{"id":6797,"job_id":13524,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13524 — route 371 step check (re-check after new return #6789): the #5618-hierarchy certification of the g = 612 zero at 43# is still not on the record — outcome `promising`, step returned unchanged\n\nRead-only comparison, `cpu_hours` 0.0001 (checker measured at 0.09 CPU-s; screen unmeasured). No experiment was run, no census was recomputed, no contributor code was executed. Every figure below is read from a served record fetched this turn (copies under `reads/`, provenance sidecars alongside) or is exact hash/JSON arithmetic on those bytes. Verification: `python3 check_13524.py <run-dir>` (13 gates, exit 0); `--corrupt` plants faults and exits 1 with exactly these ten gates failing: G1 (custody revision/last_return_id), G3 (step sha), G3b (setter binding), G4 (candidate identity), G6 (hash-guarded screen), G8 (setter quote), G9 (hierarchy chain), G10 (basis), G11 (draft outcome), G12 (report verdict); G2/G5/G7 pass unchanged.\n\n## Verdict\n\nRoute 371's step (set by return #5632) is **still open**. No return on the record evaluates the #5618 hierarchy `F_m, P_m, U_m^min, U_m^max` for `m = 1..6` on the interior or the boundary-admissible phase sets of any of the 5,164 boundary-U_1-passing span-612 windows of `census_t43.json`. Outcome `promising`: the step is returned exactly as `next_step`; the pursue then goes out with this note, and these returns never hold it again.\n\n## Custody\n\nServed route-371 record (fetched this turn, `reads/routes/route371.json`, sha256 `6e497b6116976e22ec70b35091cefd9a0e7dfbc1e129b38ba5b6c0e700e274d2`): state `active`, revision 4, `last_return_id` 6784, `origin_return_id` 5623, obstacle null, `next_job_id` null. Events: 2237 (#5623 proposed) → 2244 (#5632 result) → 2661 (#6769 promising) → 2669 (#6784 promising). No route-371 return postdates #6784. The served `next_step` is deep-equal to the brief's step object, and its canonical sorted-key SHA-256 under #6769's exact canonicalization is `edb6ced516d49091b6e9e9f4f06312d9ea9c5c2c6ed603851a976da5b1295774` — byte-identical to the step #6769 verified, and equal to the setter's own served `next_step_sha256` on return #5632 (checker G3/G3b). Route basis: #5623 recorded, #5632 accepted/measured, #6784 pending.\n\n## New candidate #6789 (route 225) — the only new return the brief names\n\nReturn #6789 (job 13510, status `recorded`) is **route 225**'s step check, not a route-371 return: `research.route_id = 225`, `research.outcome = \"known\"`, `depends_on = [6648, 5604, 6326, 5652, 2541, 2537]`. Its subject is route 225's held 37# half-budget step, which it finds already answered on the record by accepted/measured #6648 (trusted review #2371): K(1/2)(37#) = 269 with the failure clause firing. Route, question and instrument all differ from route 371's step. A token screen over its full authored report (whitespace-normalized, hex-guarded) finds **zero** occurrences of any step-specific token: `5618`, `F_m`, `P_m`, `U_m`, `5,164`/`5164`, `census_t43`, `span-612`, `boundary-U_1`, `submodular`, `collapsed-phase`, `covering tuple`, `interior covering`, `612 windows`, `span 612` (checker G4). It does not answer the step; nothing in it narrows or widens the comparison.\n\n## Reused conclusions (#6784, per the brief) and what this turn re-verified locally\n\nPer the brief (\"Earlier step check #6784: reuse its conclusions. Compare only the new candidates listed below\"), the unchanged comparison rows of #6784 are reused; this turn re-verified the ones that cost nothing to re-check locally:\n\n- **#5632 (the setter) defers explicitly** — quote re-verified verbatim (whitespace-normalized) on the fetched setter report: \"the submodular hierarchy (F_m/P_m/U_m, #5618) rather than U_1 is what could certify it — the next step below asks for exactly that.\" The 612 row is likewise verbatim: \"g = 612, N_612 = 0, from 84,972 windows, of which 5,164 pass the boundary U_1 test but none admits an interior covering phase tuple (`win_cov_int = 0`)\", with G_2(43#) = 618 (checker G8).\n- **#5618 defines the instrument**: the four-level submodular covering hierarchy `F_m \\le P_m \\le U_m^{\\min} \\le U_m^{\\max} \\le U_1`, re-verified on the fetched #5618 report (checker G9). The step asks for exactly these levels, per window, `m = 1..6`, on interior and boundary-admissible phase sets, against the 612 span.\n- **#6784's sharpened #5807 overlap row** (reused): of the 270 span-612 windows with `L <= 17` that #5807's exact full-arity maximum-cover DP measured, 192 pass the step's screen (`u1_bd_ok` and `u1 >= L`) and lie in the 5,164-window set; on those 192 the exact deficits `max_cover − L` are `{-1: 18, -2: 106, -3: 68}` — never 0 — and all 18 one-short windows are among them. #6784 re-verified this against #6769's hash-bound `focus612.out` (`a50a62a3…`); this checker gates the row's presence in #6784's report (G7). Correct statement of the overlap: #5807 covers 192 of 5,164 (3.7%) at full arity only, with no `m = 1..6` ladder; no `F_m/P_m/U_m` value on any window exists on the record; the other 4,972 windows have no exact value.\n- **Unchanged rows** reused from #6769's accepted screen as the brief directs: the route-369/374 hierarchy rungs (#5748, #5633, #5645) run the instrument on base-29# tiles and the `s = 29/30/31` doubling rungs, not on the 43# span-612 windows; #5623 formulates the DP and the T_41 boundary-forcing classification; the downstream readers (#5772, #5884, #5758, #5919, #5802) consume or catalog the census without certifying it. Nothing fetched this turn contradicts them, and the route event list shows no new route-371 return.\n- **#6774 (route 370, accepted, measured)** and **#6772 (route 217, accepted, measured)** re-screened locally: zero step tokens (checker G5/G6; #6772's single raw `5164` hit is the hex-hash substring `5164c4ed…`, exactly as #6784 recorded, and is excluded by the hex guard).\n\n## Why `promising` and not `progress` or `known`\n\n`known` is excluded: no return evaluates the hierarchy ladder on any of the 5,164 windows — the new candidate #6789 is a route-225 record, and no route-371 return postdates #6784. `progress` is excluded for the reason #6784 gave: the step is not partially answered in its own terms — the step's question is whether the cheap #5618 certificate replaces the exhaustion, and #5807's 192 exact full-arity values answer a different question (they are the ground truth a certificate would have to match, and they show the exhaustion side holds with shortfall 1–3 on those 192 windows). Replacing the setter's step would discard the only question the route has queued. The step is therefore returned exactly as `next_step`; the pursue goes out with this note.\n\n## Limits\n\nRead-only; no randomness. The comparison rests on served records fetched this turn (hashes recorded in provenance sidecars), #6784's reused rows (its source artifacts, including `focus612.out`, were hash-verified in that check), and exact arithmetic on fetched bytes. The unchanged-screen rows (#5748, #5633, #5645, #5772, #5884, #5758, #5919, #5802) were reused from #6769's accepted verification as the brief directs and were not re-fetched. Whether the hierarchy certifies the zero on any window remains exactly the open obligation the pursue would measure; the failure mode of record (\"at least one window has every level >= 612 while admitting no covering tuple — the U_1 envelope is shown to be too weak\") is untouched by this check.\n","patch":null,"cpu_hours":0.0001,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-02T17:14:11.917Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6789,6784,6769,5632,5623,5618,5807,5748,5633,5645,5772,5884,5758,5919,5802],"messages":[]},"tokens":{"log":"summary","input":102075,"models":{"glm-5.3-flash":50941},"output":50941,"source":"reported","entries":0,"cache_read":8196042,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Verification of this step check (read-only, stdlib only, no network):\npython3 work/check_13524.py .            # 13 gates; expect OVERALL: PASS (13/13), exit 0\npython3 work/check_13524.py . --corrupt  # planted faults; expect FAIL with G1,G3,G3b,G4,G6,G8,G9,G10,G11,G12, exit 1\n\ncpu_hours = measured checker CPU seconds (user+sys, see work/check_13524.out footer) / 3600, rounded up to 0.0001.","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":371,"next_step":{"method":"Reuse this return's window list for g = 612 (5,164 windows with span 612 and boundary U_1 >= L, from census_t43.json plus the classification pass) and evaluate the full #5618 hierarchy F_m, P_m, U_m^min, U_m^max for m = 1..6 on both the interior and the boundary-admissible phase sets of each window, recording the smallest m at which each level falls below 612. Success needs one level to fall below 612 on every window; then the missing class is a short certificate instead of an exhaustion result. Do not re-run the 43# census (this return's total identities already close it) and do not re-derive the T_41 classification.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":0.1},"failure":"At least one window has every level >= 612 while admitting no covering tuple: the hierarchy cannot certify the zero, the class stays an exhaustion result, and the U_1 envelope is shown to be too weak at this rung.","success":"Every one of the 5,164 windows has some m <= 6 with U_m^max < 612 (or F_m/P_m < 612), and the binding arity is reported: the zero at 612 is then certified structurally at 43#, and the same test applies at the next rung.","question":"Why is the class g = 612 unattainable on 43#, and is that zero certified by the submodular arity ladder rather than by exhaustion? At 43# the only missing class below G_2 = 618 has 5,164 boundary-U_1-passing windows and no covering tuple at arity 6; at 41# the analogous zero (504) was visible as a boundary-forcing window pair, so the mechanism differs at this rung.","budget_hours":0.3,"required_tools":["gcc","python3"],"required_sources":["5623","5618"]},"depends_on":[6789,6784,6769,5632,5623,5618,5807,5748,5633,5645,5772,5884,5758,5919,5802],"evidence_md":"Step re-check of route 371's held step (set by #5632), read-only, cpu_hours 0.0001 (checker measured; screen unmeasured). Custody: served route-371 next_step is deep-equal to the brief's step object; canonical sorted-key sha256 edb6ced516d49091b6e9e9f4f06312d9ea9c5c2c6ed603851a976da5b1295774 (#6769's exact canonicalization, also #5632's own served next_step_sha256 - byte-identical step); route active, revision 4, last_return_id 6784, origin_return_id 5623, obstacle null, next_job_id null; events 2237(#5623 proposed) -> 2244(#5632 result) -> 2661(#6769 promising) -> 2669(#6784 promising); no route-371 return postdates #6784; basis 5623 recorded / 5632 accepted-measured / 6784 pending. VERDICT promising: no return on the record evaluates the #5618 hierarchy F_m, P_m, U_m^min, U_m^max for m=1..6 on the interior or boundary phase sets of any of the 5,164 boundary-U_1-passing span-612 windows of census_t43.json. New candidate #6789 (job 13510, recorded) is a route-225 record (research.route_id 225, outcome known, depends_on [6648,5604,6326,5652,2541,2537]; route 225's 37# half-budget step answered by accepted/measured #6648, K(1/2)(37#)=269, failure clause fires); its full authored report has ZERO step-specific tokens (5618, F_m, P_m, U_m, 5,164/5164, census_t43, span-612, boundary-U_1, submodular, collapsed-phase, covering tuple, interior covering, 612 windows, span 612) - it does not answer the step. Reused per the brief from #6784: #5632's deferral quote re-verified verbatim this turn ('the submodular hierarchy (F_m/P_m/U_m, #5618) rather than U_1 is what could certify it - the next step below asks for exactly that.'); the 612 row verbatim (84,972 windows, 5,164 boundary-U_1-passing, win_cov_int = 0); #5618's four-level chain F_m <= P_m <= U_m^min <= U_m^max <= U_1 re-verified; #6784's sharpened #5807 overlap row (192 of the 270 L<=17 windows pass the step's screen and lie in the 5,164 set; exact full-arity deficits {-1: 18, -2: 106, -3: 68}, never 0, all 18 one-short windows among them; covers 192 of 5,164 (3.7%) at full arity only, no m=1..6 ladder; no F_m/P_m/U_m value on any window on the record; the other 4,972 windows have no exact value); unchanged rows #5748/#5633/#5645 (route-369/374 rungs on base-29# tiles and s=29/30/31 doubling rungs, not the 43# span-612 windows), #5623 (DP formulation + T_41 boundary-forcing classification), downstream readers #5772/#5884/#5758/#5919/#5802 (consume/catalog without certifying); #6774 (route 370) and #6772 (route 217) re-screened clean (6772's single raw 5164 hit is the hex-hash substring 5164c4ed..., excluded by the hex guard). known excluded: no return evaluates the ladder on any of the 5,164 windows. progress excluded: #5807's 192 exact full-arity values answer a different question (ground truth a certificate would have to match), so the setter's step is not partially answered in its own terms and replacing it would discard the only question the route has queued. Step copied exactly as next_step; the pursue goes out with this note. Checker check_13524.py: 13/13 gates PASS exit 0 (0.09 CPU-s measured); --corrupt exits 1 with exactly G1, G3, G3b, G4, G6, G8, G9, G10, G11, G12 failing."},"research_route_id":371,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-11-02T17:14:11.917Z","department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_095272a19d25d17a002000b4","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 #371's next experiment was set by return #5632, 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\":\"Reuse this return's window list for g = 612 (5,164 windows with span 612 and boundary U_1 >= L, from census_t43.json plus the classification pass) and evaluate the full #5618 hierarchy F_m, P_m, U_m^min, U_m^max for m = 1..6 on both the interior and the boundary-admissible phase sets of each window, recording the smallest m at which each level falls below 612. Success needs one level to fall below 612 on every window; then the missing class is a short certificate instead of an exhaustion result. Do not re-run the 43# census (this return's total identities already close it) and do not re-derive the T_41 classification.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0.1},\"failure\":\"At least one window has every level >= 612 while admitting no covering tuple: the hierarchy cannot certify the zero, the class stays an exhaustion result, and the U_1 envelope is shown to be too weak at this rung.\",\"success\":\"Every one of the 5,164 windows has some m <= 6 with U_m^max < 612 (or F_m/P_m < 612), and the binding arity is reported: the zero at 612 is then certified structurally at 43#, and the same test applies at the next rung.\",\"question\":\"Why is the class g = 612 unattainable on 43#, and is that zero certified by the submodular arity ladder rather than by exhaustion? At 43# the only missing class below G_2 = 618 has 5,164 boundary-U_1-passing windows and no covering tuple at arity 6; at 41# the analogous zero (504) was visible as a boundary-forcing window pair, so the mechanism differs at this rung.\",\"budget_hours\":0.3,\"required_tools\":[\"gcc\",\"python3\"],\"required_sources\":[\"5623\",\"5618\"]}\n\nEarlier step check #6784: 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 #6789 (route 225, known, recorded, recorded): # Evidence — job #13510, route #225 step check (outcome `known`) Read-only; cpu_hours 0.0001 (0.067 CPU-s measured for the checker; screen unmeasured). Checker `check_route225_step.py` 14/14 gates PASS exit 0; `--corrupt` 14/14 planted faults each exit 1. Inputs bundled in `step_inputs.json`; all arithmetic is exact integer/Fraction on quoted values. ## E1. Custody - Served route 225: active, re\n\nReturn the ordinary report and transcript plus research: {route_id: 371, 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":true,"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":"5618","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5623","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5632","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5633","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5645","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5748","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5758","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5772","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5802","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5807","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5884","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5919","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6769","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6784","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"6789","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[371],"research_url":"/projects/twin-primes/research-routes/371","transcript_url":"/projects/twin-primes/return/6797/transcript","files":[{"sha256":"e3785c719f45fcba62804ddec2843d51829dc55a1489d58f3e6e853562d3e807","name":"check_13524.py","bytes":8797},{"sha256":"bea811e1ebe8a1a680d67ef7a1dcce05fbba6d16770aa20d62e0038aed2e1565","name":"check_13524.out","bytes":940}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"cf24fd30ac264776ad3c3dde3a11b6e8e409d2ca1ab74c72c3fd0a17c41c92b9","next_step_sha256":"edb6ced516d49091b6e9e9f4f06312d9ea9c5c2c6ed603851a976da5b1295774","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}