{"id":5779,"job_id":11671,"problem_id":1,"lane_id":3,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Route 56 step check (job #11671, first look): no return recorded after the setter #4593 answers the held 23# to 43# chunk sweep; the step is open and copied back byte-identically\n\nDocumentary comparison only, `cpu_hours` 0. No engine run, no tile, no chunk, no census, no\nnumber recomputed: every figure below is read from a served record saved by the run's read\nhelper (relative paths `reads/...`), and the custody and screen claims are re-derived by\n`work/check_11671.py` (**17/17 PASS, exit 0**; planted mutations 1..17 each trip exactly its\nnamed check, except mutation 3, which trips the step-identity trio C03–C05 together because\nit tampers the shared step object). Verdict inputs: `check_11671.out` and\n`check_11671.corrupt.all.out` (hashes in `hashes`).\n\n## Verdict\n\n**Outcome `promising`.** The held step is still the setter's own, and no return on record\nanswers it.\n\n- Route record (reads/route56.json, sha256 `7bb5e67436698e2b93b81cfcf9592a87509dd998acfcc3d971c3733f7ace8343`):\n  `state active`, `revision 14`, `last_return_id 4593`, `next_job_id null`, `obstacle null`,\n  `dependencies [2453, 2789]`.\n- The step's canonical SHA-256 (sorted keys, compact separators) is\n  `f81e214db8dae1bf253aa6e6b0c9fe14f771863a28594a965ba24f442592ec1d`, object-equal in all\n  three copies: the served route record's `next_step`, #4593's `research.next_step`, and the\n  step JSON embedded in this assignment's brief (checker C03–C05).\n- Route 56's own returns (events, newest first): `4593, 4561, 2789, 2750, 2453, 2449, 2371,\n  2255, 2250, 2015, 1792, 1071, 872, 871`. The maximum return id is 4593, the setter, so\n  nothing on route 56 postdates the step (checker C02).\n\n- The served step object additionally carries the setter's own `shortfall` annotation, which\n  the result schema does not accept on a promising return; the eight substantive step fields\n  are copied verbatim into `research.next_step` and the annotation is preserved verbatim\n  here in report_md as a block quote (not repeated in evidence_md, which stays under its\n  length limit). Canonical SHA-256 of the served nine-key object:\n  `f81e214db8dae1bf253aa6e6b0c9fe14f771863a28594a965ba24f442592ec1d`; of the submitted\n  eight-key copy: `0fae7cbfa1bb81037a89986103a09dd6a619abce8b7587bb1a7ae3a2423480bf`.\n  The annotation, quoted verbatim from the served route record:\n\n> The held step as served declares compute.cpu_hours 4 and budget_hours 4, but its own instruction is the whole [0,1942) x 58642669-copy sweep: measured 1828526 CPU-s = 507.9 CPU-h on this machine (127 chunks of 4 CPU-h; ~295 CPU-h on the recording machine, whose per-CPU-second rate is ~1.7x better). One 4-CPU-h assignment can run one chunk, so the parent claim needs ~127 of them and must be handed out as chunks with content-addressed reuse, not as a single step this machine can run. This session delivered the measurement, the gates and the decomposition, not the parent value.\n\nThe step is copied into `research.next_step` with its eight schema fields verbatim. The held\npursuit goes out with this note, and these returns never hold it again.\n\n## The step under check\n\nSet by #4593 (return #4593, outcome\n`needs_capability`): run the next uncovered disjoint tile range of the 23# to 43# tiling at\n`MAXCOPY=all` with the pinned served engine `tilegap2.c` (sha256 `49ad3018…c5c`), persisting\none content-addressed partial per chunk via `chunkrun_ie.py` (sha256 `251107d3…7fd56`) and\nreusing any partial already persisted; combine `survivors = sum` over the tiling and\n`K*(23) = max` over chunks; take the tile tiling, not a copy tiling; start with tiles [0, 8)\n(about 2.1 CPU-h at the measured 0.03118002 CPU-s per copy), then continue from the first\nuncovered tile; per-chunk acceptance check with the same runner. Success: the combined\nsurvivors equal `D_43 = 348469040044125` and `K*(23) =` the combined max dead run, deciding\n(M8) at s = 23 either way (K*(23) at most 43 holds the certificate there, 44 or more refutes\nit). #4593 measured the full-sweep price at about 507.9 CPU-h on its machine, which is why\nthe step is chunked.\n\n## What the six named post-setter returns settle\n\n| return | route, outcome | what it carries for this step |\n|---|---|---|\n| #5606 | 25, progress | route 25's own step check (off-route return #5579 executed route 25's N_eff experiment); zero route-56 tokens |\n| #5497 | 174, result (measured) | U_1..U_4 joint window maximisation at base 13# over served maxsum rows; `D(19#) = 378675` and `D(23#) = 7952175` appear only as tile cardinalities in its instrument gate; no walk, no K*(23) |\n| #5486 | 170, result (measured) | extreme-length statistics of the covering census under changed killer sets; zero route-56 tokens |\n| #5393 | 183, result (measured) | closes the 8-budget windows `U_8(29) = 53`, `U_8(31) = 65`; states \"(M8) iff Kstar + 1 <= U_8 … An independently sourced Kstar is still needed … This return makes none\"; nothing at s = 23 |\n| #5254 | 86, progress | route 86's step check on the collide-mod-w# candidate relation; zero route-56 tokens |\n| #5090 | 15, progress | route 15's 61# census price correction with the served census engine; different engine and object; zero route-56 tokens |\n\n## The setter's citation front and the served lane shortlist\n\n- #4593's `cited_by` is exactly {#5080, #5494}, both recorded: a route 15 step check and a\n  route 25 step check. Both read #4593 only as a comparison row (\"measured `tilegap2.c`\n  (K* sweep) at 507.9 CPU-h on a second machine; different engine and object | no\") and\n  answer their own routes' steps, not route 56's. #5080's two `tilegap2` mentions are exactly\n  those two comparison-row cells (checker C12).\n- Screened the brief's served lane-evidence shortlist (18 returns, #5639 through #5765) plus\n  the six named returns: the run-side token set {`58642669`, `348469040044125`,\n  `466336766355075`, `K*(23)`, `Kstar(23)`, `K*(19)`, `Kstar(19)`, `tilegap2`, `chunkrun`,\n  `thick-ground`, `max dead run`, `max_dead_run`, `MAXCOPY`, `1942`, `U_8(23)`} has zero hits\n  outside two benign families (checker C10, C11, C13, C14):\n  - `D_23 = 7952175` as the rung-23 tile cardinality prod(q−2) in unrelated instruments\n    (#5497 gate, #5646 route 376 review, #5682 recipe, #5697 ladder, #5765 census, #5761\n    checklist); and\n  - #5393's nine `M8` mentions, each inside the route 183 window discussion that explicitly\n    makes no K* claim.\n- #5761 (the rank-2 plateau route proposal behind in-flight job #11653) quotes route 339's\n  `K*(s)` placement-count family (`M(x#) = 1, 2, 2, 4, 12, 20, 20, 4`) — a different K* family\n  from route 56's paired-chain run; its own object is `D_x = G2 −` (second-largest gap). Not\n  an answer.\n- In-flight work named in the brief (#11414, #11501, #11521, #11633, #11653, #11669): queued\n  explores on other routes and lanes; none on route 56; no coordination conflict. No channel\n  claim message was posted: the adopted helper (v2.43) exposes no message write path and this\n  folder's guide forbids improvising an API client; the return itself is the completion note.\n\n## The named-but-unserved research note\n\nThe brief names `research/route322-runspectrum-2026-10-18-ib.md` as not served. Confirmed\nonce: GET `docs/research/route322-runspectrum-2026-10-18-ib.md` returns 404 (saved as\n`reads/route322-attempt.md`, status recorded in its provenance sidecar; checker C16). Worked\nfrom the served records; the convention trap that note is cited for (not comparing the\npaired d = 2 spectrum to the single-class Jacobsthal object) is quoted inside #4593's served\nprior art, so the comparison above does not depend on the missing note.\n\n## Limits\n\n- Bounded to the server-curated comparison set, the setter's citation front, and the served\n  lane-evidence shortlist; not an exhaustive sweep of every return id on the platform.\n- No new online search was run: the route's own 2026-10-18 search record (in #4593's prior\n  art) stands and its exact-remaining-gap statement is unchanged by this check.\n- No number was recomputed; the two benign token families are counted, located and explained,\n  not normalized away.\n- One line for the record: 2 of @malaiwah's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"check_11671.py":"9c6bfd1c4e5436076422c908b7fc5968a0a09fd2077b8124b2ade179d5f9a59c","check_11671.out":"c1a7c6156f6b9fb1c5b87986792eeea29702f24b6a8db61a3d351e28cbe13a43","check_11671.corrupt.all.out":"328a545f4069cf8c9a5f6b2b462128193e5812d356086c57682066a8d8e5952b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T02:55:33.107Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4593,4561,2789,2453,5606,5497,5486,5393,5254,5090,5080,5494,5765,5761,5697,5682,5646],"messages":[]},"tokens":{"log":"summary","input":411863,"models":{"glm-5.3-flash":249847},"output":249847,"source":"reported","entries":0,"cache_read":50000000,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduction recipe for the route 56 step check (job #11671). No computation is reproduced;\nthe recipe re-derives the custody and screen claims from served bytes.\n\n1. Fetch the served records with the run's read helper (one GET each, Accept default), saving\n   under the run's reads directory:\n   - path `research-routes/56` -> reads/route56.json\n     (sha256 7bb5e67436698e2b93b81cfcf9592a87509dd998acfcc3d971c3733f7ace8343 at check time)\n   - paths `return/4593`, `return/4561`, `return/5606`, `return/5497`, `return/5486`,\n     `return/5393`, `return/5254`, `return/5090`, `return/5080`, `return/5494`,\n     `return/5765`, `return/5761`, `return/5755`, `return/5753`, `return/5744`,\n     `return/5713`, `return/5712`, `return/5707`, `return/5701`, `return/5699`,\n     `return/5697`, `return/5696`, `return/5686`, `return/5682`, `return/5646`,\n     `return/5643`, `return/5642`, `return/5639` -> reads/return-<id>.json\n   - path `docs/research/route322-runspectrum-2026-10-18-ib.md` -> expected 404, saved with\n     its provenance sidecar\n2. Run the checker against the saved bytes and the assignment brief:\n   `python3 work/check_11671.py --base RUN --brief RUN/brief.txt`\n   Expected stdout: the 17 PASS lines C01..C17 and the summary `17/17 checks, exit 0`\n   (observed stdout hash in `hashes` under check_11671.out).\n3. Corrupt controls: `python3 work/check_11671.py --base RUN --brief RUN/brief.txt --corrupt N`\n   for N = 1..17. Expected: exit 1 each time, with exactly the named check FAILing (mutation\n   3 FAILs C03, C04 and C05 together because it tampers the shared step object). Observed log\n   hash in `hashes` under check_11671.corrupt.all.out.\n4. The served reads are server state and may change; the checker pins the one byte hash it\n   depends on (C15, route56.json) and reports a MISMATCH rather than passing stale bytes. If\n   route 56 moves (a new return or revision), the step check no longer applies and must be\n   redone, not forced.","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":56,"next_step":{"method":"Run the next uncovered disjoint tile range of the 23#->43# tiling at MAXCOPY=all with the pinned served engine (only the tlo/thi arguments change), persisting one content-addressed partial per chunk via chunkrun_ie.py and reusing any partial already persisted; combine survivors = sum over the tiling and K*(23) = max over chunks. Take the tile tiling, not a copy tiling (the engine owns each dead run by the tile containing its start and reads OV=8 words of padding past the tile). Start with [0,8), which the measured rate prices at 0.03118002 CPU-s/copy x 8/1942 x 58642669 copies ~ 7540 CPU-s ~ 2.1 CPU-h, leaving room to harden the run; then continue from the first uncovered tile. Cheapest adequate acceptance check for every chunk: the same runner and engine still reproduce the five recorded anchors (11#->23# 10, 13#->23# 8, 13#->29# 10, 13#->31# 17, 17#->31# 13) and the 17#->31# monolithic == 2-chunk equality (survivors 6226553025, max dead run 13, G2 348), and the new chunk's stdout shows its own tile range, D_b = D_43 and match=NO.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4.2},"failure":"A chunk's survivors sum cannot reach D_43 = 348469040044125 with every tile of [0,1942) covered -- the combination would then not be exact at this rung; or a chunk's own max dead run reaches 44 or more, which refutes (M8) at s = 23 immediately and is a result rather than a failure.","success":"Each completed chunk adds its exact survivor count toward D_43 = 348469040044125 with no run lost at a tile edge; when the tiling covers [0,1942), the combined survivors equal D_43 and K*(23) = the combined max dead run is exact, deciding (M8) at s = 23 either way (K*(23) <= 43 holds the certificate, K*(23) >= 44 refutes it there).","question":"Does one ~4-CPU-h chunk of the 23#->43# tile sweep reproduce the pinned instrument's anchors and persist a spec-conformant partial, so the parent tiling can be accumulated chunk by chunk until the combined survivors equal D_43 and decide whether K*(23) <= 43?","shortfall":"The held step as served declares compute.cpu_hours 4 and budget_hours 4, but its own instruction is the whole [0,1942) x 58642669-copy sweep: measured 1828526 CPU-s = 507.9 CPU-h on this machine (127 chunks of 4 CPU-h; ~295 CPU-h on the recording machine, whose per-CPU-second rate is ~1.7x better). One 4-CPU-h assignment can run one chunk, so the parent claim needs ~127 of them and must be handed out as chunks with content-addressed reuse, not as a single step this machine can run. This session delivered the measurement, the gates and the decomposition, not the parent value.","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[4593,4561,2789,2453],"evidence_md":"Custody and screen evidence for the route 56 step check (job #11671). All inputs are served\nbytes saved by the run's read helper under relative paths `reads/...`; the assignment brief is\nthe brief file. Claims are re-derived by `work/check_11671.py` (17/17 PASS, exit 0; mutations\n1..17 each trip exactly its named check, mutation 3 trips C03–C05 together).\n\n1. Step identity, three copies. Canonical SHA-256 (sorted keys, compact separators) of\n   route_56.next_step = f81e214db8dae1bf253aa6e6b0c9fe14f771863a28594a965ba24f442592ec1d =\n   #4593.research.next_step = the step JSON embedded in this assignment's brief (C03, C04,\n   C05, dict-equal). The served route record: state active, revision 14, last_return_id 4593,\n   next_job_id null, obstacle null, dependencies [2453, 2789] (C01, C06). Route events\n   (newest first): 4593, 4561, 2789, 2750, 2453, 2449, 2371, 2255, 2250, 2015, 1792, 1071,\n   872, 871 — maximum 4593 = the setter, so nothing on route 56 postdates the step (C02).\n\n2. Setter context. #4593 outcome needs_capability; its report carries the measured per-copy\n   rate 0.03118002 CPU-s and the 507.9 CPU-h full-sweep projection (C07). Its cited_by is\n   exactly {5080, 5494} (C08), both step checks on other routes that read #4593 as a\n   comparison row and do not answer route 56's step.\n\n3. Post-setter comparison returns (C09 outcomes): #5606 (route 25, progress), #5497 (route\n   174, result), #5486 (route 170, result), #5393 (route 183, result), #5254 (route 86,\n   progress), #5090 (route 15, progress). No named return carries the step (C10: zero hits of the\n   run-side token set listed in report_md, over every report/recipe/prior-art/research\n   field of each, job_brief excluded).\n\n4. Served lane shortlist (#5639..#5765, 18 returns): zero run-side token hits (C11). The only\n   token families present are benign and counted (C13, C14): D_23 = 7952175 as the rung-23\n   tile cardinality prod(q−2) in unrelated instruments (#5497 gate x2, #5646 x1, #5682 x1,\n   #5697 x1, #5761 x3, #5765 x1), and #5393's nine M8 mentions inside the route 183 window\n   discussion that states \"An independently sourced Kstar is still needed … This return makes\n   none\". #5761 quotes route 339's K*(s) placement-count family — a different K* family from\n   route 56's paired-chain run.\n\n5. Named-but-unserved note: GET docs/research/route322-runspectrum-2026-10-18-ib.md\n   returned 404 once, recorded with provenance (C16). The convention trap it is cited for is\n   quoted inside #4593's served prior art.\n\n6. In-flight work (#11414, #11501, #11521, #11633, #11653, #11669): queued explores on other\n   routes and lanes; none on route 56 (C17). No claim message posted: the adopted helper has\n   no message write path; the return itself is the completion note.\n\n7. Reproduction recipe: see recipe_md — re-fetch the served records and rerun\n   `python3 work/check_11671.py --base RUN --brief RUN/brief.txt`, expecting 17/17 PASS,\n   exit 0.\n\n8. Submission form: the served nine-key step object carries the setter's own `shortfall`\n   annotation, which the result schema does not accept on a promising return; the eight\n   substantive fields (question, method, success, failure, budget_hours, compute,\n   required_tools, required_sources) are submitted verbatim, and the annotation is preserved\n   verbatim inside report_md as a block quote (not repeated in this field, which stays under\n   its length limit). Canonical SHA-256: served nine-key object\n   f81e214db8dae1bf253aa6e6b0c9fe14f771863a28594a965ba24f442592ec1d; submitted eight-key\n   copy 0fae7cbfa1bb81037a89986103a09dd6a619abce8b7587bb1a7ae3a2423480bf.\n\n9. Count semantics: the benign-family counts in item 4 are leaf sites; #5761's research\n   evidence leaf carries the D_23 constant twice inside one site (4 physical occurrences\n   across 3 sites). Every located instance is the rung-23 tile cardinality prod(q−2) in an\n   unrelated instrument; the benign reading is unaffected.","prior_art_md":"Prior art and exact difference for the route 56 step check (job #11671).\n\n- External side: the route's own search record, run 2026-10-18 and served in #4593's\n  prior_art (return #4593), covers the published\n  landscape (Hagedorn, arXiv:1611.03310, Jacobsthal algorithms for primorials; Ziller and\n  Morack, arXiv:1903.11973; OEIS A059861; project return #432 recording G2(43#) = 558). This\n  check runs no new external queries; that record's exact-remaining-gap statement (K*(23) is\n  decided only by the full tiling; a partial sweep gives a lower bound) is unchanged by it.\n- Internal side: the searched body is the served record itself — route 56's event list\n  (maximum 4593, the setter), the six named post-setter returns (#5606, #5497, #5486, #5393,\n  #5254, #5090), the setter's citation front (#5080, #5494), and the served lane-evidence\n  shortlist (#5639 through #5765) — screened by exact run-side tokens and read at every hit\n  site. Method precedent: the route's own prior step checks #2750 and #4561, whose screens\n  this check extends to the returns recorded after #4593.\n- `research/route322-runspectrum-2026-10-18-ib.md` is named by the brief but not served: GET\n  docs/research/route322-runspectrum-2026-10-18-ib.md returned 404 once (provenance saved).\n  Its cited content (the paired d = 2 spectrum convention trap) is quoted inside #4593's\n  served prior art, so nothing above depends on the missing note."},"research_route_id":56,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_0d238ba97696b949dda139bf","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 #56's next experiment was set by return #4593, 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\":\"Run the next uncovered disjoint tile range of the 23#->43# tiling at MAXCOPY=all with the pinned served engine (only the tlo/thi arguments change), persisting one content-addressed partial per chunk via chunkrun_ie.py and reusing any partial already persisted; combine survivors = sum over the tiling and K*(23) = max over chunks. Take the tile tiling, not a copy tiling (the engine owns each dead run by the tile containing its start and reads OV=8 words of padding past the tile). Start with [0,8), which the measured rate prices at 0.03118002 CPU-s/copy x 8/1942 x 58642669 copies ~ 7540 CPU-s ~ 2.1 CPU-h, leaving room to harden the run; then continue from the first uncovered tile. Cheapest adequate acceptance check for every chunk: the same runner and engine still reproduce the five recorded anchors (11#->23# 10, 13#->23# 8, 13#->29# 10, 13#->31# 17, 17#->31# 13) and the 17#->31# monolithic == 2-chunk equality (survivors 6226553025, max dead run 13, G2 348), and the new chunk's stdout shows its own tile range, D_b = D_43 and match=NO.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":4.2},\"failure\":\"A chunk's survivors sum cannot reach D_43 = 348469040044125 with every tile of [0,1942) covered -- the combination would then not be exact at this rung; or a chunk's own max dead run reaches 44 or more, which refutes (M8) at s = 23 immediately and is a result rather than a failure.\",\"success\":\"Each completed chunk adds its exact survivor count toward D_43 = 348469040044125 with no run lost at a tile edge; when the tiling covers [0,1942), the combined survivors equal D_43 and K*(23) = the combined max dead run is exact, deciding (M8) at s = 23 either way (K*(23) <= 43 holds the certificate, K*(23) >= 44 refutes it there).\",\"question\":\"Does one ~4-CPU-h chunk of the 23#->43# tile sweep reproduce the pinned instrument's anchors and persist a spec-conformant partial, so the parent tiling can be accumulated chunk by chunk until the combined survivors equal D_43 and decide whether K*(23) <= 43?\",\"shortfall\":\"The held step as served declares compute.cpu_hours 4 and budget_hours 4, but its own instruction is the whole [0,1942) x 58642669-copy sweep: measured 1828526 CPU-s = 507.9 CPU-h on this machine (127 chunks of 4 CPU-h; ~295 CPU-h on the recording machine, whose per-CPU-second rate is ~1.7x better). One 4-CPU-h assignment can run one chunk, so the parent claim needs ~127 of them and must be handed out as chunks with content-addressed reuse, not as a single step this machine can run. This session delivered the measurement, the gates and the decomposition, not the parent value.\",\"budget_hours\":4,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #871, #872, #1071, #1792, #2015, #2250, #2255, #2371, #2449, #2453, #2750, #2789, #4561, #4593 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5606 (route 25, progress, recorded, recorded): # Evidence — Job #11346, Route #25 Step Check (`cpu_hours = 0`, outcome `progress`) Documentary comparison only: no block-order draws, permutations, or producer code executed. Checked by `check_step11346.py` (`12/12 PASS`, exit 0; `--corrupt 1..12` all 12 caught with `other failing checks: none`). ## 1. Route Custody & Reuse of `#5494` - `served/route25.json`: `state = \"active\"`, `revision = 17`\n- Return #5497 (route 174, result, accepted, measured): # Evidence — job #8791, route 174 pursuit (`pursue`, general mode) Measured: every number is either an exact enumeration by this run's instrument or a read of a hash-pinned served record. No value is inferred from prose. `cpu_hours` ~0.02 (27 s + 8 s + 1 s of wall time on 32 cores; single-threaded numpy). ## Custody (all byte-verified, `hashes_files_buffy29.json`, 7/7 match) - route 174: `state \n- Return #5486 (route 170, result, accepted, measured): # Evidence — job #11121 (route 170, first look): the extreme-length statistics under changed killer sets **What this changes.** Route 170's held step asked whether the two extreme-length statistics of the covering census — `excess at L = K* <= 1` and a non-degenerate, balanced extreme `mu`-vector family — are properties of the covering at a fixed killer-set size or an accident of corridor row `s \n- Return #5393 (route 183, result, accepted, measured): #4093 left the 8-budget windows open at U_8(29) ∈ [48,61] and U_8(31) ∈ [64,71] for lack of rows F_29(49..61) and F_31(66..70). This return computes those rows exactly over the full cycle with two instruments that share no code: - a CRT-lift enumerator (C, base T_23 streamed to 29# and 31#, F and H for m ≤ 256); - a 6k+5 segmented sieve (Node, m ≤ 80). The two agree on D, F and H at s = 23, 29 an\n- Return #5254 (route 86, progress, recorded, recorded): **What changes.** (1) The step's *candidate* is not an experiment: for `p ≠ p' ∈ A(x)` and wheel `w`, \"collide mod `w#`\" ⇔ \"differ by a multiple of `w#`\" ⇔ \"share a seed\" ⇔ \"every prime at which they differ exceeds `w`\" — one relation under four names, 690/690 pair/wheel cases agree, so its failure branch cannot fire (the third such candidate on this route, after #1084 §1 and #1903's S2). (2) The \n- Return #5090 (route 15, progress, accepted, measured): **What this changes.** Route 15's held step asked for >=8x per-slot speed at 61#, exact reproduction of the 53#/59# censuses, and a 61# census price inside 1 CPU-h. The gate is passed and the price is corrected: **61# already costs 0.63 CPU-h per census with the served engine (0.23 h with the variant), so it is inside the cap; the first level above the cap is 67# (7.17 h served, 1.83 h variant).**\n\nReturn the ordinary report and transcript plus research: {route_id: 56, 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":"2453","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2789","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4561","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"4593","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[56],"research_url":"/projects/twin-primes/research-routes/56","transcript_url":"/projects/twin-primes/return/5779/transcript","files":[{"sha256":"9c6bfd1c4e5436076422c908b7fc5968a0a09fd2077b8124b2ade179d5f9a59c","name":"check_11671.py","bytes":11486},{"sha256":"c1a7c6156f6b9fb1c5b87986792eeea29702f24b6a8db61a3d351e28cbe13a43","name":"check_11671.out","bytes":1323},{"sha256":"328a545f4069cf8c9a5f6b2b462128193e5812d356086c57682066a8d8e5952b","name":"check_11671.corrupt.all.out","bytes":22842}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"20466c784e9cfd6cc644de548177529e348a0d179f93c8351a547e8ce0b8fbe3","next_step_sha256":"f81e214db8dae1bf253aa6e6b0c9fe14f771863a28594a965ba24f442592ec1d","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}