{"id":6851,"job_id":13545,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13545 — route 374 step check after #6801 and the accepted route-371 result #6805: the fixed-base 29# nine-prime rung remains unexecuted — outcome `promising`, step returned unchanged\n\nRead-only comparison; `cpu_hours` 0. No covering search, census, capacity pass or envelope evaluation; no contributed program executed. Gate `check_13545.py`: 9/9 gates, exit 0; `--corrupt` 9/9 injected faults caught by their named gates.\n\n## Custody\n\nServed route 374: `active`, revision 6, `last_return_id` 6801, updated `2026-11-02T19:14:21.629Z`. The revision bump is #6801's own recording; #6801's returned `next_step` is identical to the served `route.next_step` on method/success/failure/question, and the brief's step object deep-equals the served `next_step` (gate G5). The step set by #6200 is unchanged in substance.\n\n## What changed since #6801\n\n1. Route 374 revision 5 → 6 by #6801's own recorded comparison (outcome promising, step preserved verbatim).\n2. #6805 (route 371, job 11393, gpt-6.1-sol, recorded 2026-11-02T19:41:56Z): the issuing brief listed it as \"route 371, result, pending\"; the served record now reads status `accepted`, `final_rung` measured (G2) — a status change after brief generation, so this check is made against the accepted text.\n\n## The compared candidate\n\n#6805 measures the span-612 hierarchy at parent wheel 19# (W = 9,699,690, D = 378,675), six entering primes Q = (23, 29, 31, 37, 41, 43), over the 5,164 boundary-U1-passing windows: four families (Umin/Umax/P/F) at arities 1..6 on interior and boundary phase domains. First strict-exclusion arities: interior F m2..6 = (4498, 506, 104, 44, 12), boundary F m2..6 = (4752, 310, 66, 34, 2). F5 excludes 5,162/5,164 boundary and 5,152/5,164 interior windows; the two reflected L = 17 windows k = 166239 and k = 212418 require full arity while exact maximum coverage is 16. Units correction: mu, F, P and U count covered slots and compare to L, not to the physical span 612.\n\n## Why it does not answer the step\n\n- Different wheel and prime set: parent 19# with six primes, versus the step's fixed 29# base (D_29 = 214,708,725) with nine primes Q_34 = {31, 37, 41, 43, 47, 53, 59, 61, 67}.\n- Different question: whether proper-arity bounds short-certificate exact cover on a boundary capacity screen, versus the step's exact nine-prime rung values K*(34), MS(34), the five CM families m = 1..9, the m = 8 certificate-or-integer-dual determination against G_hat(68) = 1284, and Route #170 boundary_loss at L = K*(34).\n- #6805 says so itself: \"Base29# doubling computations on routes369/374 are different objects\" (G8). Token scan over its authored fields: zero occurrences of Q_34, K*(34) and its K-star spelling, CM_m(34), nq = 9, G_hat(68) (G3). Its `depends_on` = [5618, 5632, 5807] and its `cites` exclude every route-374 premise return (G2, G9).\n- Its units correction does not transfer: route 374's hierarchy convention already compares covered-slot bounds (mu_W; MS(31) = A_29(29#) = 1356, A_28 = 1320) to window lengths, not to a physical span. Its finding that proper-arity bounds can fail to close at full arity is a caution relevant to the step's m = 8 clause (a negative answer there would look like #5645's arity-7 dual obstruction), but it establishes nothing about the nine-prime rung.\n\n## Reused #6801 conclusions\n\nReport digest re-verified against the served record (G7). #6801 screened ten issued candidates plus the route and lane state: no record covers the live outputs; #6388 only catalogs s = 34 as unexecuted; #936 is accepted/verified on the base-31# tile with a different Q and is not this rung's value; #5586 (accepted, measured) supplies CERT(1284) = 0, COUNT(1284) = 2 at 67# as a cited ceiling, not to be rerun; the relaxation K*(34) ≥ 29 with both k = 29 starts persisting stays conditional on #5645's recorded witnesses. All of that carries over unchanged: no new route-374 return exists after #6801 (G4).\n\n## Outcome and limits\n\n`promising`: not known (no compared record covers the live outputs), not progress (no new candidate answers a hierarchy clause or changes the method). The step is returned exactly as served (G5) and the held pursuit goes out with this note.\n\nSearch scope: the served route record, the brief, #6801 (reused, digest verified), #6805 (report and research fields read in full, served digest verified). #6805's 3.9 MB `full.json` data file was not downloaded; its report text is the compared claim carrier and its independent checker is described in the report. This is a coverage and custody verdict on the served record, not a global absence proof, not independent validation of recorded predecessors, and not evidence for twin-prime infinitude. No external search was needed for this internal comparison. No computation was reproduced; my own compute is 0 CPU-hours (gate run only).\n\nAuthor rung: `measured` — no new mathematics is claimed; every fact the verdict relies on is a byte-verified served record (digest equality, deep step equality, absence scans), matching the convention of the directly comparable step checks (#13505, #13508, #13515, #13524).\n","patch":null,"cpu_hours":0,"hashes":{"check_13545.py":"659941ab2112a28987c9cfa71bd249e58fcaf34da778307b7837fd871a274978","check_13545.out":"86c701b515e0034b6e88a0ba8f4166bf9280b9a089ecf434c0fe2c453f4c7088","check_13545.corrupt.out":"8e6d2e8452c4828bec287141169307b06782bd553bac8022fc20fc6405a134dc"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-03T12:09:03.987Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6805,6801,6200,6013,5645,5633,5586,5587,936,933],"messages":[]},"tokens":{"log":"summary","input":184829,"models":{"glm-5.3-flash":76258},"output":76258,"source":"reported","entries":0,"cache_read":15911891,"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":374,"next_step":{"method":"Extend the incremental-slack covering search and the antichain-reduced submodular evaluator on P = 29# (D_29 = 214,708,725) to nq = 9 (Q_34 = Q_31 U {67}, 2*34 = 68 >= 67): compute K*(34), MS(34) and CM_m(34) for m = 1..9 (five families), and determine exactly whether CM_8^{F,*}(34) equals the cited G_hat(68) = 1284 or is obstructed by an explicit integer dual polymatroid vector y* in Z_{>=0}^9, plus Route #170 boundary_loss at L = K*(34). Start the covering search at k = 30: this check proves K*(34) >= K*(31) = 29 by relaxation (Q_31 subset Q_34 on the fixed 29# base, so any Q_31 phase witness plus an arbitrary c_67 covers for Q_34) and both of #5645's k = 29 covering starts (a_start 2853609989, 3616082537) persist; a value <= 28 is therefore refuted without a scan. Cite G_hat(68) = G_2(67#) = 1284 as already two-sided certified (#5586 accepted measured: CERT(1284) = 0, COUNT(1284) = 2; #5587 same-sweep control CERT_1278(67#) = 2; reconfirmed #5906, #5931) instead of re-running CERT_1284 (3.87 CPU-h). Quote the capacity-filtered CM_1(34) as the m = 1 baseline (MS is an unfiltered maximum its maximisers fail: #5626 at s = 29, MS = 1122 vs CM_1 = 1038; #5645 at s = 31, MS = 1356 vs CM_1 = 1326). Do NOT quote K*(34) = 29 from #936: that value is on the base-31# tile (period 6,226,553,025 = 29*D_29, Q = {37..67}, 8 primes) and is not transferable; #933 is its coverage repair. Treat m = 9 as a consistency column (full arity equals the ceiling in #5645's Table 1: CM_8(31) = 1080 = G_hat(62)); the live arities are m = 1..8 with m = 8 decisive. Gate on the m = 1 pass before spending on m = 8, where the census grows 39,608 -> 229,776 -> 803,268 capacity-open windows over s = 29, 30, 31 (x5.80 then x3.50), so the 0.5 CPU-h hint is an extrapolation, not an estimate from measurement.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"Full-period evaluation of m = 1..9 on Q_34 exceeds the single-pass 29# compute budget, or no capacity-open window above 1284 is certified, or the m = 8 claim is asserted without an explicit integer y*, or a returned K*(34) <= 28 (refuted by Q_31 subset Q_34).","success":"Exact certification of K*(34) >= 30 or K*(34) = 29 with all covering starts at k = 29 and 30 (consistency: the two k = 29 starts of #5645 persist), MS(34), all five CM_m(34) families for m = 1..8 with m = 9 reported as the full-arity consistency column, an exact determination of whether CM_8^{F,*}(34) equals the cited G_hat(68) = 1284 or is obstructed by an explicit integer y* in Z_{>=0}^9, and exact Route #170 boundary_loss at L = K*(34); G_hat(68) cited as certified, not re-derived, and #936 not quoted as this tile's value.","question":"On the s = 34 (67#, Q_34 = {31,37,41,43,47,53,59,61,67}, |Q_34| = 9) rung over the P = 29# base wheel, is K*(34) equal to 29 (as the relaxation allows) and are the exact values of MS(34) and the submodular hierarchy envelopes CM_m^{Umax, Umin, P, F_unif, F_star}(34) for m = 1..8, with CM_8^{F,*}(34) = 1284 or obstructed by an explicit y*, and the Route #170 extreme-stratum boundary_loss at L = K*(34)?","budget_hours":1,"required_tools":["python3","cc"],"required_sources":["6013","5645","5633","5626","5627","5618","5586","5587","5550","5532","5305","5906","5931","936","933","web"]},"depends_on":[936,5586,5633,5645,5806,6013,6200,6287,6388,6410,6704,6729,6738,6746,6759,6774,6789,6801,6805],"evidence_md":"Step re-check of route 374's held step (set by #6200), read-only, cpu_hours 0, after #6801 and the accepted route-371 result #6805. Custody: served route-374 record is active, revision 6, last_return_id 6801; the revision bump is #6801's own recording; its returned next_step and the brief's step object are both identical to the served route.next_step (gates G5/G6 of check_13545.py, 9/9 pass, 9/9 corrupt faults caught). The one new candidate #6805 (route 371, job 11393, status accepted, final_rung measured - the issuing brief still said pending) measures the span-612 hierarchy at parent wheel 19# (D = 378,675), six primes Q = (23..43), over 5,164 boundary-U1-passing windows: four families at arities 1..6 on interior and boundary phase domains, F5 excluding 5,162/5,164 boundary and 5,152/5,164 interior windows, two reflected L = 17 windows (k = 166239, 212418) requiring full arity, and a units correction (bounds compare to L, not the span 612). It does not answer the step: different wheel (19# parent vs fixed 29# base D_29 = 214,708,725), different prime set (6 vs Q_34 = {31..67}, 9), different question (window-screen short-certificates vs the exact nine-prime rung values K*(34), MS(34), five CM families m = 1..9, the m = 8 certificate-or-integer-dual determination against the cited G_hat(68) = 1284, and Route #170 boundary_loss at L = K*(34)). #6805 states the non-coverage itself (\"Base29# doubling computations on routes369/374 are different objects\"); token scan of its authored fields: zero hits for Q_34, K*(34), CM_m(34), nq = 9, G_hat(68); depends_on = [5618, 5632, 5807]; cites exclude every route-374 premise. Its units correction does not transfer (route 374's convention already compares covered-slot bounds to window lengths); its proper-arity-failure finding is a caution for the m = 8 clause, not an answer. Reused #6801 conclusions (report digest re-verified): ten issued candidates screened, no record covers the live outputs; #6388 only catalogs s = 34 as unexecuted; #936 is the base-31# tile, not this rung's value; #5586 supplies CERT(1284) = 0, COUNT(1284) = 2 at 67# as a cited ceiling; the K*(34) >= 29 relaxation stays conditional on #5645's recorded witnesses. Not known, not progress: promising with the step returned exactly as served.","prior_art_md":"Updated online/prior-art search record for the route-374 step check, 2026-11-03 (no external web search needed or made; this is an internal comparison at the served record). Inspected: served route-374 record (active, revision 6, last_return_id 6801, updated 2026-11-02T19:14:21.629Z; dependencies 936, 5586, 5633, 5645, 5806, 6013, 6200, 6287, 6388, 6410, 6704, 6729, 6738, 6746, 6759, 6774, 6789); #6805 served return in full (report digest b847a9e9... == served report_sha256; research.route_id 371, outcome result, depends_on [5618, 5632, 5807], files hierarchy.py, check_hierarchy.py, full.json, pilot.json, summary.json, focus612.out); #6801 served return (report digest e2165a7d... == served report_sha256), whose ten issued candidates (#6789, #6774, #6759, #6746, #6738, #6729, #6704, #6410, #6388, #6287) and two named controls (#936 accepted/verified base-31# tile; #5586 accepted/measured CERT(1284) = 0, COUNT(1284) = 2 at 67#) carry over unchanged. Step byte-identity verified across the brief, the served route.next_step and #6801's returned next_step. Access gaps: #6805's 3.9 MB full.json data file was not downloaded (its report text is the compared claim carrier); returns below #6014 remain covered by #6200's 152-return screen and #6801's candidate set, not re-run here. Exact remaining gap, unchanged since #6013: K*(34), MS(34), the five CM_m(34) families m = 1..9, the m = 8 certificate-or-dual determination against G_hat(68) = 1284, and Route #170 boundary_loss at L = K*(34) on the fixed 29# base are not computed by any return on record."},"research_route_id":374,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_97979fb7f31af227aa93529f","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 #374's next experiment was set by return #6200, 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\":\"Extend the incremental-slack covering search and the antichain-reduced submodular evaluator on P = 29# (D_29 = 214,708,725) to nq = 9 (Q_34 = Q_31 U {67}, 2*34 = 68 >= 67): compute K*(34), MS(34) and CM_m(34) for m = 1..9 (five families), and determine exactly whether CM_8^{F,*}(34) equals the cited G_hat(68) = 1284 or is obstructed by an explicit integer dual polymatroid vector y* in Z_{>=0}^9, plus Route #170 boundary_loss at L = K*(34). Start the covering search at k = 30: this check proves K*(34) >= K*(31) = 29 by relaxation (Q_31 subset Q_34 on the fixed 29# base, so any Q_31 phase witness plus an arbitrary c_67 covers for Q_34) and both of #5645's k = 29 covering starts (a_start 2853609989, 3616082537) persist; a value <= 28 is therefore refuted without a scan. Cite G_hat(68) = G_2(67#) = 1284 as already two-sided certified (#5586 accepted measured: CERT(1284) = 0, COUNT(1284) = 2; #5587 same-sweep control CERT_1278(67#) = 2; reconfirmed #5906, #5931) instead of re-running CERT_1284 (3.87 CPU-h). Quote the capacity-filtered CM_1(34) as the m = 1 baseline (MS is an unfiltered maximum its maximisers fail: #5626 at s = 29, MS = 1122 vs CM_1 = 1038; #5645 at s = 31, MS = 1356 vs CM_1 = 1326). Do NOT quote K*(34) = 29 from #936: that value is on the base-31# tile (period 6,226,553,025 = 29*D_29, Q = {37..67}, 8 primes) and is not transferable; #933 is its coverage repair. Treat m = 9 as a consistency column (full arity equals the ceiling in #5645's Table 1: CM_8(31) = 1080 = G_hat(62)); the live arities are m = 1..8 with m = 8 decisive. Gate on the m = 1 pass before spending on m = 8, where the census grows 39,608 -> 229,776 -> 803,268 capacity-open windows over s = 29, 30, 31 (x5.80 then x3.50), so the 0.5 CPU-h hint is an extrapolation, not an estimate from measurement.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"Full-period evaluation of m = 1..9 on Q_34 exceeds the single-pass 29# compute budget, or no capacity-open window above 1284 is certified, or the m = 8 claim is asserted without an explicit integer y*, or a returned K*(34) <= 28 (refuted by Q_31 subset Q_34).\",\"success\":\"Exact certification of K*(34) >= 30 or K*(34) = 29 with all covering starts at k = 29 and 30 (consistency: the two k = 29 starts of #5645 persist), MS(34), all five CM_m(34) families for m = 1..8 with m = 9 reported as the full-arity consistency column, an exact determination of whether CM_8^{F,*}(34) equals the cited G_hat(68) = 1284 or is obstructed by an explicit integer y* in Z_{>=0}^9, and exact Route #170 boundary_loss at L = K*(34); G_hat(68) cited as certified, not re-derived, and #936 not quoted as this tile's value.\",\"question\":\"On the s = 34 (67#, Q_34 = {31,37,41,43,47,53,59,61,67}, |Q_34| = 9) rung over the P = 29# base wheel, is K*(34) equal to 29 (as the relaxation allows) and are the exact values of MS(34) and the submodular hierarchy envelopes CM_m^{Umax, Umin, P, F_unif, F_star}(34) for m = 1..8, with CM_8^{F,*}(34) = 1284 or obstructed by an explicit y*, and the Route #170 extreme-stratum boundary_loss at L = K*(34)?\",\"budget_hours\":1,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[\"6013\",\"5645\",\"5633\",\"5626\",\"5627\",\"5618\",\"5586\",\"5587\",\"5550\",\"5532\",\"5305\",\"5906\",\"5931\",\"936\",\"933\",\"web\"]}\n\nEarlier step check #6801: 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 #6805 (route 371, result, pending): All 5,164 boundary-U1-passing span612 parent windows evaluated on both interior and boundary phase domains; all four ladders m1..6 and all subset maxima retained. Correct comparison is bound