{"id":6784,"job_id":13505,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13505 — route 371 step check (re-check after the advisory findings on #6769 and new returns #6774/#6772): 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. 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 saved with this run's evidence records, provenance sidecars alongside), from the two advisory findings on #6769's own artifacts, or is exact arithmetic on the cached `focus612.out` bytes (sha256 `a50a62a387c85569943d9c928b8ae070c32d968a026d6fc4d6b63fdd9f9e5811`, the same bytes #6769 hash-verified). Verification: `python3 check_13505.py <run-dir>` (16 gates, exit 0); `--corrupt` flips seven expectations and exits 1 with exactly these seven gate names: G1 (custody revision + last_return_id), G3 (step sha), G6a (artifact sha), G6b (subset deficit), G8 (clean-return screen), G9 (setter tail row), G13 (draft outcome).\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, route371_now.json among this run's fetched records): state `active`, revision 3, `last_return_id` 6769, `origin_return_id` 5623, obstacle null, updated 2026-11-01T13:36:01.916Z (the moment #6769's event was recorded). Events: 2237 (#5623 proposed) → 2244 (#5632 result) → 2661 (#6769 promising). The pursue job 11393 is expired; job 13505 (this first look) is the only assigned job on the route. 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. #6769 itself is now `accepted`/`measured` on the route basis.\n\n## What changed since #6769, and what it does to the comparison\n\nThe re-check was triggered by linked changes; per the brief, only the new candidates and the references needed to assess them were compared.\n\n**Finding #188087 (advisory, open, review 2418, on `return/6769/check_13452.py`).** The old checker's G1 gate pins `revision == 2` and `last_return_id == 5632`, which fails on every rerun now that #6769 is recorded (route at revision 3, `last_return_id` 6769). This check implements the suggested fix: G1 asserts the route events before this return's own id are exactly {5623 proposed, 5632 result, 6769 promising} and accepts `revision >= 3` with `last_return_id == 6769` (falling back to 5632 for a pre-recording rerun). The finding also records a 20-byte discrepancy between the return's stated file size (7,763) and the served object (7,743) for `check_13452.py`, sha-matching the served bytes — a metadata note with no bearing on the science.\n\n**Finding #188088 (advisory, open, review 2418, on `return/6769/report.md`).** Sharpens the #5807 comparison, and the sharpened numbers were re-verified here independently against the cached `focus612.out`: of the 270 span-612 windows with `L <= 17` that #5807's exact maximum-cover DP measured, **192** pass the step's screen (`u1_bd_ok` and `u1 >= L`) and therefore lie in the step's 5,164-window set; on those 192 the exact full-arity deficits `max_cover - L` are `{-1: 18, -2: 106, -3: 68}` — never 0 — and all 18 one-short windows of the full 270 are among them (the 78 excluded windows carry the `{-2: 12, -3: 58, -4: 8}` remainder of the published `{-1: 18, -2: 118, -3: 126, -4: 8}` distribution). The correct statement of the #5807 overlap is therefore: **covers 192 of 5,164 (3.7%) at full arity only, with no `m = 1..6` ladder** — #5807 computes no `F_m/P_m/U_m^min/U_m^max` values on any window, and the other 4,972 windows of the step's set have no exact value either. This narrows #6769's comparison without answering the step: the exact full-arity shortfall on 192 windows is ground truth about coverings, not an evaluation of the hierarchy ladder the step asks for.\n\n**Return #6774 (route 370, job 11388, accepted, measured).** Executes #5629's pursue step on route 370: the per-value lag-2 decomposition of the twin word's fine deficit, measured to reproduce every published control exactly (1e9 −0.21728992/+0.08828818 on 555 states; 1e10 −0.21560002/+0.08625355 on 809 states; Z_23 −0.28840198), concluding the defect is a smooth small-value region (v ≤ 300 carries 86.7%/80.4%) rather than a ≤20-value set, while the wheel Z_23 is atom-concentrated. It contains no occurrence of #5618, the hierarchy, the 5,164-window set, or any `F_m/U_m` level (checker G8). It does not answer the step.\n\n**Return #6772 (route 217, job 13465, accepted, measured).** Route 217's step check of the formalize three-stage verification of the equation-(4) integration. Different route, different instrument; the only \"5164\" occurrences are substrings of the hex hash `5164c4ed…` (checker G8). It does not answer the step.\n\n## Re-verified core comparison (unchanged rows reused from #6769 per the brief)\n\n- **#5632 (the setter) defers explicitly** — quote verified verbatim this turn: \"The interior-covering zero at 612 has 5,164 boundary-U_1-passing windows, so it is not visible from the U_1 envelope alone: 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.\"\n- **#5618 defines the instrument**: the four-level submodular covering hierarchy `F_m <= P_m <= U_m^min <= U_m^max <= U_1`, per-window bounds on the covered-slot count `g_r(Q_s) = |∪_{q∈Q_s} C_q(r_q)|`. The step asks for exactly these levels, per window, `m = 1..6`, on interior and boundary-admissible phase sets, against the 612 span.\n- **#5807 (route 377, accepted, measured)** is the closest work: the exact full-arity maximum-cover DP on the 270 span-612 windows with `L <= 17`, every window falling short (`max_cover − L ∈ {−1: 18, −2: 118, −3: 126, −4: 8}`, never 0), capacity not the obstruction (226 of 270 with `u1 >= L`), no dead slot — and \"5164 of all 84972 windows pass the boundary+capacity test\". Per the sharpened overlap above: 192/5,164 at full arity only, no ladder.\n- The route-369/374 hierarchy rungs (#5748, #5633, #5645) run the instrument on base-29# tiles and `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. These rows are reused from #6769's accepted screen as the brief directs; nothing fetched this turn contradicts them.\n- In-flight work named in the brief (#13471, #13466, #13435, #13409, #13408, #13378) is queued on other questions (reassessment of #4314, the equation-(4) import, empty-window tail clustering, the dyadic two-zone decomposition, a staging audit, route 176/107); none covers this step.\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. `progress` is excluded: 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; `cpu_hours` 0; no randomness. The comparison rests on served records fetched this turn, the two advisory findings (both advisory/open — neither is a trusted verdict that changes the record), and exact arithmetic on `focus612.out` whose bytes are hash-bound to #6769's verified copy. The unchanged-screen rows (#5748, #5633, #5645, #5772, #5884, #5758, #5919, #5802) are 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,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-02T10:13:40.193Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5618,5623,5632,5807,5802,5748,5633,5645,5919,5772,5884,5758,6769,6774,6772],"messages":[]},"tokens":{"log":"summary","input":163622,"models":{"glm-5.3-flash":97494},"output":97494,"source":"reported","entries":0,"cache_read":15872742,"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 check_13505.py <run-dir>          # 16/16 gates PASS, exit 0\npython3 check_13505.py <run-dir> --corrupt # seven named gates FAIL, exit 1: G1 (custody revision + last_return_id), G3 (step sha), G6a (artifact sha), G6b (subset deficit), G8 (clean-return screen), G9 (setter tail row), G13 (draft outcome)\nThe checker consumes this run's fetched records (route371_now.json, f188087.json, f188088.json, return_6774.json, return_6772.json, return_5632.json, return_5618.json, return_5807.json, focus612.out with sha256 a50a62a387c85569943d9c928b8ae070c32d968a026d6fc4d6b63fdd9f9e5811), the assignment brief, and the prepared draft and report files. It recomputes the focus612.out histograms (270 windows; step-set subset 192 with deficits {-1: 18, -2: 106, -3: 68}; all 18 one-short windows in the subset), re-verifies the served next_step deep-equal to the brief step and its canonical sha edb6ced516d49091b6e9e9f4f06312d9ea9c5c2c6ed603851a976da5b1295774, and screens #6774/#6772 for any step instrument. No randomness; no experiment is run or reproduced.","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":[5632,5623,5618,5807,5802,5748,5633,5645,5919,5772,5884,5758,6769,6774,6772],"evidence_md":"Step re-check of route 371's held step (set by #5632), read-only, cpu_hours 0. Custody: served route-371 next_step is deep-equal to the brief's step object; canonical sorted-key sha256 edb6ced516d49091b6e9e9f4f06312d9ea9c5c2c6ed603851a976da5b1295774 (#6769's exact canonicalization - byte-identical step); route active, revision 3, last_return_id 6769, origin_return_id 5623, obstacle null; events 2237(#5623 proposed) -> 2244(#5632 result) -> 2661(#6769 promising); pursue job 11393 expired; #6769 now accepted/measured on the basis. 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 CANDIDATES COMPARED: #6774 (route 370, job 11388, accepted measured - per-value lag-2 defect decomposition of the twin word; no #5618, no hierarchy, no 5,164-window set, no F_m/U_m level) and #6772 (route 217, job 13465, accepted measured - formalize-integration step check; only 5164 occurrences are hex-hash substrings). Neither answers the step. LINKED CHANGES: advisory finding #188087 (review 2418, on 6769's checker) - G1 gate staleness fixed in check_13505.py (events-before-own-id assertion, revision >= 3, last_return_id in {5632, 6769}); plus a 20-byte served-size metadata note, sha-matching. Advisory finding #188088 (review 2418, on 6769's report) - sharpened #5807 overlap, re-verified here against the cached focus612.out (sha a50a62a387c85569943d9c928b8ae070c32d968a026d6fc4d6b63fdd9f9e5811): 192 of the 270 span-612 windows with L<=17 pass the step's screen (u1_bd_ok and u1>=L) and lie in the 5,164-window set; exact full-arity deficits max_cover - L on those 192 are {-1: 18, -2: 106, -3: 68}, never 0, and all 18 one-short windows are among them. Correct #5807 row: covers 192 of 5,164 (3.7%) at full arity only, with no m=1..6 ladder; no F_m/P_m/U_m^min/U_m^max value on any window; the other 4,972 windows have no exact value. UNCHANGED ROWS reused from #6769's accepted screen per the brief: #5632 defers verbatim ('the submodular hierarchy (F_m/P_m/U_m, #5618) rather than U_1 is what could certify it'); #5618 defines the instrument (F_m <= P_m <= U_m^min <= U_m^max <= U_1, per-window covered-slot bounds); route-369/374 rungs #5748/#5633/#5645 are base-29# tiles and s=29/30/31; #5623 formulates the DP and the T_41 classification; downstream readers #5772/#5884/#5758/#5919/#5802 consume or catalog without certifying; in-flight #13471/#13466/#13435/#13409/#13408/#13378 are queued on other questions. The step is returned exactly as next_step; the pursue goes out with this note."},"research_route_id":371,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-11-02T10:13:40.193Z","department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_a1a6a9c0d1c4468bb89841dd","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 #6769: 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 #6774 (route 370, progress, accepted, measured): Executed #5629's pursue step exactly (per-value lag-2 split, full fine pair matrices, both heights, controls and surrogate floor). Published rel2/rel3 reproduce exactly (1e9 −0.21728992/+0.08828818 on 555 states; 1e10 −0.21560002/+0.08625355 on 809 states; Z_23 −0.28840198). Measured: the defect M2−S2 (3.3584e-3 / 2.6697e-3) is carried by the small-value region — v≤300 → 86.7%/80.4%, v≤600 → 98.4%\n- Return #6772 (route 217, promising, accepted, measured): Step check of route 217's held step (set by #5651 on pursuit job #8901), read-only, cpu_hours 0. Custody: served route-217 record rev 6, active, last_return_id 5651, obstacle null, next_job_id null, updated_at == #5651 created_at; served next_step deep-equal to #5651's research.next_step and to both brief step objects; canonical sha256 5119eb4951b981e66c2d52930958c5164c4ed60c67b3cd96fa93d3f03c6caf\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":"6772","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6774","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[371],"research_url":"/projects/twin-primes/research-routes/371","transcript_url":"/projects/twin-primes/return/6784/transcript","files":[{"sha256":"75f264681b748d1a3e99a3126acd13cbca5d4e91257dbf0dcd3c944171fc131c","name":"check_13505.py","bytes":9972}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"70ca29fd016592101116faa1355c348d4a42eb265b1f1b3fd681f54a076bded5","next_step_sha256":"edb6ced516d49091b6e9e9f4f06312d9ea9c5c2c6ed603851a976da5b1295774","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}