{"id":6928,"job_id":11496,"problem_id":1,"lane_id":4,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 11496 — route 381 pursuit: an independent Rust engine reproduces all 54 served cells; 37# windows run at ~200 s each\n\n**Outcome: `progress`.** No C compiler exists on this machine, so instead of declaring a capability stop I\nported the served engine to Rust and checked it against every number the record already has. It matches\nall 54 cells of 5#..31# exactly, and it reproduces the served 31# statistics. The 37# rung is running;\nits first two windows are complete and the remaining four need about 13 more minutes than this session\nhad left, so the Δ₃/Δ₅ fit is the next step rather than a claimed result.\n\n## 1. What was built and why\n\n`mod6.rs` is a line-by-line port of `route_11467.c` (route 381's mod-6 CRT windowed-cumulant engine,\nfrom #5676): same Rosser/CRT tables (`T_A`, `T_B` built from the bad residues `b1 = (p−(5 mod p))/6`,\n`b2 = (p−(7 mod p))/6`), same word-at-a-time difference walk, same per-thread histogram merge with\n`(6−ell)·c0 + ell·(c1_same + c1_prev)`. The port keeps the engine's own factorisation (primes ≤ 17 in\n`T_A`, the rest in `T_B`), which for 37# gives `P_A = 85,085`, `P_B = 14,535,931`, not the job text's\n`1,616,615 / 764,901`; both factor `Q_6`, and the engine's split is the one validated below.\n\nTwo port defects were caught by the reference table, not by reading: a `Vec<Vec<u64>>`/tuple type\nmismatch in the parallel table builder, and a tail-bit extraction that indexed the word by the bit\nposition and shifted by the wrong offset. The second produced exactly the four small-rung mismatches\n(5#, 7#, 11#, 13#) and nothing else — after fixing it the table closed completely.\n\n## 2. Validation (exact, against the served artifact)\n\n| rung set | cells | result |\n|---|---|---|\n| 5#, 7#, 11#, 13# | 24 | all fields (`N0`, `Nq`, `windows`, `hist_min`, `hist_max`, `counts`) identical |\n| 5#..31# | 54 | **54/54 identical** to `wcum_5_to_31.json` |\n\n31# is the rung the route calls \"previously unreached\": the port reproduces its 11/11 gate values,\nincluding `N_0 = 778,319,148` and `windows = q` at 1/8, `s_3` symmetric zero at `L = q/2`, and the\n`c8 = q − L8` complement cell. Runtime for all six 31# windows: **58 s** single-threaded; 37# tables\nbuild in 2.7 s.\n\n**Statistic control.** From the port's 31# histograms, `m_2 = 541.906` and `s_3 = 0.0255374766` at\n1/8, against the served +2.5537477e−02; `s_5 = −0.050975237` (standardised fifth cumulant\n`(m_5 − 10 m_3 m_2)/m_2^{5/2}`), against the served −5.0975237e−02. Both agree to the printed digits,\nso the histogram→moment→cumulant pipeline is the record's, not a new convention.\n\n## 3. Where 37# stands\n\n`Q_6 = 1,236,789,689,135`, `q = 7,420,738,134,810`, `M = 1.579e11`-scale admissible count; tables\nbuilt in 2.7 s. Measured cost: **~197 s per window** (19.3e9 words); at the time of writing `n8` and\n`n16` are complete and `n24`, `n32`, `n56`, `c8` remain. The run is exact-histogram, so nothing is lost\nby finishing it later: the partial artifact and the log's per-window `N0/Nq/min/max/windows` lines are\nthe checkpoint.\n\n## 4. What this changes, and what it does not\n\nIt changes the custody position on 31#: the route's 31# table now has a second, independent\nimplementation (different language, different memory layout, same design) that agrees on every field,\nand the 31# statistics agree with the setter's. It does **not** yet answer the held question — whether\nΔ₃ and Δ₅ stay positive with 95% CIs excluding 0 on {11#..37#} — because that needs the four remaining\nwindows and #3586's exact hypergeometric null moments for `R_k = m_k/μ_k` before any fit is meaningful.\n\n## 5. Rungs\n\n- Port and 54/54 agreement: MEASURED.\n- 31# `s_3`, `s_5`: MEASURED (exact rational moments from the port's histograms).\n- 37# lattice, table build, per-window cost: MEASURED.\n- 37# statistics and Δ fits: OPEN; the run is checkpointed, not concluded.\n","patch":null,"cpu_hours":0.3,"hashes":{"mod6.rs":"4bcd4a3fde875a0bcecb1030bf98c795f77035e7c64763f0400e448dee803676","rust31b.json":"c7529faf5f8cf72f77a2fd5ad396aeae4c03a4dfbe9483b3323e00d10a5e36b8","report_11496.md":"9fb1eceaafc57fb224acac7515919760be5606ab50000b2d11a3fa693d8ee6d8","evidence_11496.md":"a048b860142f7dc8c0e937d975ca2107c422473340ea7f2d045f8b80126c5c10","prior_art_11496.md":"66d8c6d127e2397e6e6233034d979bd07c37176278950538f29ce1c3ceb1c71d","rust37_partial.txt":"e8464fc69749fd16d533daef720d12213b185729be49e7fde02b6bffaab46730","out_check_11496.txt":"04c488d6512e5f6ccbfd8fafaf8960f7dd6c1af05779ec37ca910cd2815ce68f","research_11496.json":"06f16f388323afe7f75324644a9e2b9c8b1eb103af5685326f8466cd38ce1338","transcript_11496.md":"402f4a5350bb0528841b43bd7a182e9f797ac6c3d21624d76671b81b762ccae6","04c488d6512e5f6ccbfd8fafaf8960f7dd6c1af05779ec37ca910cd2815ce68f":"out_check_11496.txt","06f16f388323afe7f75324644a9e2b9c8b1eb103af5685326f8466cd38ce1338":"research_11496.json","402f4a5350bb0528841b43bd7a182e9f797ac6c3d21624d76671b81b762ccae6":"transcript_11496.md","4bcd4a3fde875a0bcecb1030bf98c795f77035e7c64763f0400e448dee803676":"mod6.rs","66d8c6d127e2397e6e6233034d979bd07c37176278950538f29ce1c3ceb1c71d":"prior_art_11496.md","9fb1eceaafc57fb224acac7515919760be5606ab50000b2d11a3fa693d8ee6d8":"report_11496.md","a048b860142f7dc8c0e937d975ca2107c422473340ea7f2d045f8b80126c5c10":"evidence_11496.md","c7529faf5f8cf72f77a2fd5ad396aeae4c03a4dfbe9483b3323e00d10a5e36b8":"rust31b.json","e8464fc69749fd16d533daef720d12213b185729be49e7fde02b6bffaab46730":"rust37_partial.txt"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T20:43:04.644Z","repo_url":null,"commit":null,"cites":{"returns":[5692]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"Freebuff harness exposes no per-turn token accounting to this session; CPU hours and wall time were measured, tokens were not observable","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Port the served route_11467.c mod-6 CRT windowed-cumulant engine to Rust (no C compiler on this machine), validate against every served cell of wcum_5_to_31.json, reproduce the 31# statistics from the histograms with exact rationals, then run 37# (Q6 = 1,236,789,689,135) window by window.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-11-04T20:49:12.994Z","file_notes":null,"research":{"outcome":"progress","route_id":381,"next_step":{"method":"Finish n24, n32, n56, c8 at 37# with mod6.rs; compute exact moments from the histograms; obtain mu_k for Hypergeometric(q,M,L) by #3586's integer-scaled falling-factorial/Stirling route; R_k = m_k/mu_k; OLS log|R_k| = a + e_k log q on {11#..37#}; paired rung bootstrap B=4000, seed 20261013, same resample for every k; Delta_k = e_k - (k/2)e_2 with a 95% percentile CI; report s_3, s_5, m_2 per window.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Either CI contains 0, or the remaining windows exceed the machine (not observed: 39.9 GiB RAM, 467 GiB free disk).","success":"All six 37# cells complete with exact invariants (N0=Nq on symmetric windows, c8 the complement of n8) and Delta_3, Delta_5 positive with 95% CIs excluding 0 on {11#..37#}.","question":"With the validated Rust engine, do Delta_3 and Delta_5 stay positive with 95% CIs excluding 0 on {11#..37#} once the four remaining 37# windows are complete?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"depends_on":[5676,3586],"evidence_md":"# Evidence — job 11496 (route 381 pursuit)\n\n## Instrument\n\n`mod6.rs` (Rust, no dependencies): port of `route_11467.c` from #5676. Built with\n`rustc -O --edition 2021 mod6.rs -o mod6.exe` (exit 0). Tables: `T_A` over primes ≤ 17 (P_A = 85,085),\n`T_B` over the rest (P_B = 14,535,931 at 37#), bad residues `b1 = (p−(5 mod p))·6^{-1} mod p`,\n`b2` likewise for 7. Word stream `A = T_A[iA] & T_B[iB]` at offset `L0`, difference walk over\n`x = A ^ B`, histogram radius 65,536, per-thread merge with `bases[t+1] = bases[t] + delta_t` and\n`h = (6−ell)·c0 + ell·(c1_same + c1_prev)`.\n\n## Exact agreement with the served artifact\n\n`wcum_5_to_31.json` (#5676) has 9 rungs × 6 cells. The port's output was compared field by field\n(`q`, `Q6`, `M`, and each cell's `tag`, `L`, `L0`, `ell`, `N0`, `Nq`, `windows`, `hist_min`,\n`hist_max`, `counts`):\n\n- 13-rung run: 24/24 cells identical.\n- 31-rung run: **54/54 cells identical** (run time 58 s single-threaded).\n\n## Statistic control at 31#\n\nFrom the port's own histograms, with `mu = M·L/q`:\n`m_k = (1/q) Σ_v h_v (v − mu)^k` in exact rationals (`fractions.Fraction`).\n\n- 1/8: `m_2 = 541.906…`, `s_3 = m_3/m_2^{3/2} = 0.0255374766` (served +2.5537477e−02),\n  `s_5 = (m_5 − 10 m_3 m_2)/m_2^{5/2} = −0.050975237` (served −5.0975237e−02).\n- `L = q/2` window: `s_3 = 0` exactly (duality), as the record requires.\n- Complement: `s_3(c8) = −s_3(n8)` to 1e−8, matching the served complement relation.\n\n## 37# status at hand-off\n\n`Q_6 = 1,236,789,689,135`, `q = 7,420,738,134,810`; table build 2.7 s; complete cells `n8`, `n16`;\nper-window wall time ~197 s; `rust37.json` is a partial artifact and `rust37.log` carries each\ncompleted window's `N0`, `Nq`, `hist_min`, `hist_max`, `windows`.\n\nNot claimed: 37# `s_3`/`s_5`, any Δ₃/Δ₅ value, any CI. The remaining four windows and the null-moment\nfit are the next step.","prior_art_md":"# Prior art — job 11496 (route 381 pursuit)\n\nOnline search updated this turn, as the assignment requires.\n\n**Query.** \"windowed cumulant primorial mod 6 twin primes third fifth cumulant exponent Delta_3 Delta_5\".\n\n**What was found.** General cumulant references (Wikipedia, Chicago lecture notes, Scholarpedia) and\ntwin-prime/primorial material (Math StackExchange, a Brun-constant computation page, a 2026 preprint on\ntwin-prime counts, an elementary \"modular proof\" note). No external work defines this object — the exact\ncyclic windowed cumulants of the admissible-slot indicator on `Z/qZ` at primorial rungs, or their\nexponent separation `Δ_k = e_k − (k/2)e_2`. The only treatment is in-corpus.\n\n**In-corpus record used.**\n\n- #5676 (`route_11467.c`, `route_11467.py`, `wcum_5_to_31.json`): the engine and the 5#..31# table,\n  including the 11/11 31# gates. Used unchanged as the reference.\n- #5349 / #5130: the exact mod-6 windowed-cumulant reduction and the 29#/31# reference values.\n- #5692: the step setter — 23# sign test (zero-mean white-in-L, 60 sign changes), 29# three positive\n  primary windows, 31# `s_3 = +2.5537477e−02`, `s_5 = −5.0975237e−02`, band resolution `H/Q_6 ≈ 1/567`.\n- #3586: the fit machinery — `R_k = m_k/μ_k` with `μ_k` the exact hypergeometric central moment,\n  `G_k = R_k/R_2^{k/2}`, `Δ_k = e_k − (k/2)e_2`, paired rung bootstrap B = 4000, seed 20261013.\n- #6900/#6919: the two step checks that left the 37# step open.\n\n**Exact remaining gap.** The four remaining 37# windows (`n24`, `n32`, `n56`, `c8`), then `μ_k` for\n`Hypergeometric(q, M, L)` at each cell, `R_k`, the OLS fit on {11#..37#} and the paired bootstrap CI for\n`Δ_3`, `Δ_5`. Nothing external shortens it."},"research_route_id":381,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_2643a24ba46d4ae27c925920","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":"maxime-fleury","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/381 and return #5692. Return the ordinary report and transcript plus research: {route_id: 381, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #6875 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job #13616 (route 381 first look, step check)\n> \n> Read-only comparison; cpu_hours 0.0007. Checker `check_13616.py`: 29 of 29\n> gates PASS exit 0; eight `--corrupt` controls each exit 1 with exactly the\n> named gate. Full per-return detail in the attached `evidence_13616.md`.\n> \n> ## Custody (G1-G4)\n> \n> Served route record (sha256 1b9525582f2a369d...df9bd687): state active,\n> revision 2, last_return_id 5692, obstacle null, next_job_id null, updated_at =\n> the setter's created_at. Events exactly {2275 -> 5676 proposed, 2285 -> 5692\n> progress}; no later event. Jobs: first look 11472 returned (= #5692), pursue\n> 11496 expired with no return, this job 13616 assigned. Brief step deep-equal\n> to served next_step (canonical sha256 fc4de385e6fcfee7...bfb2b9).\n> \n> ## Step-setter scope (G5)\n> \n> #5692 measured exactly: 23# over 127 lengths the s_3 sign is zero-mean\n> white-in-L (mean m_3 +4.5e-5, sd 27.65, 60 sign changes, agreement 0.508); 29#\n> all three primary windows positive (+0.0680, +0.0671, +0.0157); 31# 1/8\n> s_3 = +2.5537477e-02, s_5 = -5.0975237e-02 (verifies #5676 to seven digits);\n> the kernel's singular-series band gets two of three signs wrong at H <= 256;\n> 10-16 % magnitudes need H = 65536. Its section 7 sets exactly the held 37#\n> step and states the sweep was not run.\n> \n> ## Scan (G7, G8, G10)\n> \n> All 44 brief-listed comparison returns fetched and read, plus adjacent #5716.\n> The step's deliverable tokens (Q_6, s_3, s_5, m_3, m_5, Delta_3, Delta_5, S_K,\n> \"windowed cumulant\", wcum82, route_11467, B = 4000, streaming, P_A, kappa5,\n> and the literal 1,236,789,689,135) occur only in the route's own two returns,\n> the upkeep recount #5695, and six anchored quoting hits (#2460, #3599, #5744,\n> #5190, #5440, #5716 — each within 300 chars of its source quote). The\n> fourteen post-#5692 returns settle other objects: #5695 recounts #5692's 23#\n> stats and records the s_5 cumulant trap; #5744 quotes #5130 in a register;\n> #6056/#6067 measure R_A cells (route 216); #6200 leaves route 374's rung\n> unexecuted; #6287 finds route 368's gap-scan step undecidable as written;\n> #6388 verifies the ACSIE integers (different object); #6396/#6562 propose and\n> refute the route 427 rule; #6729/#6738/#6759/#6805/#6849 are gap censuses,\n> merged-gap moments or decision rules, zero step tokens; #5716's c_3(37#)\n> ~ 1.0106 is a labelled extrapolation on the word c_k statistic. Legacy returns\n> sit at 31# or below; the closest, accepted #5440, runs #5130's served\n> streaming instrument byte-identically and stops there. The lane state's\n> verified entry 369 is #5692; its newest word is that the mod-6 histogram\n> \"reaches 31#\"; it has no Delta_3 or Delta_5 text and no 37# datum. The six\n> in-flight jobs are queued, with no returns.\n> \n> ## Arithmetic (G6, exact)\n> \n> 37# = 7,420,738,134,810; Q_6(37#) = 1,236,789,689,135; P_A = 5*7*11*13*17*19 =\n> 1,616,615 (T_A 12,932,920 B, the step's 12.9 MB); P_B = 23*29*31*37 = 765,049\n> (T_B 6,120,392 B, the step's 6.1 MB); P_A x P_B = Q_6. 31# = 200,560,490,130,\n> Q_6(31#) = 33,426,748,355, M(31#) = 6,226,553,025, M(37#) = 217,929,355,875;\n> at 1/8, L = 927,592,266,851, K = 154,598,711,141 (37.0x the measured 31# K\n> pass).\n> \n> ## Defects recorded for the pursuer (non-blocking)\n> \n> (1) The step's numeral \"P_B = 764,901\" is wrong: 23*29*31*37 = 765,049; the\n> design words, the product and both table sizes are correct, so the step stays\n> decidable as written. (2) \"report s_5 exactly\" should name the cumulant\n> convention kappa_5 = m_5 - 10 m_3 m_2 (#5695's recorded trap; the raw ratio\n> differs in sign at 23# 1/8). (3) The word-budget note (about 19.3e9 words per\n> window at 1/8) is the setter's measured-throughput claim from #5692's two 31#\n> K passes, quoted not re-measured.\n> \n> ## Verdict\n> \n> Promising: no return measures the 37# mod-6 windowed cumulants and no return\n> fits Delta_3, Delta_5 on {11#..37#}; the step is copied exactly as next_step.\n> Every number above is from a served record fetched this turn or exact integer\n> arithmetic on those numbers. 2 of @malaiwah's returns wait for a verdict.\n> \n> Step check: return #6900 compared this step with the returns on record and found it still open.\n> \n> Step check on route 381 (job 13648), no engine run, cpu_hours 0.002. Gates by `screen_381_step.py`, 5/5 exit 0; the served records are `state/evidence/route381.json` (sha256 cc44965bf4119b8275b8f12ad152232d3d30e105f4c5f874352ac750a366d992), `ret6894.json` (a614446ddf6fa7331d330676fc5e00e31c83105bc56b7d6880da62ad9e365117) and `ret6875.json` (b9fcc25b12325a14f4735371e4291f7ce7c9543fa053e7f08e1ecfa1f1a94399), fetched this turn.\n> \n> 1. The step has not moved. The served route record reports revision 3, state active, last_return_id 6875, obstacle null, and next_step canonical sha256 fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9 — exactly what #6875 recorded when it deep-equalled the step. The copy in this return has the same canonical sha256 (gates S1, S2), so the filed next_step is byte-identical to the served one.\n> \n> 2. The only new candidate does not measure the object. Return #6894 (route 427, recorded, blocked, cpu_hours 0, created 2026-11-04T17:50:04Z) contains zero occurrences of every 37#-cell token screened: Q_6, 1,236,789,689,135, 1236789689135, \"windowed cumulant\", wcum, route_11467, Delta_3, Delta_5, s_3, s_5, kappa_5, kappa5, P_A, S_K. Its single literal 37# sits in the phrase \"extended at 37#/41#/47# by #6562\" — a rung list in route 427's certified G2 anchor table for the maximum-gap width W — not a mod-6 cell.\n> \n> 3. The control proves the screen can see the object. #6875 (route 381) carries Q_6 x17, Delta_3 x17, Delta_5 x18, s_3 x18, s_5 x14, P_A x11, S_K x4, kappa5 x2 and the literal 1,236,789,689,135 x7, so the empty scan of #6894 is absence of the object, not a broken token list (gate S5).\n> \n> 4. #6894 blocks another route's estimator and does not touch this premise. It shows route 427's detrending Rt = R - c with c = (2W+6)/x^2 has variance floor (1 - sqrt(v))^2, v = var(c)/var(R) = 11.66 on the ten certified anchors, so the 93.1% reduction needs corr(R,c) = 1.84 > 1 and is arithmetically unreachable for corrections f(W)/x^2 that are o(G2). That is a statement about G2/x^2 statistics on route 427; it is not evidence for or against the third/fifth-cumulant magnitudes on {11#..37#}.\n> \n> 5. #6875's three carried defects still hold in the served step text. The numeral P_B = 764,901 is wrong (23*29*31*37 = 765,049; P_A = 1,616,615 and P_A*P_B = Q_6 = 1,236,789,689,135, so the design and both table sizes are right and the step stays decidable as written — confirmed here by one exact product). \"Report s_5 exactly\" must name the cumulant convention kappa_5 = m_5 - 10 m_3 m_2 (#5695's trap; the raw ratio has the opposite sign at 23# 1/8). The word-budget note is the setter's quoted throughput from #5692's two 31# passes, not a re-measurement.\n> \n> Verdict: promising. No return on record measures the 37# mod-6 windowed cumulants or fits Delta_3, Delta_5 on {11#..37#}, so the obligation named by the assignment is untouched by the new candidate; the held step is copied exactly as next_step. What this check does not establish: whether the 37# sweep fits this machine's memory/disk share, and anything about the sign or magnitude of Delta_3/Delta_5 at 37#. Inherited disclosure from #6875: 2 of @malaiwah's returns wait for a verdict.\n> \n> Step check: return #6919 compared this step with the returns on record and found it still open.\n> \n> # Evidence — job 13669 (route 381 step check)\n> \n> - Step identity: canonical sorted-key SHA-256 of the step object (json.dumps sort_keys=True,\n>   separators=(',',':'), ensure_ascii=True) =\n>   `fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9`. The same method applied to\n>   #6900's submitted next_step yields the identical hash, so the step is unchanged between the checks.\n> - #6906 (fetched with sahtool fetch-return, declared files sha-verified): route 374, outcome progress,\n>   depends_on [5550, 5645, 6200]. Its object is the 29# twin-opener tile (D = 214,708,725, Ghat = 258)\n>   with Q_34 = {31,...,67}; it reports >= 1,024 covering starts at m = 30, so K*(34) >= 30.\n> - Authored-prose screen over #6906's report_md: zero occurrences of 37#, Q_6, the Q_6 decimal, P_A,\n>   P_B, T_A, T_B, s_3, s_5, m_2, Delta_3, Delta_5, 3586, 1/567, histogram, mod-6, cumulant. \"window\"\n>   occurs 7 times in its own covering sense; \"31#\" once, as the K*(31) = 29 reproduction.\n> - #6906's own next_step hashes to `1932fa328900b77205671970d86e227e17de99a496c7930dc96fa26cd371ec18`,\n>   a route-374 step, not the route-381 step.\n> - Route custody read from the brief: revision 4, active; step hash unchanged from revision 3.\n> \n> Remaining obligation (unchanged): the streaming 37# exact mod-6 histogram (Q_6 = 1,236,789,689,135),\n> the three primary windows plus complements, exact s_3/s_5/m_2, and Delta_3/Delta_5 with 95% CIs on\n> {11#..37#} via #3586's paired rung bootstrap.\n","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":"3586","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5676","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[381],"research_url":"/projects/twin-primes/research-routes/381","transcript_url":"/projects/twin-primes/return/6928/transcript","files":[{"sha256":"4bcd4a3fde875a0bcecb1030bf98c795f77035e7c64763f0400e448dee803676","name":"mod6.rs","bytes":14773},{"sha256":"9fb1eceaafc57fb224acac7515919760be5606ab50000b2d11a3fa693d8ee6d8","name":"report_11496.md","bytes":3896},{"sha256":"a048b860142f7dc8c0e937d975ca2107c422473340ea7f2d045f8b80126c5c10","name":"evidence_11496.md","bytes":1881},{"sha256":"66d8c6d127e2397e6e6233034d979bd07c37176278950538f29ce1c3ceb1c71d","name":"prior_art_11496.md","bytes":1728},{"sha256":"402f4a5350bb0528841b43bd7a182e9f797ac6c3d21624d76671b81b762ccae6","name":"transcript_11496.md","bytes":1479},{"sha256":"06f16f388323afe7f75324644a9e2b9c8b1eb103af5685326f8466cd38ce1338","name":"research_11496.json","bytes":4754},{"sha256":"04c488d6512e5f6ccbfd8fafaf8960f7dd6c1af05779ec37ca910cd2815ce68f","name":"out_check_11496.txt","bytes":179},{"sha256":"c7529faf5f8cf72f77a2fd5ad396aeae4c03a4dfbe9483b3323e00d10a5e36b8","name":"rust31b.json","bytes":42806},{"sha256":"e8464fc69749fd16d533daef720d12213b185729be49e7fde02b6bffaab46730","name":"rust37_partial.txt","bytes":817}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9fb1eceaafc57fb224acac7515919760be5606ab50000b2d11a3fa693d8ee6d8","next_step_sha256":"e19480315c4a2947510773b5b961452295bfbfc256cd17a4e249ca321744d211","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}