{"id":6770,"job_id":13457,"problem_id":1,"lane_id":3,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13457 — Route 376 step check: the held `37# -> 41#` class-2 step is **still open**; outcome **`promising`**, step preserved byte-for-byte\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) or is exact integer/`Fraction` arithmetic on those numbers. Checker `check_13457.py`: **18/18 gates PASS, exit 0**; **6/6 planted faults caught, each tripping its own named gate** (`check_13457_faults.out`).\n\n## 1. Custody: the step has not moved\n\n| item | value |\n|---|---|\n| route 376 | `state active`, **revision 3**, `last_return_id` **`6408`**, `updated_at` `2026-10-28T17:10:47.658Z` = #6408's `created_at` |\n| events | **#6408** (`promising`), **#5646** (`promising`), **#5638** (`proposed`) — exactly three; the revision 2 -> 3 delta is the #6408 step-check event itself |\n| jobs | `#13457 first_look assigned` (this), `#12786 first_look returned` (= #6408), `#11402 first_look accepted` (= #5646), `#11414 pursue expired` — **no pursue handed out after the setter** |\n| step | `sha256(canon(route.next_step))` = **`52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499`** = served `#5646.next_step_sha256` = `sha256(canon(#5646.research.next_step))` = `sha256(canon(#6408.research.next_step))`; all four copies deep-equal; deep-equal to the brief's printed step object (all eight fields) |\n\nSo the issued task still holds #5646's own replacement step, unchanged since #6408 verified it. Its 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`-odds relations.\n\n## 2. The new comparison set — none of it answers the step\n\nThe brief's new candidates (recorded after #6408's comparison) plus the cited/dependent evidence and the trusted applicability screenings, all read in full this turn:\n\n| return | status / route | what it says | step content |\n|---|---|---|---|\n| #6738 | recorded, route 366 | route 366's own failure clause fires: G2(37#) = 528 in both conventions, h(37#) = 66, r/D(37#) = 51765/32768 = 1.5797 >= 1.40 | none; quotes #5564/#5602's already-on-record 41# census and moment sums (the identities re-verified in §3) but none of the step's clauses (no evaluator extension, no 15-field table, no E_mv/E_ans(41#)) |\n| #6729 | recorded, route 92 | K*(29# -> 53#) = 22 already computed by accepted #5550; two base-31 cells open | none |\n| #6562 | accepted measured, route 427 | route 427's descent-rule claim refuted at source level (obstacle `claim_refuted`); G2 anchors reconfirmed incl. G2(41#) = 546 | none; a max-gap anchor, not the class-2 table |\n| #6410 | recorded, route 293 | #5627 already publishes the 41# values; the lag-2 functional is the only clause left | none; `41#` only as a census reference |\n| #6769 | pending, route 371 | route 371's g = 612 hierarchy step open; #5807's DP narrows the mechanism | near hits are benign: quotes 8,499,244,879,125 as #5564's T_41 census total and lists #6408 in a catalog sentence of returns read |\n| #6746 | recorded, route 367 | the held 31-shift 37# dilation sweep already answered by #6655 | none |\n| #6701 | recorded, route 395 | the held fixed-window rho_PV sweep still open | none |\n| #6377 | recorded, route 293 | the held lag-2 fusion step still open | none |\n| #6726/#6681/#6550/#6516/#6488 | recorded screenings | trusted applicability screenings linking the lambda1 sieve-weight family (#6312/#6304/#6220/#6212/#6204) to the formalize lane | none; a different object (sieve-weight lower bounds), no evaluator or class-2 content |\n\nMarker scan over all 13 full reports: **zero hits** for the unambiguous step markers `r295_stream`, `EMBEDDED_LIFTS`, `k_over_N`, `merged-gap length`, `N_A(41` (`G3-no-step-markers`).\n\n## 3. What the record settles at 41# — re-verified from served bytes this turn\n\nReuses #6408's conclusions; the arithmetic is re-checked here on the fetched bytes:\n\n1. **The 41# census.** #5602's `c_37_41.json` (sha `69240f1a…`, hash-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`. The step's printed census is these numbers with the `m = run length + 1` convention; `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): 91 classes; summing here gives `Σ N_g = 8,499,244,879,125 = 39 · N_Q(37#)` = the step's `N_A(41#)`, `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 values. Clause (i)'s numbers are not new; what it buys is the evaluator's own-output self-check.\n3. **The step's printed `k/N` is right.** `432,481,162,322 / 8,499,244,879,125 = 0.050884657222221849…` (exact `Fraction` in the checker).\n4. **The 37# reference table.** #5646's `lift_31_37.json` (sha `099000f2…`): `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; class-2 `k = 12,223,428,142`, `T2 = 61,899,524,064,648`, `X12 = 45,955,904,642,568`.\n5. **uint64 headroom (#6408's correction (a), re-verified).** `k(41#) over k(37#) = 432,481,162,322 over 12,223,428,142 = 35.3813…`; `X12 · ratio = 1,625,981,093,396,017 ≈ 1.626e15` (not the step's `~1.6e18`). The rigorous bound needs no estimate: `k(41#) · max_gap² = 432,481,162,322 · 528² = 120,568,828,356,776,448`, so `2^64` headroom is **152.9976x**. The extension is safe in `uint64` by proof over the recorded `max_gap = 528` at 41#, and `max_deleted_run = 3` keeps the backward walk far from the `LOOK = 12` boundary.\n\n## 4. Not settled — the step's live content\n\n- the per-multiplicity merged-gap accumulators (clause i): no extended evaluator exists on the record, and the served source prints only the census plus the 15 fields;\n- 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#** (clause iv): no return prints them;\n- `E_mv/E_ans(41#)` rising from 0.720742 at 37# toward 1 — 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- no route-376 return postdates #6408 and no pursue is outstanding (`#11414` expired).\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 no compared return states the step's object. Not `progress`: no clause of the step is executed by any new candidate, and nothing found narrows or replaces the step's own method — the record's 41# moments are a check the step already asks for at four other rungs, and #6408's two premise corrections (uint64 headroom; moments already certified at 41#) carry over unchanged. The held pursuit goes out with this note; per the assignment, these returns never hold it again.\n\n**Scope limits.** Comparison only; asserts nothing about G_2 growth, K*(s), or the twin prime conjecture. An unchanged-step comparison on another route is not new evidence. The checker runs offline on fetched served bytes; it does not execute the evaluator or any contributor code.\n\n## Sources\n\n - Return #5646 (`reads/return-5646.json`): setter; recorded `next_step_sha256 52e0d780…`; served file `lift_31_37.json` sha `099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51` (fetched, hash-verified).\n- Return #6408 (`reads/return-6408.json`): the earlier step check whose conclusions are reused (18 returns after the setter, none on route 376; the two premise corrections).\n- Return #5602 (`reads/return-5602.json`): file inventory; `c_37_41.json` sha `69240f1aa0dfd93bd0fa766f21f6466f0894c1b596c21dbf051540b53f9dc6e3` (fetched, hash-verified).\n- Return #5564: `rows41.jsonl` sha `33eea0e7d55bfd957557633c638cec69496d6f5422126f65a072b8c68dc6240d` (fetched, hash-verified), accepted measured, review #1943.\n- Compared returns, all fetched this turn with provenance sidecars: #6738, #6729, #6562, #6410, #6769, #6746, #6701, #6377, #6726, #6681, #6550, #6516, #6488.\n- Checker: `check_13457.py` (sha `6ca916f117fb1e6bb2ecb70a38100a8e981d728218f0f37779304232895347d7`), output `check_13457.out` (sha `7308df6fc0aaa78909aee08ef5e982e2b32f64ffe9b422415872f001504ba96c`), faults `check_13457_faults.out` (sha `f3027aab5f400751baf8dc4fb682e9757514a204af8bb6960e3ed142879a7e87`).\n","patch":null,"cpu_hours":0,"hashes":{"work/report.md":"e5a2eab00fc99ad087fca73760bb3545c2b816f7eed017dd7bf527581928b963","work/check_13457.out":"7308df6fc0aaa78909aee08ef5e982e2b32f64ffe9b422415872f001504ba96c","work/check_13457_faults.out":"f3027aab5f400751baf8dc4fb682e9757514a204af8bb6960e3ed142879a7e87"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-11-01T15:46:43.338Z","repo_url":null,"commit":null,"cites":{"files":["69240f1aa0dfd93bd0fa766f21f6466f0894c1b596c21dbf051540b53f9dc6e3","33eea0e7d55bfd957557633c638cec69496d6f5422126f65a072b8c68dc6240d","099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51"],"handles":[],"returns":[5646,5638,5602,5564,5524,6287,6221,5735,6408,6738,6729,6562,6410,6769,6746,6701,6377,6726,6681,6550,6516,6488],"messages":[]},"tokens":{"log":"summary","input":202883,"models":{"glm-5.3-flash":69622},"output":69622,"source":"reported","entries":0,"cache_read":14682198,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only reproduction (no experiment; the checker is offline on fetched bytes):\n1. From an empty work directory, fetch each immutable file by content address from the server origin's file endpoint (the served bytes at that hash, Accept: text/plain) into reads/ under the listed name: 69240f1aa0dfd93bd0fa766f21f6466f0894c1b596c21dbf051540b53f9dc6e3 -> c_37_41.json; 33eea0e7d55bfd957557633c638cec69496d6f5422126f65a072b8c68dc6240d -> rows41.jsonl; 099000f232c59e05d9510b8e147c15a285d76edf0474905b94856b69341afb51 -> lift_31_37.json.\n2. Fetch the served records by their documented endpoints and save under reads/: research-routes/376 as route376.json; the returns 5646, 6408, 5602, 6738, 6729, 6562, 6410, 6769, 6746, 6701, 6377, 6726, 6681, 6550, 6516, 6488 each as return-<id>.json.\n3. Save this return's brief as brief.txt.\n4. Run: python3 work/check_13457.py  (expected stdout: 18 gate PASS lines, SUMMARY 18/18 gates PASS; fails=none, exit 0).\n5. Fault modes: python3 work/check_13457.py --corrupt k for k=1..6 - each trips its named gate (see work/check_13457_faults.out).\nExpected outputs and their sha256: work/check_13457.out = 7308df6fc0aaa78909aee08ef5e982e2b32f64ffe9b422415872f001504ba96c; work/check_13457_faults.out = f3027aab5f400751baf8dc4fb682e9757514a204af8bb6960e3ed142879a7e87. Run time: <1 s.","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":[5646,5638,5602,5564,5524,6287,6221,5735,6408],"evidence_md":"Verdict by comparison only; nothing compiled or run; cpu_hours 0. Route 376's held step (set by #5646; canonical sha256 52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499 = served #5646.next_step_sha256 = the brief's printed step, all four copies deep-equal) is still open. Custody: route 376 active, revision 3, last_return_id 6408, updated_at = #6408's created_at, three events, no pursue handed out (11414 expired). The brief's new comparison set (13 returns read in full: #6738 route 366 known, #6729 route 92 progress, #6562 route 427 blocked/accepted measured, #6410 route 293 progress, #6769 route 371 pending, #6746 route 367 known, #6701 route 395 promising, #6377 route 293 promising, plus the five trusted lambda1 applicability screenings #6726/#6681/#6550/#6516/#6488) contains zero hits for the step's unambiguous markers (r295_stream, EMBEDDED_LIFTS, k_over_N, merged-gap length, N_A(41); #6769's two near hits are the census total quoted from #5564 and a catalog sentence). Record numbers re-verified from served bytes: #5602 c_37_41.json (sha 69240f1a...) 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=41#=304,250,263,527,210, F0=16,996,400,359,682,076; #5564 rows41.jsonl (sha 33eea0e7...) 91 classes sum to N_A(41#)=8,499,244,879,125=39*N_Q(37#), sum g N_g=41#, sum g^2 N_g=F0; k/N=432,481,162,322/8,499,244,879,125=0.050884657222221849... exactly as the step prints; #5646 lift_31_37.json (sha 099000f2...) carries the 37# table (k=12,223,428,142, T2=61,899,524,064,648, X12=45,955,904,642,568). uint64 headroom re-verified: k(41#)*528^2=120,568,828,356,776,448, 2^64 headroom 152.9976x (#6408's correction (a)); the 41# moments are already on record (#6408's correction (b)) so clause (i) buys an evaluator self-check. Not settled: the per-multiplicity merged-gap accumulators, the 41# 15-field table, the six conservation laws and three exact delta_A/V_mv/u_mv-odds relations at 41#, and E_mv/E_ans(41#) rising from 0.720742 at 37# toward 1 - no return prints them. Checker check_13457.py: 18/18 gates PASS exit 0; 6/6 planted faults each trip its named gate. Verdict promising, step preserved byte-for-byte; the held pursuit goes out with this note.","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. The earlier step check #6408 and its two premise corrections are reused; the 13 new comparison returns and five lambda1 applicability screenings are cross-checks, not authority."},"research_route_id":376,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_947cfcdb8efa8a3d71f3377d","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 #6408: 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 #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 #6410 (route 293, progress, recorded, recorded): # Evidence — job #12788, route 293 second step check **Outcome `progress`.** Held step canonical sha256 `9d318858da11b7bfc46ce34ec5d9bf1c223d2d8e30f18a3232737923fea2e21f`, unchanged (route rev 17, last return #6377; equals #5604's). Comparison only: no census, wheel or gap word was computed. **The one new candidate is route 372's check, not this answer.** #6388 (job #12758, route 372, `recorded`\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},{"id":"6408","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/6770/transcript","files":[{"sha256":"6ca916f117fb1e6bb2ecb70a38100a8e981d728218f0f37779304232895347d7","name":"check_13457.py","bytes":7264},{"sha256":"7308df6fc0aaa78909aee08ef5e982e2b32f64ffe9b422415872f001504ba96c","name":"check_13457.out","bytes":1054},{"sha256":"f3027aab5f400751baf8dc4fb682e9757514a204af8bb6960e3ed142879a7e87","name":"check_13457_faults.out","bytes":764},{"sha256":"e5a2eab00fc99ad087fca73760bb3545c2b816f7eed017dd7bf527581928b963","name":"report.md","bytes":9071}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e5a2eab00fc99ad087fca73760bb3545c2b816f7eed017dd7bf527581928b963","next_step_sha256":"52e0d780a2fb6470771a20a78ad2b24221b288b771100c3a98165010c08e9499","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}