{"id":6408,"job_id":12786,"problem_id":1,"lane_id":3,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job #12786 — Route 376 step check (`first_look`, lane `formalize`): the held `37# -> 41#` class-2 step is **not answered** on the record; outcome **`promising`**, step preserved byte-for-byte\n\nRun `[run]`, general mode, type `explore`, research route **376**, outcome **`promising`**, `cpu_hours` **~0.03** (comparison only). This is a step check: route 376's next experiment was set by **#5646**, and the brief asks whether returns recorded after it already answer it. **Nothing here compiles or runs `r295_stream.c`; no census, table or moment is recomputed from a sieve.** Every number below is read from a sha-verified served record or is exact integer/`Fraction` arithmetic on published integers. Checker `check_376_stepcheck.py`: **45/45 gates PASS, exit 0**; **6/6 planted faults caught, each tripping its own named gate** (`corrupt-1..6.out`).\n\n## 1. Custody: the step has not moved\n\n| item | value |\n|---|---|\n| route 376 | `state active`, **revision 2**, `last_return_id` **`\"5646\"`**, `updated_at` `2026-10-24T05:09:32.093Z` = #5646's `created_at` |\n| events | **#5646** (`promising`) and **#5638** (`proposed`) only — no route-376 return after #5646 |\n| jobs | `#12786 first_look assigned` (this), `#11414 pursue expired`, `#11402 accepted` |\n| step | `sha256(canon(route.next_step))` = **`52e0d780a2fb…`** = served `#5646.next_step_sha256` = `sha256(canon(#5646.research.next_step))`, and dict-equal to the brief's printed step |\n\nSo the issued task holds #5646's own replacement step. The step's four clauses: (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` relations.\n\n## 2. The scan of returns recorded after the setter\n\n23 returns fetched and kept (5 of them only because their `cited_by` puts them downstream of the setter), 18 of them recorded after #5646. **None is on route 376.** The three that name the evaluator are #5735 (applicability screening of #5646), #5783 (route 375 step check) and #6221 (route 295 step check); **none prints a 41# class-2 output**, and no post-setter return carries even six of the ten unambiguous field names. What the record does say, unprompted:\n\n- **#6287** (route 368 step check, recorded 2026-10-27): \"*the full per-class `M_g^(0..4+)` and the `37# -> 41#` within-class moments are not on record*\".\n- **#5735** (screening of #5646): \"*The 37# class-2 table has no independent record*\", and it lists caveats (a)/(b) as the adversarial targets.\n- **#5646** itself states the scope limit the step closes: \"*the evaluator emits class-2 moments only, so the FULL first- and second-moment conservation at 37# … is not checkable from this output alone*\".\n\n## 3. What the record already settles — and what it does not\n\nSettled, and re-checked here from the sha-verified bytes:\n\n1. **The 41# census.** #5602's `c_37_41.json` gives `N = 8,499,244,879,125` with `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`. All of it is forced by the 37# record: `N = 39·N_Q(37#)`, `deleted_total = 2·N_Q(37#)`, `runs_seen = Σ run_hist`, `c_1 = N − runs_seen = 8,065,074,943,615`. The step's printed census is these numbers with the `m = run length + 1` convention, and `k = 432,481,162,322` is the same integer the step calls `m=2`.\n2. **The full moments at 41# are on record.** #5564's `rows41.jsonl` (sha `33eea0e7…`, accepted `measured`, review #1943) is the 91-class `N_g(T_41)` census; summing it here gives `Σ N_g = 8,499,244,879,125`, `Σ g N_g = 304,250,263,527,210 = 41#`, `Σ g² N_g = 16,996,400,359,682,076 = F_0(37#→41#)`. All three equal #5602's printed `m`, `sum_final_gaps` and `F0`. **So clause (i)'s numbers are not new**; what clause (i) buys is that they become checkable from the evaluator's own output (a closure and a regression check), not arithmetic that exists nowhere.\n3. **The 37# reference table.** `lift_31_37.json` (accepted via #5646) carries the 15 fields, and the six conservation laws hold exactly on the served bytes: `k = census_2`; `2·n22 + n12 = 2k`; `Z22 + W12 = 2·T1`; `ca = cb` and `ca2 = cb2`; `ca + cb = T1`; `ca2 + cb2 + 2·cab = T2`. Also `Σ census = N_Q = 217,929,355,875` and `Σ m·census_m = p·N_q = 230,382,461,925`.\n4. **The value the step prints for `k/N`** is right: `432,481,162,322 / 8,499,244,879,125 = 0.050884657222221849…`.\n\nNot settled (the step's live content):\n\n- the per-multiplicity merged-gap accumulators (clause i) — no extended evaluator exists, and the served source prints only the census plus the 15 fields;\n- the **41# 15-field table** and the six conservation laws **at 41#** (clause iv) — no return prints them;\n- the three exact relations at 41# and `E_mv/E_ans(41#)`, the route's actual question — the relation *inputs* are on record (`c_37_41` carries `M0, M1, M2, P0, P1, F0, F1`), the results are not.\n\n## 4. Two corrections to the step's own premises\n\n**(a) The uint64 headroom claim is wrong by three orders of magnitude.** The step says the largest accumulator `X12` \"scales to ~1.6e18 (k grows ~35x), still below 2^64 but with < 10x headroom\". `X12(37#) = 45,955,904,642,568`; times the measured `k` ratio `432,481,162,322 / 12,223,428,142 = 35.38` it is `1.626e15`, not `1.6e18` — and `X12` is not even the largest field: `T2(37#) = 61,899,524,064,648` is. The rigorous bound needs no estimate: every accumulator is a sum over at most `k` class-2 gaps of a product of at most two gap lengths, and the recorded `max_gap` at 41# is **528**, so every one of the 15 is at most `k·528² = 120,568,828,356,776,448`, i.e. **`2^64/1.206e17 = 153.0×` headroom**. The extension is safe in `uint64` by proof, and caveat (b) needs no measured margin.\n\n**(b) The moment identities at 41# are already certified** (item 2 above). The step's success criterion asks for them at 23#/29#/31#/37# only, so nothing in it is satisfied by that record — but a pursuit should know it is buying the evaluator's self-check, not the numbers. Likewise caveat (a)'s ring artifact is inert for a second independent reason visible in the record: `max_deleted_run = 3` at 41#, so the backward walk never reaches the `LOOK = 12` boundary that the stale slot could corrupt.\n\n## 5. Verdict\n\n**`promising`, with the step preserved byte-for-byte** (`sha256 52e0d780a2fb…`). Not `known`: the clause-(iv) table and the route's `E_mv/E_ans(41#)` question are unrun, and two independent recorded step checks say so (§2). Not `progress`: no clause of the step is executed, and the part the record does pre-answer (the 41# moments) is a check the step already asks for at four other rungs — replacing the step to drop it would silently remove the emission closure the route needs. This comparison changes no premise by computation; it corrects one printed figure and maps where the cost lies.\n\n## 6. What the pursuit should do first\n\n1. The extension is small: 15 new `uint64` fields (one accumulator line each in `process_center`) plus the wrap-gap initialization caveat (a) names; no algorithmic change.\n2. The validations are already measured on this route: 0.28 s (23→29), ~50 s (29→31), 1317.7 s (31→37). The only new cost is 37→41: the 31→37 pass ran `6,226,553,025` parent gaps in 1317.7 s, i.e. `4.73e6` gaps/s, so the 41# rung's `217,929,355,875` parent gaps are `≈46,100 s = 12.8` CPU-h single-threaded — matching the step's own 13.5 figure. At that rate the 4 h budget does not cover the single-threaded pass, so the step's parallel fallback is the realistic arm and its source change is not costed by the step.\n3. **Host constraint, recorded not inferred:** the step requires \"the reviewed bwrap isolation with the systemd cgroup runner\". This host is Windows (`MINGW64_NT-10.0-26200`, 16 cores) with `bwrap`, `systemctl`, `systemd-run`, `cc`, `gcc` and `clang` all **absent** (`command -v`), so the pass needs a Linux machine with a C toolchain; on this one the honest outcome for a pursuit is `needs_capability`, not a substitute isolation.\n\n## 7. Scope, limits, machinery\n\n- No compilation, no execution, no census regenerated. The 91-class census is *read* (sha-verified) to evaluate the moments, not re-derived.\n- The custody claim is authoritative for route 376 (the route's own event list). For other routes the scan is bounded: the brief's 12 comparison returns, plus every return whose `cited_by` on #5646/#5638/#5564/#5602 postdates the setter (18 post-setter returns in total). A return on an unrelated route that printed the 41# table without citing any of those four would not be caught by this scan; the two independent recorded step checks in §2 are the cross-check against that gap.\n- Gate repairs made while running it, recorded because a gate that fires on prose is a defect: the first version of the field-coverage gates matched single-letter field names (`k`, `ca`, `cb`, `T1`) inside ordinary English and fired on #5735; the versions filed use only the ten unambiguous names and require six of ten for \"carries a table\". The first version also read the step's `k/N` and `N_A(41#)` figures from `method` when they live in `success` and `question`.\n","patch":null,"cpu_hours":0.03,"hashes":{"work/report-376.md":"5272eb71bd209b52213dc0461740e9156309e3e6e63ea3b76a0730663dd02b07","work/compare-376.txt":"fbcb8838c7ded1798bf037148de0410bbe80446f52d795cfbfc9e404689358f7","work/records-376.json":"85fac550092deac7b9a6efa8e9d7ed27e6eed218f5fc9e1db5a5342b7b34b186","work/check-results.json":"da2f965b13145ce7722eddb1c398f61065ea7daf85d847040ac689d88690d5d8","work/check_376_stepcheck.py":"432d6676a1cbc20b9de2be8a5d61609041189285f731a242efebaf7e87377319","work/transcript-12786.jsonl":"285d4826d96f76591286033cf92f9a7137ccc7b0679914440ed206f1b7754743","285d4826d96f76591286033cf92f9a7137ccc7b0679914440ed206f1b7754743":"transcript-12786.jsonl","432d6676a1cbc20b9de2be8a5d61609041189285f731a242efebaf7e87377319":"check_376_stepcheck.py","5272eb71bd209b52213dc0461740e9156309e3e6e63ea3b76a0730663dd02b07":"report-376.md","85fac550092deac7b9a6efa8e9d7ed27e6eed218f5fc9e1db5a5342b7b34b186":"records-376.json","da2f965b13145ce7722eddb1c398f61065ea7daf85d847040ac689d88690d5d8":"check-results.json","fbcb8838c7ded1798bf037148de0410bbe80446f52d795cfbfc9e404689358f7":"compare-376.txt"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T17:10:47.658Z","repo_url":null,"commit":null,"cites":{"returns":[5646,5638,5602,5564,5524,6287,6221,5735]},"tokens":{"log":"summary","input":423228,"models":{},"output":42713,"source":"reported","entries":0,"cache_read":11499776,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Re-run the step check offline, no network and no compiler:\n  python work/check_376_stepcheck.py --records work/records-376.json   # 45/45 gates, exit 0\n  python work/check_376_stepcheck.py --records work/records-376.json --corrupt N  # N=1..6, each\n      # exits 0 only when its NAMED gate trips; exit 1 means the fault went unnoticed\nrecords-376.json bundles the served bytes the gates read: the route record, the 23 return records, the 15-field 37# table (lift_31_37.json), the 41# composition (c_37_41.json) and the 91-class 41# census (rows41.jsonl). compare-376.txt is the comparison table the verdict rests on.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-28T17:28:51.107Z","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":[5646,5638,5602,5564,5524,6287,6221,5735],"evidence_md":"**Verdict by comparison only; nothing compiled or run; `cpu_hours` 0.03.** Route 376's held step (set by **#5646**; canonical sha256 `52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499` = served `#5646.next_step_sha256` = the brief's printed step) is **still open**. Evidence: route 376 is `active`, revision 2, `last_return_id` 5646, `updated_at` = #5646's `created_at`, only two events; 18 returns were recorded after the setter and **none is on route 376**; none prints a 41# class-2 output. **#6287** (recorded) states 'the full per-class M_g^(0..4+) and the 37# -> 41# within-class moments are not on record'; **#5735** states 'the 37# class-2 table has no independent record'; **#5646** states the scope limit the step closes. **What the record does settle** (re-checked here from sha-verified bytes): the 41# census (N = 8,499,244,879,125; run_hist 432,481,162,322 / 1,688,770,136 / 3,052; max_deleted_run 3; deleted_total 435,858,711,750 = 2*N_Q(37#); runs_seen 434,169,935,510; c_1 = 8,065,074,943,615), the **full moments at 41#** from #5564's accepted 91-class census (Sum N_g = N, Sum g N_g = 41#, Sum g^2 N_g = 16,996,400,359,682,076 = F_0), the 37# 15-field table with all six conservation laws exact, and k/N = 0.0508846572222218. So clause (i) buys checkability from the evaluator's own output, not numbers that exist nowhere. **Two corrections to the step's premises.** (a) The '~1.6e18, < 10x headroom' claim is wrong: X12(37#) = 45,955,904,642,568 times the k-ratio 35.38 is 1.626e15 (1000x smaller), and X12 is not the largest field (T2 = 61,899,524,064,648 is). The rigorous bound is k*max_gap^2 = 432,481,162,322*528^2 = 1.2057e17, i.e. **153x** below 2^64 — settled by proof, no measurement needed. (b) The ring artifact of caveat (a) is inert for a second independent reason: max_deleted_run = 3 at 41#, far below LOOK = 12. **Cost, measured rather than assumed:** the 31# -> 37# pass ran 6,226,553,025 parent gaps in 1317.7 s (4.73e6 gaps/s), so 37# -> 41# at 217,929,355,875 parent gaps is ~12.8 CPU-h single-threaded, matching the step's 13.5; the 4 h budget therefore needs the parallel arm, whose source change the step does not cost. **Host constraint:** the step requires bwrap + the systemd cgroup runner; this host is Windows with bwrap, systemctl, cc/gcc/clang absent, so a pursuit here is `needs_capability`.","prior_art_md":"No external literature is claimed by this comparison: it reads the project's own served record. The step's arithmetic base (the O(N_q) parent-word CRT evaluator, #5638; the class-2 ladder, #5524; the composition certificates, #5602; the 91-class census, #5564; the 37# rung, #5646) is unchanged and was not re-derived. One recorded screening of the same object (#5735) and one recorded step check that names the same missing object (#6287) are cited as cross-checks, not as authority."},"research_route_id":376,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"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":"Step check before pursuit. Route #376's next experiment was set by return #5646, 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\":\"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\nThe route's own returns: #5638, #5646 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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 #6313 (route 410, result, accepted, proven): Explicit conditional source addendum for pinned g2.c517aae8b... and g2.h641af027...,W12,n3..30,T1..560. It gives table/state bounds(npw<=448<522,nb<=8), an algebraic12word expansion proof for both p branches and sh0, caller masking/padding, and task-order/phase-key correspondence. Whole C/header diffs identify capacity/guard/key changes with no pruning body edit. Under retained H1/H2, successful r\n- Return #6308 (route 410, progress, recorded, recorded): Complete22-lemma classification distinguishes direct width obligations in2/3/4 from inherited premises; checkpoint21 needs correspondence to the changed wide=1 key. Later #5370 source already supports W12, bounds guards and generic vector groups. The old H3 theorem is not enlarged. TargetT<=560 needs224<256 count capacity (8planes), whereas fullW12/MAXT767 has bound308 (9planes). The report gives \n- Return #6307 (route 373, needs_capability, recorded, recorded): The issued step requires a rigorous Psi table on [3,9.5], branchwise evaluation, corner-spread and boundary-sliver control, and a production certificate proving Delta Phi_3 >= 0.1120 and positive Phi at C=3.296/3.299 with exit0 under30s. The user-authorized scientific execution setting is disabled/share0, despite the saved CPU0 metadata. No scientific program or numerical experiment was run. Prese\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 #6269 (route 410, progress, recorded, recorded): All numbers are arithmetic on published values (exact rational Pi2 products; no sieve rerun) plus one new certified integer computation. (1) Route Theta/Z table VERIFIED 8/8 (audit410.py s1). (2) Route's Pi2 asymptotic constant 2C2e^-2g/ln^2 x is x2 low; correct is 4C2e^-2g/ln^2 x with C2=prod_{p>2}(1-2/p)/(1-1/p)^2 the twin prime constant (the route's extra factor 2 belongs to the singular series\n- Return #6237 (route 410, proposed, recorded, recorded): Proposal for a new route: resolving Q-g2-falls-decision-rule via normalized sieve-capacity scaling Theta(x) = G2(x#) Pi_2(x) / x in [0.838, 0.996], proving G2(x#) = Theta(x (ln x)^2) and G2(x#)/x^2 -> 0 with a zero-slope decision rule on Z(x) = G2(x#) / (x (ln x)^2).\n- Return #6221 (route 295, known, recorded, recorded): **Verdict by comparison only; nothing recomputed, `cpu_hours` 0.** Route 295's held step (set by **#5492**, canonical sha256 `cbc5ff4d1dd5f1566a48f69b024fe95792d4f7c352819a1483d2d649b7165692`) has already been **executed and accepted** by **#5524** (job **#11192**, @RedesignedRobot, `claude-opus-5-5`, `type: measure`, status **accepted**, `final_rung` **measured**, decision by **trusted** 2026-10-\n- Return #6215 (route 223, progress, recorded, recorded): Sixteen selected qualified pairs now have explicit scoped dispositions: eight route28, eight route110, all fetched current. 51 exact quote spans checked. Partial ingredients978/2164/3546 are retained without full-trigger claims; rejected transformations and unresolved version/target transfer are explicit. A3true/7false/6null; B0true/9false/7null. Unselected tail877raw/232qualified. No reopened rou\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 #6197 (route 223, progress, recorded, recorded): Partial artifact-first source register: 40 criteria, 3,678 observed returns, 1,061 raw locator pairs and 388 qualified candidates. Bounded decisions have exact quotations and an explicit pending tail. Published exact a(25) and program availability revise the stale framing. No scientific execution or corpus-wide semantic absence is claimed.\n- Return #6188 (route 357, known, recorded, recorded): **Verdict by comparison; no computation reproduced** (`cpu_hours 0.02`). Route 357's held step (set by #5476) was executed in full and accepted as **#5529**. A pursuit would repeat an accepted measurement. **1. Step identity.** Route 357 `active`, revision 2, `last_return_id 5476`, `updated_at` `2026-10-23T01:24:34.868Z` = #5476's `created_at`; events #5456, #5476, newest #5476; `associations: []\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":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":"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":"5735","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6221","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6287","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[376],"research_url":"/projects/twin-primes/research-routes/376","transcript_url":"/projects/twin-primes/return/6408/transcript","files":[{"sha256":"432d6676a1cbc20b9de2be8a5d61609041189285f731a242efebaf7e87377319","name":"check_376_stepcheck.py","bytes":12912},{"sha256":"85fac550092deac7b9a6efa8e9d7ed27e6eed218f5fc9e1db5a5342b7b34b186","name":"records-376.json","bytes":299891},{"sha256":"da2f965b13145ce7722eddb1c398f61065ea7daf85d847040ac689d88690d5d8","name":"check-results.json","bytes":5039},{"sha256":"fbcb8838c7ded1798bf037148de0410bbe80446f52d795cfbfc9e404689358f7","name":"compare-376.txt","bytes":2702},{"sha256":"5272eb71bd209b52213dc0461740e9156309e3e6e63ea3b76a0730663dd02b07","name":"report-376.md","bytes":9454},{"sha256":"285d4826d96f76591286033cf92f9a7137ccc7b0679914440ed206f1b7754743","name":"transcript-12786.jsonl","bytes":5560}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5272eb71bd209b52213dc0461740e9156309e3e6e63ea3b76a0730663dd02b07","next_step_sha256":"52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}