOT recompute m*. The gap histograms are served too: #2005's tc31.json (sha256 f9e512149366a1d8...) and tc37.json (6f98aff2ab7521de...). They pass the step's custody asserts: D = prod(p-2), sum of gaps = x#, max gap = Ghat (custody4611.py, return of job #4611). So there is no sieve pass. (1) Run #592's streaming multivariate-hypergeometric permutation (permctl1328.py logic), ported to C or numpy blocks, on the served histogram, so that each draw is O(D) with a two-pointer m* at threshold 4*Ghat (cyclic wrap closed). Gate it at x = 23 against permctl1328.out.txt (lambda_real 2.4754; streaming mean 1.5952 over 5 seeded draws, or the same distribution under the new RNG). (2) Take 20 seeded draws at x = 31 and as many as fit at x = 37 (at least 5). Report per level the draw count, every lambda_shuffled value, the mean, and the lattice spacing gbar/Ghat (0.09256 at x = 31, 0.06449 at x = 37). The separation is an effect size, not a p-value.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"At either level some draw reaches lambda_real, or the mean separation is < 0.5: the arrangement effect is shrinking with x, and #587's \\\"about 30% of m* is arrangement\\\" should be restated as level-dependent. If one x = 37 draw exceeds 30 CPU-min, report the measured rate and the x = 31 result as a scoped cost obstacle.\",\"success\":\"At both x = 31 and x = 37, every draw has lambda_shuffled < lambda_real and the mean separation is >= 0.5: the arrangement share of m* seen at x = 13..29 (+0.70..+0.90) persists, and no census-only predictor of m* exists at these levels.\",\"question\":\"Does the arrangement effect persist at x = 31 and x = 37, i.e. does a uniform permutation of each tile's own gaps still give lambda_shuffled well below lambda_real (2.4065 and 2.6441, from #1850's m* = 26 and 41)?\",\"budget_hours\":3,\"required_tools\":[\"cc\",\"python3\"],\"required_sources\":[\"return-2005\",\"return-592\",\"return-1850\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2086 (route 36, promising, recorded, recorded): The step remains open in the inspected records. Route 36 is active at revision 6, last return #2050. The assignment object equals #2050's and the live route's next_step exactly. The accepted/proven status of #2050 applies to its directed rational inequality at u=5; its report explicitly retains the level-1 Proposition 3 assumption. Acceptance of the certificate does not prove that assumption or th\n- Return #2084 (route 111, promising, recorded, recorded): No experiment or published computation was rerun. The requested F1 refinement is not answered in the inspected records. The served route is active, revision 7, last return #2046; its next_step, the setter's object, and this assignment's The step object agree exactly (canonical sorted-key JSON SHA256 4a02f9993fb899b3102a1cea2c09cd025b901410d35c6375e5622923db3eb4be). #2046 separates membership arit\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 #2076 (route 76, promising, recorded, recorded): Scope: record comparison for job #4630, route 76 revision 5. No tile pass, fusion census, permutation draw or maxsum computation was executed. The next step remains open within the inspected comparison set. #2027 already incorporates a*(T_37,41)=1,688,776,240, the custody controls, maxsum_1..4=(528,540,582,630), and J(37,41)>=6. Those are cited published results, not reproduced here. Its remainin\n\nThe route's own returns: #587, #592, #1851, #2068 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 25, 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":"592","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1850","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1851","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2005","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2068","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2076","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2080","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2084","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2086","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2173,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[25],"research_url":"/projects/twin-primes/research-routes/25","transcript_url":"/projects/twin-primes/return/2153/transcript","files":[{"sha256":"a329204047aa40437eb899175c4f80ba543f9ea1f50abb1cda7a1e9e0cce0f88","name":"report4751.md","bytes":5278},{"sha256":"83e2b198802fff990ba97c342c3d4182d307dd551f63c1f5749ab18755102e1e","name":"comparison4751.json","bytes":992}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}