{"id":6875,"job_id":13616,"problem_id":1,"lane_id":4,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13616 — route 381 first look (step check): the 37# mod-6 windowed-cumulant step is unanswered on the record\n\nRead-only comparison; no experiment run and no published computation\nreproduced. Checker `check_13616.py` (Python 3 stdlib only): 29 of 29 gates\nPASS exit 0; eight `--corrupt` controls each exit 1 with exactly the named\ngate; suite cost 2.61 CPU-s. Full evidence, per-return table and arithmetic in\n`evidence_13616.md`; recipe with observed output hashes in the recipe field.\n\n**Custody (checker G1-G4).** Served route record: state `active`, revision 2,\n`last_return_id 5692`, obstacle null, `next_job_id` null, `updated_at` equal\nto the step-setter's `created_at` (route record sha256 1b9525582f2a369d...).\nEvents exactly {2275 -> 5676 proposed, 2285 -> 5692 progress}; no later event.\nRoute jobs: first look 11472 returned (= #5692), pursue 11496 expired with no\nreturn, this job 13616 assigned. The brief's step and the served `next_step`\nare deep-equal, canonical sha256\nfc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9.\n\n**What the step-setter settles (checker G5).** #5692 (recorded) measured, in\nexact rational arithmetic: at 23# over 127 lengths the sign of s_3 is a\nzero-mean, essentially white-in-L fluctuation (mean m_3 +4.5e-5 against sd\n27.65, 60 sign changes in 126 steps, adjacent sign agreement 0.508); at 29#\nall three primary windows are positive (s_3 = +0.0680, +0.0671, +0.0157); at\n31# the 1/8 window gives s_3 = +2.5537477e-02 and s_5 = -5.0975237e-02,\nverifying #5676's cell to seven digits with a different implementation; and\nthe 3-point Fourier resonance identity's band ladder at 23# shows the\nsingular-series band H <= 256 gets two of three primary-window signs wrong\nwhile all three need H ~ 4096 and 10-16 % magnitudes need H = 65536, about\nQ_6 over 567. Its section 7 sets exactly the held step: extend the engine to\n37# (Q_6 = 1,236,789,689,135) in a streaming word-table form, measure s_3,\ns_5, m_2 exactly at 1/8, 1/4, 3/8 plus complements, and fit Delta_3, Delta_5\non {11#..37#} by the paired-rung bootstrap of #3586 (B = 4000), without the\nthree-sign test.\n\n**The comparison (checker G7, G8, G10).** All 44 returns the brief lists were\nfetched this turn and read, plus the adjacent route-385 synthesis #5716 named\nby the lane state. The step's deliverable vocabulary (Q_6, s_3, s_5, m_3, m_5,\nDelta_3, Delta_5, S_K, \"windowed cumulant\", wcum82, route_11467, B = 4000,\nstreaming, P_A, kappa5, and the literal 1,236,789,689,135) occurs only in the\nroute's own two returns, the lane-upkeep recount #5695, and six anchored\nquoting hits (#2460, #3599, #5744, #5190, #5440, #5716 — each within 300\ncharacters of its source quote, verified). What the fourteen post-#5692\nreturns actually settle: #5695 recounts #5692's 23# statistics independently\nand records the s_5 cumulant trap; #5744 is a route-2 register table quoting\n#5130; #6056/#6067 (route 216) measure fixed-L R_A cells on a different\nstatistic; #6200 (route 374) leaves its s = 34 rung unexecuted; #6287 (route\n368) finds its 37# -> 41# gap-scan step not decidable as written; #6388\n(route 372) verifies the ACSIE integers S_3(R(37#)) and siblings from #5633 —\nmoments of a different object; #6396/#6562 (route 427) propose and then\nrefute the G2 descent rule; #6729 (route 92), #6738 (route 366, the\nG2(37#) = 528 gap-census record — its only \"s_3\" text is the substring of\n`chunks_37.bin`), #6759 (route 232, the K(h) rule at 29#), #6805 (route 371,\nspan-612 boundary windows) and #6849 (route 376, per-multiplicity merged-gap\nmoments m = 2..16 through 31# -> 37#) are all different functionals with zero\nstep tokens. #5716's c_3(37#) ~ 1.0106 is an explicitly labelled extrapolation\nabout the word block-local c_k statistic. The measure-lane state document's\nverified entry 369 is #5692 itself and the corpus summary's newest word on\nthis object is that the mod-6 histogram \"reaches 31#\"; the document contains\nno Delta_3 or Delta_5 text and no 37# windowed-cumulant datum. The six\nin-flight jobs in the brief are queued explorations with no returns.\n\n**Arithmetic on the step's constants (checker G6, exact).** 37# =\n7,420,738,134,810; Q_6(37#) = 1,236,789,689,135; P_A = 5*7*11*13*17*19 =\n1,616,615 with T_A = 12,932,920 bytes (the step's 12.9 MB); P_B = 23*29*31*37\n= 765,049 with T_B = 6,120,392 bytes (the step's 6.1 MB); P_A x P_B = Q_6.\n31# = 200,560,490,130, Q_6(31#) = 33,426,748,355, M(31#) = 6,226,553,025,\nM(37#) = 217,929,355,875; at 1/8, L = 927,592,266,851 and K = 154,598,711,141,\n37.0x the measured 31# K pass.\n\n**Defects found in the step text (non-blocking, recorded for the pursuer).**\n(1) The numeral \"P_B = 764,901\" is wrong: 23*29*31*37 = 765,049. The design\nwords, the product Q_6 and both table sizes are correct, so the step stays\ndecidable as written; a pursuer following the words computes the right split.\n(2) The step's \"report s_5 exactly\" should name its convention: #5695's\nrecorded caveat is that s_5 must be the cumulant kappa_5 = m_5 - 10 m_3 m_2,\nnot the raw fifth-moment ratio (the two differ in sign at 23# 1/8: -0.1317 raw\nvs +0.0372 cumulant). (3) The word-budget note (about 19.3e9 words per window\nat 1/8) is the setter's measured-throughput claim from #5692's two 31# K\npasses (802.6 s and 693.8 s), quoted and not re-measured here.\n\n**Verdict: promising.** The returns on record answer none of the step: no\nreturn measures the 37# mod-6 windowed cumulants and no return fits Delta_3,\nDelta_5 on {11#..37#}. The step is copied exactly as `next_step` and the held\npursuit goes out with this note.\n\nLimits: every rung number above is read from a served record fetched this turn\nor is exact integer arithmetic on those numbers. The route's own returns\n(#5676, #5692) and the 31# assembly (#5440) are recorded or accepted-but-finite\nmeasurements, not proofs, and none is scientific acceptance of this check.\nRung per claim: this report is a comparison verdict at rung `measured` only in\nthe sense that its checker execution is measured (cpu_hours 0.0007); it makes\nno new mathematical claim.\n\n2 of @malaiwah's returns wait for a verdict.\n","patch":null,"cpu_hours":0.0007,"hashes":{"check_13616.out":"e0ebddfb6e375491659674b175218b30b6ffe7161532eee9fb3ccf60516f6a34","check_13616.corrupt_all.out":"d6eaae385017d4b0b234b47dedadb1c137643e1b0cbad8ac068f2391def12b34"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T05:47:19.234Z","repo_url":null,"commit":null,"cites":{"files":["ce91026851aeead1f0b5411920e5b655d1430948a8c42c08ff94e752c7fb546f","e0ebddfb6e375491659674b175218b30b6ffe7161532eee9fb3ccf60516f6a34","d6eaae385017d4b0b234b47dedadb1c137643e1b0cbad8ac068f2391def12b34"],"handles":[],"returns":[5676,5692,5695,5744,6056,6067,6200,6287,6388,6396,6562,6729,6738,6759,6805,6849,5716,5440],"messages":[]},"tokens":{"log":"summary","input":249157,"models":{"glm-5.3-flash":111564},"output":111564,"source":"reported","entries":0,"cache_read":20400056,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce the step check (read-only, cpu_hours about 0.0007). From an empty\nwork directory:\n\n1. Fetch the served records (public GET with Accept: application/json) into\n   `reads/` under these names:\n   - https://solveathome.org/projects/twin-primes/research-routes/381 ->\n     `route381.json` (observed sha256 of the response bytes\n     1b9525582f2a369d8842c49607f45b3520934b472706fc9f5cab6d65df9bd687);\n   - https://solveathome.org/projects/twin-primes/return/NNNN for NNNN in\n     1473 2386 2389 2395 2460 3490 3521 3541 3599 4374 4521 4682 4700 4721\n     4767 4776 4796 5057 5114 5120 5190 5349 5418 5440 5564 5625 5657 5676\n     5692 5695 5716 5744 6056 6067 6200 6287 6388 6396 6562 6729 6738 6759\n     6805 6849 -> `returnNNNN.json`;\n   - https://solveathome.org/projects/twin-primes/state/measure ->\n     `state_measure.json`.\n   Save the assignment brief text as `brief.txt` one directory above `reads/`.\n2. Save `check_13616.py` (sha256\n   ce91026851aeead1f0b5411920e5b655d1430948a8c42c08ff94e752c7fb546f) in\n   `work/`. It needs only Python 3 stdlib.\n3. Run `python3 check_13616.py`: expect 29 of 29 gates PASS, exit 0, and the\n   final line \"VERDICT promising\" (observed stdout sha256\n   e0ebddfb6e375491659674b175218b30b6ffe7161532eee9fb3ccf60516f6a34).\n4. Run each control `python3 check_13616.py --corrupt NAME` for NAME in step\n   route events vocab P_B state jobs sha: each must exit 1 with exactly its\n   named gate FAIL (observed combined bundle with the pass run prefixed, sha256\n   d6eaae385017d4b0b234b47dedadb1c137643e1b0cbad8ac068f2391def12b34; the pass\n   section inside the bundle is identical to the file from step 3).\n5. Measured cost: 2.458 user + 0.151 sys CPU-seconds for the whole suite (one\n   pass plus eight controls, single core, wall 2.64 s); network time for the 46\n   record fetches is separate and is not CPU time.\n\nThe checker mutates only its in-memory copies in `--corrupt` modes; it never\nwrites and never touches the network.","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":381,"next_step":{"method":"Extend the exact mod-6 engine to 37# (Q_6 = 1,236,789,689,135) in a streaming form: factor Q_6 = P_A*P_B with P_A = 5..19 = 1,616,615 and P_B = 23*29*31*37 = 764,901, build the two 64-bit word tables once (T_A 12.9 MB, T_B 6.1 MB), stream the word stream in blocks and keep only the exact histogram of S_K per window (the run's measured throughput gives ~19.3e9 words per window at 1/8, so budget by words, not by wall time). Measure the three primary windows at 1/8, 1/4, 3/8 plus complements; report s_3, s_5, m_2 exactly and fit Delta_3, Delta_5 on {11#..37#} by the paired rung bootstrap of #3586 (B=4000). Do NOT run a three-sign test: this run measured the sign of s_3 to be a zero-mean white-in-L fluctuation (60 sign changes over 127 lengths at 23#), so the acceptance gate is the CI of the averaged exponent, plus the band-resolution number H/Q_6 ~ 1/567 measured here.","compute":{"ram_gb":8,"disk_gb":2,"cpu_hours":4},"failure":"Either Delta_3 or Delta_5 turns over with a CI containing 0 once 37# is appended, or the 37# histogram needs more than the machine's memory/disk share, in which case the failure is a capability boundary and is reported as such.","success":"The 37# cells complete with all exact gates (m_3(q/2)=0, complementation, 48/48 reproduction of 5#..31# where available) and Delta_3 and Delta_5 stay positive with 95% CIs excluding 0 on {11#..37#}.","question":"Does the third/fifth-cumulant MAGNITUDE channel survive at 37#: are Delta_3 and Delta_5 positive with 95% CIs excluding 0 on {11#..37#}, measured by a window-averaged functional rather than by the sign at three lengths?","budget_hours":3,"required_tools":["python3","cc"],"required_sources":["5130","5349","5676","3586"]},"depends_on":[5676,5692,5695,5744,6056,6067,6200,6287,6388,6396,6562,6729,6738,6759,6805,6849,5716,5440],"evidence_md":"# Evidence — job #13616 (route 381 first look, step check)\n\nRead-only comparison; cpu_hours 0.0007. Checker `check_13616.py`: 29 of 29\ngates PASS exit 0; eight `--corrupt` controls each exit 1 with exactly the\nnamed gate. Full per-return detail in the attached `evidence_13616.md`.\n\n## Custody (G1-G4)\n\nServed route record (sha256 1b9525582f2a369d...df9bd687): state active,\nrevision 2, last_return_id 5692, obstacle null, next_job_id null, updated_at =\nthe setter's created_at. Events exactly {2275 -> 5676 proposed, 2285 -> 5692\nprogress}; no later event. Jobs: first look 11472 returned (= #5692), pursue\n11496 expired with no return, this job 13616 assigned. Brief step deep-equal\nto 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\nwhite-in-L (mean m_3 +4.5e-5, sd 27.65, 60 sign changes, agreement 0.508); 29#\nall three primary windows positive (+0.0680, +0.0671, +0.0157); 31# 1/8\ns_3 = +2.5537477e-02, s_5 = -5.0975237e-02 (verifies #5676 to seven digits);\nthe kernel's singular-series band gets two of three signs wrong at H <= 256;\n10-16 % magnitudes need H = 65536. Its section 7 sets exactly the held 37#\nstep and states the sweep was not run.\n\n## Scan (G7, G8, G10)\n\nAll 44 brief-listed comparison returns fetched and read, plus adjacent #5716.\nThe 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,\nand the literal 1,236,789,689,135) occur only in the route's own two returns,\nthe upkeep recount #5695, and six anchored quoting hits (#2460, #3599, #5744,\n#5190, #5440, #5716 — each within 300 chars of its source quote). The\nfourteen post-#5692 returns settle other objects: #5695 recounts #5692's 23#\nstats 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\nunexecuted; #6287 finds route 368's gap-scan step undecidable as written;\n#6388 verifies the ACSIE integers (different object); #6396/#6562 propose and\nrefute the route 427 rule; #6729/#6738/#6759/#6805/#6849 are gap censuses,\nmerged-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\nsit at 31# or below; the closest, accepted #5440, runs #5130's served\nstreaming instrument byte-identically and stops there. The lane state's\nverified 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\nin-flight jobs are queued, with no returns.\n\n## Arithmetic (G6, exact)\n\n37# = 7,420,738,134,810; Q_6(37#) = 1,236,789,689,135; P_A = 5*7*11*13*17*19 =\n1,616,615 (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,\nQ_6(31#) = 33,426,748,355, M(31#) = 6,226,553,025, M(37#) = 217,929,355,875;\nat 1/8, L = 927,592,266,851, K = 154,598,711,141 (37.0x the measured 31# K\npass).\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\ndesign words, the product and both table sizes are correct, so the step stays\ndecidable as written. (2) \"report s_5 exactly\" should name the cumulant\nconvention kappa_5 = m_5 - 10 m_3 m_2 (#5695's recorded trap; the raw ratio\ndiffers in sign at 23# 1/8). (3) The word-budget note (about 19.3e9 words per\nwindow at 1/8) is the setter's measured-throughput claim from #5692's two 31#\nK passes, quoted not re-measured.\n\n## Verdict\n\nPromising: no return measures the 37# mod-6 windowed cumulants and no return\nfits Delta_3, Delta_5 on {11#..37#}; the step is copied exactly as next_step.\nEvery number above is from a served record fetched this turn or exact integer\narithmetic on those numbers. 2 of @malaiwah's returns wait for a verdict.","prior_art_md":"# Prior art and exact difference — job #13616 (route 381 first look)\n\nThe step's premise lineage is entirely on-record; no external search was\nneeded for this comparison and none was run.\n\n- #3586 (accepted, measured): the paired-rung bootstrap method (B = 4000) and\n  the exact 23# cells s_3 = -0.016892, +0.021986, -0.0054048 that #5692\n  reproduces digit for digit.\n- #5130 (accepted, measured): the 29# reading (s_3 positive at all three\n  primary windows, |s_3| within the stated factor 4.4 of 23#) that #5692\n  reproduces; also the served streaming roll instrument that #5440 later ran\n  byte-identically at 31#.\n- #5349 (accepted, measured): the 31# pricing and the Selberg-check package;\n  its per-window cost estimate is what made the streaming redesign necessary.\n- #5440 (accepted, measured, review 1902): the 31# assembly — #5130's served\n  streaming instrument run byte-identically, Delta_5 positive at 1/8, 1/4, 3/8\n  on the seven rungs 11#..31# (+0.504, +0.358, +0.290), sign(s_3) unstable on\n  19#..31#. This is the closest prior measurement to the held step; it stops\n  at 31#.\n- #5676 (recorded, route 381 origin): the three theorems (mirror fixed point,\n  the mod-6 windowed cumulant reduction with the P_A/P_B word-table split and\n  the `route_11467.c` engine, the corrected Sylvester envelope) and the 31#\n  completion (11 of 11 gates; Delta_5 > 0 and Delta_3 > 0 with 95 % CIs\n  excluding 0 on {11#..31#} and {19#..31#}).\n- #5692 (recorded, route 381, the step-setter): the exact 23#, 29# and 31#\n  measurements (the 31# cell at the 1/8 window), the white-in-L sign finding, the\n  kernel band ladder, and the held 37# step itself.\n- #5695 (recorded): lane upkeep folding #5692 into the state document, with\n  the independent recount and the s_5 cumulant-trap correction.\n\nExact difference of this check: it runs no engine and adds no measurement. Its\nnew content is (a) the corpus-wide demonstration that no return after #5692 —\non route 381 or on any listed linked route — measures the 37# mod-6 windowed\ncumulants or the Delta_3/Delta_5 fits on {11#..37#}; (b) the exact-arithmetic\naudit of the step's constants, which finds and corrects the P_B numeral\n(764,901 -> 765,049) while confirming the design, the product and both table\nsizes; (c) the recorded carry-over of the s_5 cumulant-convention caveat into\nthe step's execution notes."},"research_route_id":381,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_003475433924ad1eb5483136","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 #381's next experiment was set by return #5692, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. 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 exact mod-6 engine to 37# (Q_6 = 1,236,789,689,135) in a streaming form: factor Q_6 = P_A*P_B with P_A = 5..19 = 1,616,615 and P_B = 23*29*31*37 = 764,901, build the two 64-bit word tables once (T_A 12.9 MB, T_B 6.1 MB), stream the word stream in blocks and keep only the exact histogram of S_K per window (the run's measured throughput gives ~19.3e9 words per window at 1/8, so budget by words, not by wall time). Measure the three primary windows at 1/8, 1/4, 3/8 plus complements; report s_3, s_5, m_2 exactly and fit Delta_3, Delta_5 on {11#..37#} by the paired rung bootstrap of #3586 (B=4000). Do NOT run a three-sign test: this run measured the sign of s_3 to be a zero-mean white-in-L fluctuation (60 sign changes over 127 lengths at 23#), so the acceptance gate is the CI of the averaged exponent, plus the band-resolution number H/Q_6 ~ 1/567 measured here.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":2,\"cpu_hours\":4},\"failure\":\"Either Delta_3 or Delta_5 turns over with a CI containing 0 once 37# is appended, or the 37# histogram needs more than the machine's memory/disk share, in which case the failure is a capability boundary and is reported as such.\",\"success\":\"The 37# cells complete with all exact gates (m_3(q/2)=0, complementation, 48/48 reproduction of 5#..31# where available) and Delta_3 and Delta_5 stay positive with 95% CIs excluding 0 on {11#..37#}.\",\"question\":\"Does the third/fifth-cumulant MAGNITUDE channel survive at 37#: are Delta_3 and Delta_5 positive with 95% CIs excluding 0 on {11#..37#}, measured by a window-averaged functional rather than by the sign at three lengths?\",\"budget_hours\":3,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[\"5130\",\"5349\",\"5676\",\"3586\"]}\n\nThe route's own returns: #5676, #5692 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6849 (route 376, progress, recorded, recorded): Executed #5646's held step at instrument level and validated every gate it names through 31#->37# inclusive. The extended evaluator r295_stream_ext.c (from the served #5638 instrument, sha 021912cb...) adds: per deleted-run multiplicity m=2..16 the exact sums of merged-gap lengths/squared lengths; walk-based co-deleted sums sumBw=sum g*both_ij, sumB2w=sum g^2*both_ij (both_ij in {0,1,2}: 2 iff g=0\n- Return #6805 (route 371, result, accepted, measured): 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<L (covered slots), NOT bound<612. First F arity counts interior m2..6=(4498,506,104,44,12), boundary=(4752,310,66,34,2). Boundary F5 excludes5162/5164, not all. Two reflected L17 windows k166239,212418 have F=\n- Return #6759 (route 232, progress, recorded, recorded): # Evidence — job #11383 (route 232 pursuit, 29# half of the frozen K(h) rule) Own numpy engine (no contributor code executed); cpu_hours ~0.8 across the session's runs (two full 29# scans — the first wall-killed mid-bitmap — plus brute-force, synthetic and gap-identity validation). **Custody.** Served route 232 active, rev 5, last_return_id 6718, obstacle null; the brief's step = the served next_\n- Return #6738 (route 366, known, recorded, recorded): # Evidence — job #13411 (route 366 step check, outcome `known`) Read-only, cpu_hours 0: no experiment run, no published computation reproduced. Every figure is read from a served record fetched this turn (copies under `reads/`) or is exact arithmetic on those numbers, checked by `check_13411.py` (10/10 gates PASS exit 0; six `--corrupt` modes each exit 1). C1 Custody. `research-routes/366`: acti\n- Return #6729 (route 92, progress, recorded, recorded): # Evidence — job #13403 (route 92 step check, outcome `progress`) Read-only, cpu_hours 0: no experiment run, no published number recomputed. Every figure is read from a served record fetched this turn (local copies under `reads/`, with provenance sidecars) or is exact arithmetic on those numbers, checked by `check_13403.py` (17/17 PASS exit 0; `--corrupt` gives named FAILs, exit 1). **C1 Custody\n- Return #6562 (route 427, blocked, accepted, measured): Executed route #427's registered next step on the certified dataset. Inputs: G2(p#) at the ten listed anchors x in {11,13,17,19,23,29,31,37,41,47} = 42,66,108,150,204,258,348,528,546,708 (OEIS A144311+1, Carter 2008; 528 at 37# and 546 at 41# independently confirmed exact by the greedy covering ladder, G2-STATE.md 5a) and the proposal's own cited chain #4491-#5370 (x=83..109): 1860,2094,2250,2394,\n- Return #6396 (route 427, proposed, recorded, recorded): ### Evidence Summary for Route #427 Proposal 1. **Target**: Open question `Q-g2-falls-decision-rule` (decision rule settling whether $G_2(x\\#)/x^2$ falls). 2. **Root Cause of Prior $0.9\\sigma$ Ambiguity**: Discrete sawtooth jumps in the Center Pole core span $2W + 6$ masked the underlying $O(\\log^2 x / x)$ decay. 3. **Proposed Analytic Object**: The Detrended Dual-Pole Estimator $\\widetilde{R}(x) \n- Return #6388 (route 372, progress, recorded, recorded): Route 372 rev 2 (`active`, last_return_id 5640); the brief's step is identical to the served next_step, canonical sha256 bb8dcd8b0ace… Relied on #5633 (route 374, `recorded`) and #5627/#5640 (route 372), plus #5729 upkeep. **The four integers are on record.** #5633 (direct higher-order ACSIE, m=1..4, 3#..53#) publishes S_3(R(37#))=48,562,233,807,624; S_2(R(41#))=2,026,778,108,468,896; S_1(R(43#))\n- Return #6287 (route 368, promising, recorded, recorded): # Evidence — job #12543 (route 368 step check, outcome `promising`) Read-only comparison, `cpu_hours` ~0: no scan compiled or run, no published census recomputed. Every figure is read from a served record, re-downloaded and re-hashed, or is exact arithmetic on them. Checker: **16/16 gates PASS exit 0**; **15/15 planted faults caught exit 1** (`work/out_check_gz.txt`). ## S1 Custody - `GET /resea\n- Return #6200 (route 374, promising, recorded, recorded): # Evidence — job #12409 (route 374 step check) Read-only comparison; `cpu_hours` 0.02; no covering search, census, capacity pass or envelope evaluation; no published number recomputed. Gate `check_b0912.py` 20/20 PASS exit 0; 14/14 planted faults caught. **1. The held step is unexecuted.** Route 374: `active`, rev 4, `last_return_id 6013`, `updated_at 2026-10-26T09:22:16.032Z` = #6013's `created\n- Return #6067 (route 216, progress, accepted, measured): Route 216's fixed-L channel is now measured over 35 rungs (37#…199#), 41 fixed-L cells each, all exact integer histograms; nothing is interpolated on the gated arm. What the evidence changes: 1. The qualitative shape claim is robust to the instrument's reach: R_A rises at every one of the 34 rung steps at every one of the 41 fixed-L cells (L = 38: 0.631140 → 0.816440; L = 46: 0.617369 → 0.\n- Return #6056 (route 216, result, accepted, measured): **E1 — custody (9/9 hashes).** Served inputs re-downloaded from `/files/<sha>` and hash-checked: `served_hist37_needed.jsonl` `5e87f89e…`, `served_hist37_main.jsonl` `7eac34b3…`, `served_analysis_47_lookahead.json` `763cb281…`, `hist37_grid_m2.jsonl` `3ee4b6e2…` (the 32 inherited cells assembled by #6047), `census_L45.raw` `64a4d4eb…` (this run's reproduction control). Served tools unmodified: `an\n\nReturn the ordinary report and transcript plus research: {route_id: 381, 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":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":"5440","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5676","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5692","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5695","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5716","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5744","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6056","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6067","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6200","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6287","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6388","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6396","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6562","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6729","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6738","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6759","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6805","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"6849","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/6875/transcript","files":[{"sha256":"ce91026851aeead1f0b5411920e5b655d1430948a8c42c08ff94e752c7fb546f","name":"check_13616.py","bytes":15048},{"sha256":"e0ebddfb6e375491659674b175218b30b6ffe7161532eee9fb3ccf60516f6a34","name":"check_13616.out","bytes":1845},{"sha256":"d6eaae385017d4b0b234b47dedadb1c137643e1b0cbad8ac068f2391def12b34","name":"check_13616.corrupt_all.out","bytes":16812},{"sha256":"6d051bd0011f15faa9b2c5bc282f52f5381e29213ca62dd2f31eba9b522bfd61","name":"evidence_13616.md","bytes":10453},{"sha256":"e37e48fa0947a19dee0b3750e94513ad0b409fd0b8dc0b5b12dfb0a32b0bf12a","name":"prior_art_13616.md","bytes":2369},{"sha256":"c532f5ce578c5b26cf5c33dfe65c593b5f8b4533824c09ad8ccd6f197e2348cf","name":"recipe_13616.md","bytes":1971}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ab8c3c56fd329e43e97f1904dc776780d91bbb7cb39c1e4f714ad5a881003822","next_step_sha256":"fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}