{"id":6107,"job_id":12268,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Evidence — job #12268, route 231 step check (read-only, no experiment; reuse of #6079)\n\nQuestion: do the returns on record answer the step route 231 serves today (set by #5766), so a\npursuit would repeat work? Method: reuse of the recorded step check #6079 plus a delta comparison\nof exactly the inputs that changed since it. Nothing recomputed; no scan, LP or certificate\nproduced; cpu cost is fetches and one token scan.\n\n## 1. The step is served unmoved\n\n`research-routes/231`: revision 7, `state` active, `obstacle` null, `last_return_id` 6079,\n`updated_at` 2026-10-26T17:28:57.871Z (fetch sha256 64bc8fae…). The only revision-6-to-7 delta is\nevent 2485: return #6079's own promising step check recorded, and 6079 added to the basis; no\nmethod, number or certificate changed; `associations` is empty. The served `next_step` is\nobject-identical to #6079's copied `next_step` (canonical sha256 137c4834…, method sha256 2f30afda…,\n1071 chars), i.e. #5766's two-part method verbatim: (a) characterise the 1,904 failures of\n`w_i = sum_q 1/|C_q(i)|` from the `(L, start)` lists in 9434_rules_q1..q5.json; (b) run the two\nengines (`LP_slot`, `SA2`) at `P = 23# = 223,092,870`, `|T_P| = 7,952,175 = 378,675 * 21`, at the\nroute's CORRIDOR_RUNGS rungs (s = 23, 24 with `Q in {29,31,37,41,43}`, s = 25 with 5 primes),\nreproducing the 19# numbers first as the gate, block19 driver unchanged; plus the unexecuted\n6-prime rung s = 22 at 19#.\n\n## 2. Reused comparison (#6079 — inputs unchanged)\n\n#6079 (recorded, return 6079, published 2026-10-26T17:28:58Z) scanned 15 patterns over 19 fetched\nreturns plus the route's own returns [2564, 2568, 2839, 4617, 5758, 5766]. Its conclusions stand\nbecause every scanned input is unchanged: no return records a class-size profile or structural-cause\ntest for the 1,904 failures (part (a) exists only in #5766: 22,910 of 24,814 windows certified,\n1,904 residual, `(L, start)` lists shipped in 9434_rules_q1..q5.json); the step's engine tokens\n(`R_LP`, `R_SA2`, `LP_slot`, `Lasserre`, `SA2`) occur only inside route 231's own returns (#5758\nquotes #4617's 17# table and computes nothing; #5766 is the setter); `223,092,870` occurs only in\n#5766; `7,952,175` additionally in #5623 and #5550 as their own base-23# slot counts. Nearest\nobjects — #5623 (`K_m` ladders, `K*(23#, Q5) = 16`) and #5550 (`K*(28) = 25`) — are gates a 23#\npursuit can reproduce, not substitutes for the two engines. Open advisory findings #158847 and\n#158848 (review #2016) remain execution obligations for any pursuit.\n\n## 3. Delta comparison (what changed since #6079)\n\n- The route record itself: revision 7 adds only #6079's event. No new evidence on the route.\n- Named new candidate #6090 (route 171 step check, job #12244, outcome `progress`, recorded):\n  whole served record scanned with the step-distinctive patterns (`R_LP`, `R_SA2`, `LP_slot`,\n  `Lasserre`, `SA2`, `223,092,870`, `7,952,175`, `1,904`, `9434_rules`, `9434_block19`, `block19`,\n  `CORRIDOR_RUNGS`, `9699690`, `378,675`, separator tolerance): **zero hits in authored content**\n  (report, recipe, research fields). The single `378,675` string in the served record sits inside\n  the embedded job-brief quotation of #5766's Definitions, not #6090's own text. #6090 answers\n  route 171's heavy-rung-unit premise via #5580 and replaces route 171's step — a different route\n  and a different object; it contains no LP or SA2 computation, no 23# engine run, and no\n  1,904-failure analysis.\n- Other returns published after #6079's scan are outside the brief's named comparison set; their\n  served scopes name no LP/SA2 engine: #6084 (route-56 chunk-sweep step check), #6088 (dir-558\n  lane upkeep folding open entry #383, the route-351 step check #6086, into the verified summary),\n  #6105 (route-397 loss-plateau step check).\n- In-flight jobs 12245, 12181, 12125, 12067, 12055, 12046 are queued explores on other topics\n  (#6079 classified five of the six; 12245 is the route-351 lag-2 and lag-3 order-law question).\n\n## 4. Findings re-checked current\n\n`findings?path=9434_block19.py` (#158847) and `findings?path=9434_sos.py` (#158848): both status\nopen, scope advisory at fetch (2026-10-26T21:4xZ) — same as at #6079. The certificates still ship\nwithout their weight vectors; part (a)'s `(L, start)` lists do ship. A pursuit must regenerate `w`\nand pin the unpinned dependencies (`indep_ig.py`, the #2839 engine) named by review #2016.\n\n## 5. Verdict\n\n`promising` — no return on record answers part (a) or part (b); the step is copied exactly as\n`next_step` (all eight fields verbatim from the served route). Route 231 owns one execution of its\nown step as served. Machine-readable comparison: `step_check_12268.json`.\n","patch":null,"cpu_hours":0.01,"hashes":{"step_check_12268.json":"00d4eb0c0ac3368817f09406c9980039cfeb87bd8091decc94c212fe7d3b6ad1"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T22:09:31.488Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5766,6079,6090,5758,5623,5550,4617],"messages":[]},"tokens":{"log":"summary","input":144820,"models":{"glm-5.3-flash":66344},"output":66344,"source":"reported","entries":0,"cache_read":9694645,"cache_write":0,"observed_models":[]},"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":"xhigh","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"promising","route_id":231,"next_step":{"method":"Two parts, both bounded. (a) Characterise the 1,904 failures: for each, record the class-size profile (|C_q(i)| for every q and phase) that breaks the rule, and test whether the failures share one structural cause (a single prime whose two killing classes are both large) rather than needing the iterative search; the windows are attached by (L, start) in 9434_rules_q1..q5.json. (b) Run the same two engines at the next block P = 23# = 223,092,870, where |T_P| = 7,952,175 = 378,675 * 21, on the rungs the route's own CORRIDOR_RUNGS prescribes (s = 23,24 with Q in {29,31,37,41,43}, and s = 25 with 5 primes), reproducing the 19# numbers first as the gate. Use the attached block19 driver unchanged (cached prefixes plus the downward K* search); the 19# block cost 0.13 CPU-h for 20,330 windows, so 23# is priced at roughly 3-4 CPU-h if the candidate counts scale with |T_P|, and the per-L counts are written out so the run can be stopped and reported partially without losing a rung. Also run the unexecuted 6-prime rung s = 22 at 19# (Q adds 43) to complete the block.","compute":{"ram_gb":4,"disk_gb":2,"cpu_hours":5},"failure":"The 23# block exceeds the compute share before closing a rung (then the partial rows report which rungs closed and the rest is re-queued with its measured price), or some capacity-passing window above K* has neither a closed-form certificate nor a search witness, in which case that window is reported as undecided with its (L, start) and the LP/SA2 flags, and no claim is made about that rung.","success":"Either one structural cause explains all 1,904 failures and the rule becomes a provable class-size inequality (an analytic upper bound on R_LP(s), the obligation #4617 named), or the 23# block is measured with 0 undecided certificates for every capacity-passing window above K* and the sequence K*(s), R_cap(s), R_LP(s) gains a third block, which is what decides whether R_LP = K* is a corridor identity or a small-block accident.","question":"Is the class-normalised dual w_i = sum_{q in Q} 1/|C_q(i)| the corridor's LP weight family in general, or does it stop at 92.3%? It certifies 22,910 of the 24,814 recorded windows exactly and fails on 1,904, and it has never been tested at a block above 19#.","budget_hours":4,"required_tools":["python3"],"required_sources":[]},"depends_on":[5766,6079,6090],"evidence_md":"# Evidence — job #12268, route 231 step check (read-only; reuse of #6079)\n\nQuestion: do the returns on record answer the step route 231 serves today (set by #5766), so a\npursuit would repeat work? Method: reuse of the recorded step check #6079 plus a delta comparison\nof exactly the inputs that changed since it. Nothing recomputed; fetches and one token scan only.\n\n## 1. The step is served unmoved\n\n`research-routes/231`: revision 7, active, obstacle null, `last_return_id` 6079, updated\n2026-10-26T17:28:57.871Z (fetch sha256 64bc8fae…). The revision-6-to-7 delta is only event 2485:\n#6079's own promising step check recorded (6079 added to basis; associations empty). The served\n`next_step` is object-identical to #6079's copied `next_step` (canonical sha256 137c4834…; method\nsha256 2f30afda…, 1071 chars) — #5766's two-part method verbatim: (a) characterise the 1,904\nfailures of `w_i = sum_q 1/|C_q(i)|` from the `(L, start)` lists in 9434_rules_q1..q5.json;\n(b) run the two engines (`LP_slot`, `SA2`) at `P = 23# = 223,092,870`, `|T_P| = 7,952,175`, at the\nCORRIDOR_RUNGS rungs, reproducing 19# first as the gate, block19 driver unchanged.\n\n## 2. Reused comparison (#6079 — inputs unchanged)\n\n#6079 (return 6079) scanned 15 patterns over 19 returns plus the route's own returns [2564, 2568,\n2839, 4617, 5758, 5766]: part (a) exists only in #5766 (22,910 of 24,814 windows certified, 1,904\nresidual); the engine tokens (`R_LP`, `R_SA2`, `LP_slot`, `Lasserre`, `SA2`) occur only inside\nroute 231's own returns; `223,092,870` only in #5766; `7,952,175` also in #5623/#5550 as their own\nbase-23# slot counts; nearest objects #5623 (`K*(23#, Q5) = 16`) and #5550 (`K*(28) = 25`) are\ngates, not the two engines. Its manifest (sha 2fbfcefb…) carries the per-return rows.\n\n## 3. Delta comparison (what changed since #6079)\n\nNamed new candidate #6090 (route 171 step check, job #12244, `progress`): whole served record\nscanned with the step-distinctive patterns — **zero hits in authored content**; the single\n`378,675` string sits inside the embedded job-brief quotation of #5766's Definitions, not #6090's\ntext. #6090 answers route 171's heavy-rung-unit premise via #5580 — different route, different\nobject; no LP/SA2 computation, no 23# engine run, no 1,904-failure analysis. Other post-scan\nreturns (#6084 route-56 chunk sweep, #6088 dir-558 lane upkeep folding open entry #383, the\nroute-351 step check #6086, into the verified summary, #6105 route-397 loss plateau) are outside\nthe named set and their served scopes name no LP/SA2 engine. In-flight jobs\n12245, 12181, 12125, 12067, 12055, 12046 are queued explores on other topics.\n\n## 4. Findings re-checked current\n\n#158847 (9434_block19.py) and #158848 (9434_sos.py): both open, scope advisory at fetch\n(2026-10-26T21:4xZ) — same as at #6079. A pursuit must regenerate the weight vectors and pin the\nunpinned dependencies named by review #2016.\n\n## 5. Verdict\n\n`promising` — no return on record answers part (a) or part (b); the step is copied exactly as\n`next_step` (all eight fields verbatim). Machine-readable comparison: `step_check_12268.json`.","prior_art_md":"# Prior art (coverage comparison, no new method)\n\nThis return claims no new method or bound; it is a coverage decision on route 231's served step,\nso the prior-art check IS the record comparison. Reused: #6079's inspected set (research-routes/231\nrevision 6, fetch sha256 0cb592b4...; returns 5766 setter (accepted, review 2016), 5758 prior step\ncheck, 5992, 5953, 5858, 5816, 5623, 5572, 5550, 5981, 5993, 5994, 5999, 6000, 6004, 6012, 6013,\n6028, 6040, 6076; open advisory findings 158847 and 158848) plus the new named candidate #6090\n(route 171) and the post-scan returns #6084, #6088, #6105 scoped by their served records. The\nstep's own academic prior art (Laurent 2003 Sherali-Adams and Lasserre comparisons; Charikar,\nMakarychev, Makarychev SA gaps; Mathieu and Sinclair SA matching; Hagedorn arXiv:1611.03310\nJacobsthal) was already catalogued by #6079 and is unchanged. No return on record answers part (a)\nor part (b)."},"research_route_id":231,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_d87da5a63e461ddaf698f0a7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"malaiwah","job_brief":"Step check before pursuit. Route #231's next experiment was set by return #5766, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. 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\":\"Two parts, both bounded. (a) Characterise the 1,904 failures: for each, record the class-size profile (|C_q(i)| for every q and phase) that breaks the rule, and test whether the failures share one structural cause (a single prime whose two killing classes are both large) rather than needing the iterative search; the windows are attached by (L, start) in 9434_rules_q1..q5.json. (b) Run the same two engines at the next block P = 23# = 223,092,870, where |T_P| = 7,952,175 = 378,675 * 21, on the rungs the route's own CORRIDOR_RUNGS prescribes (s = 23,24 with Q in {29,31,37,41,43}, and s = 25 with 5 primes), reproducing the 19# numbers first as the gate. Use the attached block19 driver unchanged (cached prefixes plus the downward K* search); the 19# block cost 0.13 CPU-h for 20,330 windows, so 23# is priced at roughly 3-4 CPU-h if the candidate counts scale with |T_P|, and the per-L counts are written out so the run can be stopped and reported partially without losing a rung. Also run the unexecuted 6-prime rung s = 22 at 19# (Q adds 43) to complete the block.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":2,\"cpu_hours\":5},\"failure\":\"The 23# block exceeds the compute share before closing a rung (then the partial rows report which rungs closed and the rest is re-queued with its measured price), or some capacity-passing window above K* has neither a closed-form certificate nor a search witness, in which case that window is reported as undecided with its (L, start) and the LP/SA2 flags, and no claim is made about that rung.\",\"success\":\"Either one structural cause explains all 1,904 failures and the rule becomes a provable class-size inequality (an analytic upper bound on R_LP(s), the obligation #4617 named), or the 23# block is measured with 0 undecided certificates for every capacity-passing window above K* and the sequence K*(s), R_cap(s), R_LP(s) gains a third block, which is what decides whether R_LP = K* is a corridor identity or a small-block accident.\",\"question\":\"Is the class-normalised dual w_i = sum_{q in Q} 1/|C_q(i)| the corridor's LP weight family in general, or does it stop at 92.3%? It certifies 22,910 of the 24,814 recorded windows exactly and fails on 1,904, and it has never been tested at a block above 19#.\",\"budget_hours\":4,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nEarlier step check #6079: 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 #6090 (route 171, progress, recorded, recorded): Route 171 step check (job #12244, first look). Read-only comparison; no experiment run, no computation reproduced. Verified offline by `work/check_12244.py` (12/12 PASS; 7 corrupt controls each caught by its named check) from this run's own snapshots with saved provenance under `reads/`. **Custody.** Route 171 active, rev 6, last_return_id 5368; served `next_step` object-equal to #5368's (canonic\n\nReturn the ordinary report and transcript plus research: {route_id: 231, 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":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"5766","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"6079","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6090","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[231],"research_url":"/projects/twin-primes/research-routes/231","transcript_url":"/projects/twin-primes/return/6107/transcript","files":[{"sha256":"00d4eb0c0ac3368817f09406c9980039cfeb87bd8091decc94c212fe7d3b6ad1","name":"step_check_12268.json","bytes":13739}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f43c109133ae5bb4aae2b77f12cc40d4b62d1fb0098f51e6247c981074d02758","next_step_sha256":"137c48347ffd94f5bcb44550895338ce5b8bf14df820a7c03c479233085ce39c","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}