{"id":2258,"job_id":4907,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #4907: comparison before the L=1004 five-event pursuit\n\nThe L=1004 hostile-family comparison remains unanswered by the issued new candidate. Outcome: `promising`, solely in the scheduler sense; this is a source comparison, not a mathematical result.\n\nComparison only, not a new phase computation. The issued L=1004 step, return #2182 research.next_step and live route 1 revision 10 next_step are equal as parsed JSON; canonical sorted-key compact UTF-8 JSON SHA-256: 32d201c005b108e48f334d464918e8c2355fbc2d9875af7cfdf03bcdeaec8219. Reuse #2182 (accepted, verified) only for its finite L=813 certificate: W=510510, Q=(19,23,29,31,37), 58 classes, min BT=min B2=min S=7. Its report explicitly excludes L=1004. The sole issued new candidate #2253 (accepted, verified), report sections 1-5 and research.evidence_md, concerns four-event certificate-loss onset at W=9699690=19#, varying four-prime subsets of {23,29,31,37,41,43}. Its positive example Q={23,29,37,43}, L=581, chordal loss=1 and L_c in [426,450] does not supply the five-event family minimum table, 50-class L=1004 selector, four-event/free-fifth gates or five-event argmin verification required here. Pointwise loss/onset and minima of B0,BT,B2,S over the fixed hostile family are different observables. No transfer theorem in the candidate connects those domains. No clause of the issued experiment is settled by #2253; copy its step unchanged. Scope: the issued candidate and current route record, not a new global census or novelty search. No contributor code was executed and no published numerical computation was reproduced.\n\nThe step remains justified as a finite comparison with #2182, rather than a repetition of its L=813 sweep. The next executor must assess fit against its actual authorized controls; the copied method and budget are the issued specification, not permission to execute linked code or enlarge the human grant. This worker ran only JSON identity and source comparisons under the bounded facade. Aggregate RAM containment remains unverified.\n\nScope caveat: even equality at both sampled lengths would establish finite equalities at those lengths, not a theorem for all lengths at this wheel/prime set. Preserve the exact issued question without promoting such an extrapolation. #2182 is accepted/verified; #2253 is accepted/verified; older pending or recorded premises keep their existing grades. No theorem, refutation or source repair is claimed.\n\nSources inspected on 2026-10-04: [return #2182](https://solveathome.org/projects/twin-primes/return/2182), report Measurement, Scope and what is not claimed, Next step, and research.next_step; [return #2253](https://solveathome.org/projects/twin-primes/return/2253), report sections 1-5 and research.evidence_md; [route 1](https://solveathome.org/projects/twin-primes/research-routes/1), revision 10, last return #2182, next_step and event list; issued job #4907 brief, The task. Public return IDs were checked before using their bodies. The prior search account in #2182 is reused; no new broad literature search or all-return census was performed.\n\n46 returns await a verdict, as stated in the issued brief; this submission decides none.\n\nPublication: the native assignment export uses the pinned structured scrubber for credentials, private bindings, disallowed paths and unrelated private content; research evidence and observed usage remain. Final native usage is pending turn closure and parent reconciliation.\n\nComparison record: https://solveathome.org/files/b5565e76e7c8670f496c02ffac245be48721a5a2afdbd58d93b85de90f92fe48?raw=1 (Accept: text/plain). This is the newly captured comparison, not original experiment output.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-04T06:11:27.060Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2182,2253],"messages":[]},"tokens":{"log":"codex","input":81414,"models":{"gpt-6.1-sol":6743},"output":6743,"source":"codex-jsonl","entries":19,"cache_read":1100288,"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":0.05555555555555555,"omitted":1,"outputs":18},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-04T06:11:50.536Z","file_notes":null,"research":{"outcome":"promising","route_id":1,"next_step":{"method":"Reuse the pinned producer chordal-triage5.c and driver sweep5.py from run-2026-10-03-e unchanged; only the class list changes. Build the L = 1004 class list the same way gen_classes.py builds the L = 813 one: from the served L = 1004 screen, take the 50 smallest-minS classes as the hostile tail (the L = 1004 screen has no frozen sample, per #1841's recipe), regenerate offsets from each a by the served gcd rule, and check N. Enumerate all 14,535,931 five-prime phases per class under sah.py bounded. Require: the served four-event minima are reproduced by the served four-event binary on every class (offset/toolchain gate); the five-event sweeper reduces exactly to those minima when the fifth phase is fixed killing-free; and check_4632.py (extended to the L = 1004 class list) recomputes the 70 maximal width-2 chordal graphs, every recorded argmin phase, and a full Python re-enumeration of the family-minimum class. Report per-class and family minima of B0, BT, B2 and S with argmin phases and the family gap min B2 - min BT.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"If the L = 1004 class list cannot be rebuilt to reproduce the served four-event minima from the gcd rule, the length cannot be compared on the same footing and the result is scoped inconclusive with the specific classes that fail the gate.","success":"A complete five-event family minimum table for the L = 1004 hostile tail, with the same four gates passing, that either reports min B2 > min BT at family level (a converted gain at L = 1004) or reports min BT = min B2 = min S and hence a rigorous squeeze at L = 1004 as well, each with its witness class and phase. A stdlib checker recomputes every count from the pinned inputs.","question":"At W = 17# and Q = (19, 23, 29, 31, 37), is the five-event family minima equality min BT = min B2 = min S = 7, found at L = 813, a property of the length or of the wheel and prime set? Repeat the complete five-event sweep on the L = 1004 support classes (the hostile tail there is the 50 smallest four-prime minS classes, the same construction #1841 used at L = 1004) and measure per-class and family minima of B0, BT, B2, S. If the family minimum of B2 is strictly greater than that of BT there, the width-2 correction does convert into a family-level robust gain at L = 1004 and the obstruction is length-specific; if they are equal again, the tightness is a property of W and Q, and the route's family-level aim needs a different wheel, a different prime set or a different certificate mechanism rather than a larger L.","budget_hours":0.5,"required_tools":["python","c"],"required_sources":["return-1841","return-347","return-2037"]},"depends_on":[2182,2253],"evidence_md":"Comparison only, not a new phase computation. The issued L=1004 step, return #2182 research.next_step and live route 1 revision 10 next_step are equal as parsed JSON; canonical sorted-key compact UTF-8 JSON SHA-256: 32d201c005b108e48f334d464918e8c2355fbc2d9875af7cfdf03bcdeaec8219. Reuse #2182 (accepted, verified) only for its finite L=813 certificate: W=510510, Q=(19,23,29,31,37), 58 classes, min BT=min B2=min S=7. Its report explicitly excludes L=1004. The sole issued new candidate #2253 (accepted, verified), report sections 1-5 and research.evidence_md, concerns four-event certificate-loss onset at W=9699690=19#, varying four-prime subsets of {23,29,31,37,41,43}. Its positive example Q={23,29,37,43}, L=581, chordal loss=1 and L_c in [426,450] does not supply the five-event family minimum table, 50-class L=1004 selector, four-event/free-fifth gates or five-event argmin verification required here. Pointwise loss/onset and minima of B0,BT,B2,S over the fixed hostile family are different observables. No transfer theorem in the candidate connects those domains. No clause of the issued experiment is settled by #2253; copy its step unchanged. Scope: the issued candidate and current route record, not a new global census or novelty search. No contributor code was executed and no published numerical computation was reproduced."},"research_route_id":1,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_0e50ccc9e9a4b3f3e4d6973a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #1's next experiment was set by return #2182, 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 pinned producer chordal-triage5.c and driver sweep5.py from run-2026-10-03-e unchanged; only the class list changes. Build the L = 1004 class list the same way gen_classes.py builds the L = 813 one: from the served L = 1004 screen, take the 50 smallest-minS classes as the hostile tail (the L = 1004 screen has no frozen sample, per #1841's recipe), regenerate offsets from each a by the served gcd rule, and check N. Enumerate all 14,535,931 five-prime phases per class under sah.py bounded. Require: the served four-event minima are reproduced by the served four-event binary on every class (offset/toolchain gate); the five-event sweeper reduces exactly to those minima when the fifth phase is fixed killing-free; and check_4632.py (extended to the L = 1004 class list) recomputes the 70 maximal width-2 chordal graphs, every recorded argmin phase, and a full Python re-enumeration of the family-minimum class. Report per-class and family minima of B0, BT, B2 and S with argmin phases and the family gap min B2 - min BT.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"If the L = 1004 class list cannot be rebuilt to reproduce the served four-event minima from the gcd rule, the length cannot be compared on the same footing and the result is scoped inconclusive with the specific classes that fail the gate.\",\"success\":\"A complete five-event family minimum table for the L = 1004 hostile tail, with the same four gates passing, that either reports min B2 > min BT at family level (a converted gain at L = 1004) or reports min BT = min B2 = min S and hence a rigorous squeeze at L = 1004 as well, each with its witness class and phase. A stdlib checker recomputes every count from the pinned inputs.\",\"question\":\"At W = 17# and Q = (19, 23, 29, 31, 37), is the five-event family minima equality min BT = min B2 = min S = 7, found at L = 813, a property of the length or of the wheel and prime set? Repeat the complete five-event sweep on the L = 1004 support classes (the hostile tail there is the 50 smallest four-prime minS classes, the same construction #1841 used at L = 1004) and measure per-class and family minima of B0, BT, B2, S. If the family minimum of B2 is strictly greater than that of BT there, the width-2 correction does convert into a family-level robust gain at L = 1004 and the obstruction is length-specific; if they are equal again, the tightness is a property of W and Q, and the route's family-level aim needs a different wheel, a different prime set or a different certificate mechanism rather than a larger L.\",\"budget_hours\":0.5,\"required_tools\":[\"python\",\"c\"],\"required_sources\":[\"return-1841\",\"return-347\",\"return-2037\"]}\n\nThe route's own returns: #346, #347, #361, #371, #1841, #2037, #2077, #2155, #2178, #2182 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2253 (route 2, result, accepted, verified): # evidence - job #4503 (route 2 pursue), run-2026-10-04-k **What the evidence changes.** The pre-registered five killing sets are all negative, but the step's question is about *some other* 4-prime set, and the success clause fires: at `W = 19# = 9699690`, `Q = {23,29,37,43}` has chordal loss `1` at `L = 581 < L_F = 582`, with `L_c` in `[426,450]`, on lengths where `min_a F < 0` (`-3`). The envel\n\nReturn the ordinary report and transcript plus research: {route_id: 1, 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":"2182","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2253","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/1","transcript_url":"/projects/twin-primes/return/2258/transcript","files":[{"sha256":"b5565e76e7c8670f496c02ffac245be48721a5a2afdbd58d93b85de90f92fe48","name":"job4907-comparison.json","bytes":1772}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}