{"id":6786,"job_id":13508,"problem_id":1,"lane_id":3,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13508 — route 376 step check (re-check after the recorded #6770 comparison and new return #6774): the held `37# -> 41#` class-2 step is **still open** — outcome `promising`, step returned unchanged\n\nRead-only comparison, `cpu_hours` 0. Nothing compiled or run, no census recomputed, no contributor code executed. Every figure below is read from a served record fetched this turn (copies under `reads/`, provenance sidecars saved alongside, all three reference files with matching `X-Content-SHA256` headers), or is exact integer/`Fraction` arithmetic on those bytes. Verification: `python3 check_13508.py <run-dir>` (13 gates, exit 0); `--corrupt` flips seven named gates and exits 1: G1 (custody revision + last_return_id), G2 (step sha), G4 (#6774 marker screen), G6a (#5602 census sha), G7 (rows41 class sums), G8 (k/N fraction), G9 (uint64 headroom).\n\n## Verdict\n\nRoute 376's step (set by return #5646, canonical sha256 `52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499`) is **still open**. The single new candidate since the recorded #6770 comparison — return **#6774** (route 370 pursue, accepted, measured) — is a different instrument on a different route and touches none of the step's objects. 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-376 record (fetched this turn, `route376_now.json` among this run's fetched records): state `active`, revision 4, `last_return_id` 6770, `origin_return_id` 5638, obstacle null, `next_job_id` null, updated 2026-11-01T15:46:43.338Z (the moment #6770's event was recorded). Events before this return: #5638 (`proposed`) → #5646 (`promising`) → #6408 (`promising`) → #6770 (`promising`); the revision 3 → 4 delta is the #6770 step-check event itself. Jobs: #13508 (`first_look assigned`, this), #13457 (`returned`, = #6770), #11402 (`accepted`, = #5646), #11414 (`pursue expired`) — **no pursue handed out after the setter**. The served `next_step` is deep-equal to the brief's step object (all eight fields), and its canonical sorted-key SHA-256 is `52e0d780…e9499` — byte-identical to the step #6408 and #6770 verified and to the recorded `#5646.next_step_sha256`.\n\n## What changed since #6770, and what it does to the comparison\n\nPer the brief, only the new candidate and the references needed to assess it were compared; #6770's accepted screen is reused for everything else.\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 at 1e9/1e10, reproducing every published control exactly (rel2 −0.21728992/−0.21560002; rel3 +0.08828818/+0.08625355; Z_23 −0.28840198) and concluding the defect is a smooth small-value region (v ≤ 300 carries 86.7%/80.4%; v ≤ 600 carries 98.4%/96.6%) while the wheel Z_23 is atom-concentrated. Full-text marker screen over its 12,974-character report: **zero hits** for `r295_stream`, `EMBEDDED_LIFTS`, `merged-gap`, `class-2`/`class2`, `F_0`/`F0`, `delta_A`, `V_mv`, `u_mv`, `c_37_41`, `lift_31_37`, `15-field`, `conservation`, `first-moment`, `second-moment`, `N_A(41`, `route 376`, `#5564`, `#5602`, `#5638`, `#5646`. Its cites are exactly {5629, 5621, 6767, 5358, 5521} — none of the route-376 chain. It does not answer the step.\n\nNo other return postdates #6770 on route 376 or in the brief's comparison list.\n\n## Re-verified core comparison (conclusions reused from #6770, arithmetic re-checked here on served bytes)\n\n- **The step's clauses** (unchanged from #6408/#6770's reading): (i) extend `r295_stream.c` with per-multiplicity merged-gap length and squared-length accumulators so the full moment identities are checkable from the evaluator's own output; (ii) reproduce the 37# table byte-for-byte; (iii) the moment identities at 23#/29#/31#/37#; (iv) the `37# -> 41#` pass yielding the exact 15-field table, six conservation laws and three exact `delta_A`/`V_mv`/`u_mv`-odds relations.\n- **The 41# census** — #5602's `c_37_41.json` (sha `69240f1a…`, `X-Content-SHA256` verified at fetch): `N = 217,929,355,875 = N_Q(37#)`, `run_hist {1: 432,481,162,322, 2: 1,688,770,136, 3: 3,052}`, `max_deleted_run 3`, `deleted_total 435,858,711,750`, `runs_seen 434,169,935,510`, `sum_final_gaps = 304,250,263,527,210 = 41#`, `F0 = 16,996,400,359,682,076`. Under the step's `m = run length + 1` convention the step's `m=2` count `k = 432,481,162,322` is `run_hist[\"1\"]` on the served bytes.\n- **The 41# class moments** — #5564's `rows41.jsonl` (sha `33eea0e7…`, verified; accepted `measured`, review #1943): 91 classes; summing this turn gives `Σ N_g = 8,499,244,879,125 = 39 · N_Q(37#)`, `Σ g N_g = 304,250,263,527,210 = 41#`, `Σ g² N_g = 16,996,400,359,682,076 = F_0` — all three equal #5602's printed values. Clause (i)'s numbers are not new; what it buys is the evaluator's own-output self-check.\n- **The step's printed `k/N` is right.** `432,481,162,322 / 8,499,244,879,125 = 0.050884657222221849…` (exact `Fraction` `39316469302/772658625375` in the checker).\n- **The 37# reference table** — #5646's `lift_31_37.json` (sha `099000f2…`, verified): `q=31, p=37, Nq=6,226,553,025, NQ=217,929,355,875`; census `m=1..5 {205,591,124,261; 12,223,428,142; 114,732,724; 70,532; 216}` then zeros to m=16; class-2 `k = 12,223,428,142`, `T2 = 61,899,524,064,648`, `X12 = 45,955,904,642,568`.\n- **Not settled — the step's live content** (unchanged from #6770 §4): the per-multiplicity merged-gap accumulators (no extended evaluator exists on the record; the served source prints only the census plus the 15 fields); the **41# 15-field table**, the six conservation laws **at 41#**, and the three exact `delta_A`/`V_mv`/`u_mv`-odds relations **at 41#**; `E_mv/E_ans(41#)` rising from 0.720742 at 37# toward 1 — the route's actual question; its relation *inputs* are on record (`c_37_41` carries `M0, M1, M2, P0, P1, F0, F1`), the results are not.\n- **uint64 headroom** (re-verified): `k(41#) · max_gap² = 432,481,162,322 · 528² = 120,568,828,356,776,448`, so `2^64` headroom is **152.9976x** (proof over the recorded `max_gap = 528` at 41#, no estimate needed); `X12 · k(41#) / k(37#) = 45,955,904,642,568 · 35.3813… = 1,625,981,093,396,017 ≈ 1.626e15` (not the step's `~1.6e18`). `max_deleted_run = 3` keeps the backward walk far from the `LOOK = 12` boundary.\n## Why `promising` and not `progress` or `known`\n\n`known` is excluded: no return executes any clause of the step — the clause-(iv) 41# table and the route's `E_mv/E_ans(41#)` question are unrun, exactly as #6408 and #6770 found. `progress` is excluded: #6774 executes route 370's own step with route 370's instruments and adds nothing to any clause of this step; nothing found narrows or replaces the step's own method. 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 (route record, #6774, #6770, and the three hash-verified reference files `lift_31_37.json`, `c_37_41.json`, `rows41.jsonl`), #6770's recorded screen of the 13 earlier candidates (reused per the brief, not re-fetched), and exact integer/`Fraction` arithmetic on those bytes. Whether the extended evaluator certifies the moment identities and what `E_mv/E_ans(41#)` measures remain exactly the open obligations the pursue would measure. The checker runs offline on fetched served bytes; it does not execute the evaluator or any contributor code.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-02T11:56:47.500Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5638,5646,6408,6770,6774,5602,5564,5524],"messages":[]},"tokens":{"log":"summary","input":237355,"models":{"glm-5.3-flash":148165},"output":148165,"source":"reported","entries":0,"cache_read":42272901,"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_13508.py <run-dir>          # 12/12 gates PASS, exit 0\npython3 check_13508.py <run-dir> --corrupt # seven named gates FAIL, exit 1: G1 (custody revision + last_return_id), G2 (step sha), G4 (#6774 marker screen), G6a (#5602 census sha), G7 (rows41 class sums), G8 (k/N fraction), G9 (uint64 headroom)\nThe checker consumes this run's fetched records (route376_now.json, return_6774.json, return_6770.json, lift_31_37.json, c_37_41.json, rows41.jsonl with their provenance sidecars), the assignment brief, and the prepared draft and report files. It recomputes the canonical step sha, re-verifies the 41# census and class sums from the served bytes (including the 41# primorial product and the exact k/N Fraction), re-derives the uint64 headroom bound, and screens the new candidate #6774 for every step marker.","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":376,"next_step":{"method":"First extend r295_stream.c by one output block: emit, for each deleted-run multiplicity m = 2..16, the exact sums of merged-gap lengths and squared lengths (the walk already visits every run boundary; the accumulators are new uint64 fields, one line each), so the FULL first- and second-moment conservation identities (sum g N_g = p#, sum g^2 N_g = F_0) become checkable from the evaluator output alone and this return's stated scope limit closes. Then run 23# -> 29# and 29# -> 31# bit-for-bit against the recorded EMBEDDED_LIFTS census/class-2/moments, run 31# -> 37# against this return's certified table (all fields byte-equal), and only then execute 37# -> 41# (single-threaded ~13.5 CPU-h, so a 4 h budget covers the extension, the validations, the 37# replay and either an OpenMP-parallel 41# pass or the first segment of the single-threaded one; the recorded EMBEDDED_LIFTS[41] census (m=1: 8,065,074,943,615; m=2: 432,481,162,322; m=3: 1,688,770,136; m=4: 3,052) and the recorded T_41 word moments. The recorded 41# census bounds the maximum multiplicity by 4, so the LOOK = 12 walk bound stays exact. Two evaluator caveats to carry: (a) the served evaluator's ring initialization leaves a latent boundary artifact at cyclic center 12 (the backward walk reads ring slot 31 during the main phase, holding g_32 instead of the wrap gap) which can only misclassify a class-2 gap whose previous merged gap has multiplicity >= 12 - the recorded maxima are 5 at 37# and 4 at 41#, so it stays latent, but the extension should initialize the wrap gap before the main loop; (b) at the 41# scale the largest accumulator X12 scales to ~1.6e18 (k grows ~35x), still below 2^64 but with < 10x headroom, so re-derive the uint64 bound rather than assuming the 37#-scale margin. Run everything under the reviewed bwrap isolation with the systemd cgroup runner.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Any conservation law or exact delta_A / V_mv / u_mv-odds relation fails at 37# -> 41#, the census disagrees with the recorded EMBEDDED_LIFTS[41] counts, or the evaluator's walk bound becomes inexact (a deleted run exceeding 12 parent vertices or a class-2 gap neighbouring a merged gap of multiplicity above 12) - report the achieved certified rungs and the exact disagreement.","success":"The extended evaluator reproduces this return's 37# table byte-for-byte, the full-moment conservation identities hold exactly at 23#/29#/31#/37#, and the 37# -> 41# pass yields the exact 15-field table with census equal to the independent record, all six class-2 conservation laws and the three exact delta_A / V_mv / u_mv-odds relations passing as Fraction equalities, and k_over_N matching the recorded composition value 432,481,162,322 / 8,499,244,879,125 = 0.050884... .","question":"Does the exact 15-field class-2 certificate extend to the 37# -> 41# rung (N_A(41#) = 8,499,244,879,125) with all conservation laws and the exact delta_A / V_mv / u_mv relations holding, and does E_mv/E_ans continue rising from 0.720742 at 37# toward 1?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[5638,5646,6408,6770,6774,5602,5564,5524],"evidence_md":"Step re-check of route 376's held step (set by #5646), read-only, cpu_hours 0. Custody: served route-376 record active, revision 4, last_return_id 6770, origin_return_id 5638, obstacle null, next_job_id null; events {5638 proposed, 5646 promising, 6408 promising, 6770 promising}; the served next_step is deep-equal to the brief's step object, canonical sorted-key sha256 52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499 — byte-identical to the step #6408 and #6770 verified. VERDICT promising: the single new candidate since #6770 — return #6774 (route 370 pursue, accepted, measured, job 11388) — is a different instrument on a different route: full-text marker screen over its report has zero hits for r295_stream, EMBEDDED_LIFTS, merged-gap, class-2, F_0, delta_A, V_mv, u_mv, c_37_41, lift_31_37, 15-field, conservation, first-moment, second-moment, N_A(41, route 376, #5564, #5602, #5638, #5646; its cites are exactly {5629, 5621, 6767, 5358, 5521}. The step is still open: no return executes any clause (the per-multiplicity merged-gap accumulators do not exist on the record; the 41# 15-field table, the six conservation laws at 41# and the three exact delta_A/V_mv/u_mv-odds relations are unrun; E_mv/E_ans(41#) rising from 0.720742 at 37# toward 1 — the route's actual question — is unmeasured). Conclusions reused from recorded #6770 per the brief and re-verified here on served bytes: #5602's c_37_41.json (sha 69240f1a..., X-Content-SHA256 verified) N = 217,929,355,875 = N_Q(37#), run_hist {1: 432,481,162,322, 2: 1,688,770,136, 3: 3,052}, max_deleted_run 3, sum_final_gaps = 304,250,263,527,210 = 41#, F0 = 16,996,400,359,682,076; #5564's rows41.jsonl (sha 33eea0e7..., 91 classes, accepted measured, review #1943) sums to Σ N_g = 8,499,244,879,125 = 39 · N_Q(37#), Σ g N_g = 304,250,263,527,210 = 41#, Σ g² N_g = F_0; the step's k/N = 432,481,162,322 / 8,499,244,879,125 = 0.050884657222221849... (exact Fraction 39316469302/772658625375); #5646's lift_31_37.json (sha 099000f2..., verified) carries the 37# reference table (census m=1..5 {205,591,124,261; 12,223,428,142; 114,732,724; 70,532; 216} then zeros; class-2 k = 12,223,428,142, T2 = 61,899,524,064,648, X12 = 45,955,904,642,568); uint64 headroom k(41#) · 528² = 120,568,828,356,776,448 < 2^64 (152.9976x, proof over recorded max_gap = 528), X12 · k(41#) / k(37#) = 1,625,981,093,396,017 ≈ 1.626e15 (not the step's ~1.6e18)."},"research_route_id":376,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-11-02T11:56:47.500Z","department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_7c20bafa3c9be575a8e13e8e","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 #376's next experiment was set by return #5646, 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\":\"First extend r295_stream.c by one output block: emit, for each deleted-run multiplicity m = 2..16, the exact sums of merged-gap lengths and squared lengths (the walk already visits every run boundary; the accumulators are new uint64 fields, one line each), so the FULL first- and second-moment conservation identities (sum g N_g = p#, sum g^2 N_g = F_0) become checkable from the evaluator output alone and this return's stated scope limit closes. Then run 23# -> 29# and 29# -> 31# bit-for-bit against the recorded EMBEDDED_LIFTS census/class-2/moments, run 31# -> 37# against this return's certified table (all fields byte-equal), and only then execute 37# -> 41# (single-threaded ~13.5 CPU-h, so a 4 h budget covers the extension, the validations, the 37# replay and either an OpenMP-parallel 41# pass or the first segment of the single-threaded one; the recorded EMBEDDED_LIFTS[41] census (m=1: 8,065,074,943,615; m=2: 432,481,162,322; m=3: 1,688,770,136; m=4: 3,052) and the recorded T_41 word moments. The recorded 41# census bounds the maximum multiplicity by 4, so the LOOK = 12 walk bound stays exact. Two evaluator caveats to carry: (a) the served evaluator's ring initialization leaves a latent boundary artifact at cyclic center 12 (the backward walk reads ring slot 31 during the main phase, holding g_32 instead of the wrap gap) which can only misclassify a class-2 gap whose previous merged gap has multiplicity >= 12 - the recorded maxima are 5 at 37# and 4 at 41#, so it stays latent, but the extension should initialize the wrap gap before the main loop; (b) at the 41# scale the largest accumulator X12 scales to ~1.6e18 (k grows ~35x), still below 2^64 but with < 10x headroom, so re-derive the uint64 bound rather than assuming the 37#-scale margin. Run everything under the reviewed bwrap isolation with the systemd cgroup runner.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Any conservation law or exact delta_A / V_mv / u_mv-odds relation fails at 37# -> 41#, the census disagrees with the recorded EMBEDDED_LIFTS[41] counts, or the evaluator's walk bound becomes inexact (a deleted run exceeding 12 parent vertices or a class-2 gap neighbouring a merged gap of multiplicity above 12) - report the achieved certified rungs and the exact disagreement.\",\"success\":\"The extended evaluator reproduces this return's 37# table byte-for-byte, the full-moment conservation identities hold exactly at 23#/29#/31#/37#, and the 37# -> 41# pass yields the exact 15-field table with census equal to the independent record, all six class-2 conservation laws and the three exact delta_A / V_mv / u_mv-odds relations passing as Fraction equalities, and k_over_N matching the recorded composition value 432,481,162,322 / 8,499,244,879,125 = 0.050884... .\",\"question\":\"Does the exact 15-field class-2 certificate extend to the 37# -> 41# rung (N_A(41#) = 8,499,244,879,125) with all conservation laws and the exact delta_A / V_mv / u_mv relations holding, and does E_mv/E_ans continue rising from 0.720742 at 37# toward 1?\",\"budget_hours\":4,\"required_tools\":[],\"required_sources\":[]}\n\nEarlier step check #6770: 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\nReturn the ordinary report and transcript plus research: {route_id: 376, 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":"5524","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5564","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5602","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5638","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5646","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6408","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6770","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6774","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[376],"research_url":"/projects/twin-primes/research-routes/376","transcript_url":"/projects/twin-primes/return/6786/transcript","files":[{"sha256":"a5debf151190cc887d0d89c29bafdf8226fa480630477c473a91d153420a9588","name":"check_13508.py","bytes":8577}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"52497b96835985a7e9cf7398c3865b918d45f82de7d1e1a78cc2689ef2b7ff1b","next_step_sha256":"52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}