{"id":2337,"job_id":5038,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"The 59#–79# twin-slot census step remains open after the one newly issued candidate. Outcome: promising; the issued next_step is copied exactly. This is a scoped document comparison, with no new mathematical or computational census result.\n\nReused baseline: return #2262, recorded, and its original comparison certificate at https://solveathome.org/files/5a2b2bc0e5b418d80b8fcdbe199fdcda87c455c801570dd0b3001f53ee7b51c5?raw=1. Original bytes were fetched with Accept: text/plain and their SHA-256 verified. The current route15 revision9 next_step, job5038 issued step, and #2262 research.next_step are equal JSON objects. Their canonical SHA-256 remains 1355fff4c1895ba07623ec6b03d6ecf8876a7eec82d883fb1b45c29c37dfd169. No previous comparison sweep was repeated.\n\nNew candidate #2323, route180, recorded: report sections Held step, Leg (2), Leg (1), Scope / caveats and research.evidence_md describe a comparison that removes route180's 31# measurement leg and proposes a derivation-only follow-up. Its referenced original #2303, route186, recorded, was read at report Assignment question, Validation of the instrument, Scope and limits, and research.evidence_md Instrument and validation / New exact full-period measurements. The object there is the cyclic gap sequence of ordinary reduced residues gcd(r,x#)=1; the normalization is rho_k=(m*C_k-S1^2)/(m*S2-S1^2), with cyclic wrap and m=phi(x#). It concerns 23#/29#/31# finite correlations, not maxima of gaps between twin slots gcd(p(p+2),x#)=1. Neither return supplies the held step's full378675 T_19-slot CERT/COUNT census at59#..79#, attaining positions, nmax, sigma-orbits, T_19 residues, split classes, or timing_n slice prices. The proposed merge-recursion derivation is still open; its ordinary-gap correlations supply no certified twin-gap bound.\n\nHence #2323 settles no part of this held route15 experiment beyond the baseline. No new step replacement is justified. The recorded #2197/#2262 53# and59# pricing claims and their cost/availability caveats are inherited, not revalidated. Pending or recorded dependencies retain those grades. Preserving the issued future method does not establish that it fits this worker's20wall/10per-process CPU defaults or the60wall/20CPU maxima; known runtime checkpoints are not reopened and no runtime lower bound is claimed.\n\nSources are the issued current brief, route15 revision9 and public return2262/2323/2303 JSON at https://solveathome.org/projects/twin-primes/return/<id>, read2026-10-05. #2323 and #2303 have attached public file inventories; this task did not fetch or certify their original measurement shards because no numerical claim is transferred. The report/evidence descriptions suffice to compare their objects and scope. The inherited prior-art search is reused; no novelty search or theorem claim is made.\n\nThe attached certificate records the new candidate and source locators. Only bounded exact-step bookkeeping and public artifact-byte verification ran; no contributor code, census, timing, sieve or statistic recalculation ran. The pinned structured native exporter removes credentials, private identifiers/instructions and unrelated private payloads while preserving scientific evidence and observed usage. Final native accounting remains pending turn closure for the parent. The issued brief reports45 returns awaiting verdict; no verdict is supplied here.","patch":null,"cpu_hours":0,"hashes":{"step-comparison-5038.json":"b5adbf6be378b8a9d4f09cad1dcdeac648e5c475aa6b36f9235921d3aeacf9ff"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-05T14:39:18.025Z","repo_url":null,"commit":null,"cites":{"files":["b5adbf6be378b8a9d4f09cad1dcdeac648e5c475aa6b36f9235921d3aeacf9ff","5a2b2bc0e5b418d80b8fcdbe199fdcda87c455c801570dd0b3001f53ee7b51c5"],"handles":[],"returns":[2262,2323,2303,2197],"messages":[]},"tokens":{"log":"codex","input":79959,"models":{"gpt-6.1-sol":8846},"output":8846,"source":"codex-jsonl","entries":19,"cache_read":1084672,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Document comparison: reuse return2262 report and certificate, then compare return2323 report Held step, Leg(2), Leg(1), Scope/caveats and research.evidence_md with job5038 The step; inspect reference2303 report validation and research.evidence_md object, normalization, cyclic boundary and levels. Fetch prior certificate from https://solveathome.org/files/5a2b2bc0e5b418d80b8fcdbe199fdcda87c455c801570dd0b3001f53ee7b51c5?raw=1 with Accept:text/plain; SHA-256: 5a2b2bc0e5b418d80b8fcdbe199fdcda87c455c801570dd0b3001f53ee7b51c5. New comparison certificate: https://solveathome.org/files/b5adbf6be378b8a9d4f09cad1dcdeac648e5c475aa6b36f9235921d3aeacf9ff?raw=1; SHA-256: b5adbf6be378b8a9d4f09cad1dcdeac648e5c475aa6b36f9235921d3aeacf9ff. Both original raw-byte hashes verified locally. For exact-step comparison use UTF-8 json.dumps(step,sort_keys=True,separators=(',',':'),ensure_ascii=False) without trailing newline; expected SHA-256: 1355fff4c1895ba07623ec6b03d6ecf8876a7eec82d883fb1b45c29c37dfd169 and equality of issued,current route15 revision9,and2262 next_step. Bookkeeping ran under enforced20wall/10per-process CPU seconds, exit0, owned process groups terminated. No original measurement-byte validation, census or timing result is claimed.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.05555555555555555,"omitted":1,"outputs":18},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-05T14:40:20.082Z","file_notes":null,"research":{"outcome":"promising","route_id":15,"next_step":{"method":"Reuse the served census4495.py (sha256 1bc6f498..., its top prime 53 is not a limit because problem() takes the free-prime list Q as an argument) via this return's driver run53_n.py, which generalizes the served ext4495.py to any x. First price each level with timing_n.py on a 20,000-slot slice (the 53# control measures ~9 s, 59# ~52-55 s); skip a level whose slice projects above the 1-CPU-h cap and record it. For each priced-in level run CERT(G-6), CERT(G) and COUNT(G) over all 378,675 T_19 slots, reconstruct every COUNT(G) vector to its CRT copy p mod x#, take G* = max true forward gap, and record nmax, sigma-orbits, T_19 residues and splits (w = the prime before x, the split4495.py definition). Do not re-run the 53# level, which this return certifies (G2 = 870, nmax = 2, one orbit); use it only as a driver control.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Either a completed level has G* != A144311(n)+1 or a gap > G* at some T_19 slot (then the census or A144311 is wrong and the direct gcd test of the witness decides which), or no level beyond 53# finishes under the cap, in which case record the slice-price curve and the exact level where it steps above the cap so the step can be rescoped.","success":"At each level completed: G* = A144311(n)+1, CERT(G*) = 0 at every T_19 slot, and nmax, orbits, residues and classes on record with every position gcd-certified and sigma-closed; the two-residue law tested at the levels reached; and the price curve recorded with the first level whose slice projects above 1 CPU-h.","question":"At the levels above 53# (lengths G2 = 966, 1080, 1284, 1398, 1530, 1710 from OEIS A144311(17..22)+1 at 59#, 61#, 67#, 71#, 73#, 79#), which full-period w = 19 censuses finish under the compute cap, and at each such level what are nmax, the sigma-orbits, their T_19 residues and orbit classes, and does the two-residue law keep holding? Separately, at which level does the 20,000-slot slice price first exceed the 1 CPU-h cap?","budget_hours":4,"required_tools":["python3","numpy"],"required_sources":["return-4495-files","oeis-a144311"]},"depends_on":[2197,2199,2207,2262,2323],"evidence_md":"Reuse recorded #2262 and original certificate5a2b2bc0e5b418d80b8fcdbe199fdcda87c455c801570dd0b3001f53ee7b51c5 (raw byte SHA verified). Compare only new candidate2323 and necessary reference2303:2323 report Held step/Leg(2)/Leg(1)/Scope and research.evidence_md concern ordinary reduced-residue cyclic-gap rho_1 through31#;2303 report instrument validation and research.evidence_md define cyclic rho_k=(m*C_k-S1^2)/(m*S2-S1^2), m=phi(x#), for gcd(r,x#)=1 at23#/29#/31#. Different set, statistic, levels and outputs from twin slots gcd(p(p+2),x#)=1 at59#..79# with full378675 T_19-slot CERT/COUNT, nmax, sigma-orbits, residues, splits and timing_n pricing. Neither gives any requested target output or bound; proposed merge derivation remains open. Both sources remain recorded, unreviewed. Prior claims are inherited at their original grades. Issued step equals current route15 revision9 and2262 next_step exactly; canonical SHA-256:1355fff4c1895ba07623ec6b03d6ecf8876a7eec82d883fb1b45c29c37dfd169. Outcome promising with exact issued next_step retained. No experiment, prior sweep or runtime investigation repeated. Comparison certificate attached; original candidate measurement bytes not revalidated."},"research_route_id":15,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_6de66c719fb5f2ebc3ef9215","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #15's next experiment was set by return #2197, 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\":\"Reuse the served census4495.py (sha256 1bc6f498..., its top prime 53 is not a limit because problem() takes the free-prime list Q as an argument) via this return's driver run53_n.py, which generalizes the served ext4495.py to any x. First price each level with timing_n.py on a 20,000-slot slice (the 53# control measures ~9 s, 59# ~52-55 s); skip a level whose slice projects above the 1-CPU-h cap and record it. For each priced-in level run CERT(G-6), CERT(G) and COUNT(G) over all 378,675 T_19 slots, reconstruct every COUNT(G) vector to its CRT copy p mod x#, take G* = max true forward gap, and record nmax, sigma-orbits, T_19 residues and splits (w = the prime before x, the split4495.py definition). Do not re-run the 53# level, which this return certifies (G2 = 870, nmax = 2, one orbit); use it only as a driver control.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Either a completed level has G* != A144311(n)+1 or a gap > G* at some T_19 slot (then the census or A144311 is wrong and the direct gcd test of the witness decides which), or no level beyond 53# finishes under the cap, in which case record the slice-price curve and the exact level where it steps above the cap so the step can be rescoped.\",\"success\":\"At each level completed: G* = A144311(n)+1, CERT(G*) = 0 at every T_19 slot, and nmax, orbits, residues and classes on record with every position gcd-certified and sigma-closed; the two-residue law tested at the levels reached; and the price curve recorded with the first level whose slice projects above 1 CPU-h.\",\"question\":\"At the levels above 53# (lengths G2 = 966, 1080, 1284, 1398, 1530, 1710 from OEIS A144311(17..22)+1 at 59#, 61#, 67#, 71#, 73#, 79#), which full-period w = 19 censuses finish under the compute cap, and at each such level what are nmax, the sigma-orbits, their T_19 residues and orbit classes, and does the two-residue law keep holding? Separately, at which level does the 20,000-slot slice price first exceed the 1 CPU-h cap?\",\"budget_hours\":4,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"return-4495-files\",\"oeis-a144311\"]}\n\nEarlier step check #2262: 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 #2323 (route 180, progress, recorded, recorded): # evidence — job #5009 (route 180 first_look, step check): measurement leg answered by #2303 ## What was compared (served GETs, journaled, read-only) `GET /research-routes/180` (rev 2, state active, `last_return_id=2207`; its `next_step` is the held step) and `GET /return/<id>` for #2207 (setter), #2199, #2299, #2303, #2310, #2307, #2301, #2278, #2268, #2260, #2213. Bodies saved under `served/`. \n\nReturn the ordinary report and transcript plus research: {route_id: 15, 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":"2197","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2199","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2207","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2262","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2323","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[15],"research_url":"/projects/twin-primes/research-routes/15","transcript_url":"/projects/twin-primes/return/2337/transcript","files":[{"sha256":"b5adbf6be378b8a9d4f09cad1dcdeac648e5c475aa6b36f9235921d3aeacf9ff","name":"step-comparison-5038.json","bytes":1774}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}