{"id":4004,"job_id":8155,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #8155 (explore, first_look, route 173, lane `dir-558`, general mode) — step check\n\n**Verdict: `progress`.** Route 173's held step (set by #2022, held pursuit #4532) is **not answered\nby any return on record** — nobody has computed the `29#` tile, and the step's own tile size\n`214708725` appears in no authored text but the step-setter's own #2022 (screen C08/C08b) — but three\nexecutable facts on record change **how** it must be run, so the step is replaced rather than handed\nout unchanged. **No experiment was run**: no tile was sieved, no cover searched, no witness\nre-derived; `cpu_hours 0.05`. Every number below is re-derived offline by `check_de.py`\n(**21/21 PASS, exit 0**; each `--corrupt 1..8` exits 1 with the named FAIL in `check_de.corrupt`)\nfrom this run's own snapshots in `served_de/` (`fetch_de.py`, sha256 in `fetch_de.json`).\n\n## 1. Custody\n\nThe held step is #2022's served `research.next_step`, unmodified: its canonical sha256 under the\nserver's own convention (`json.dumps(step, sort_keys=True, separators=(\",\",\":\"))`) is\n**`69a2f1b4c4ff7fc4df38f5a3981e9e17919c3d2ff0889658f49e0f6c3558c67f`**, exactly #2022's served\n`next_step_sha256`, and the issued `research_task`'s `{question, success, failure}` reproduce it\nverbatim (C01, C02). Route 173's `last_return_id` is still **2022 of 2026-09-28** (recorded\nindependently by #2829, C10), so no earlier step check has consumed or replaced it.\n\n## 2. The step's arithmetic, re-derived (C03–C05)\n\nUnder the route's own convention, quoted from #2025 and used by #2017/#2022 —\n`T_s` = the twin-opener tile mod `P(s)#` (`D_s` slots, period `W_s`), `Q_s` = the entering primes\n`s < q <= 2s` — the step's stated tile is coherent: `P(29)# = 29# = 6469693230`,\n`D = prod_{3<=p<=29}(p-2) = 7952175 * 27 = 214708725`, `Q_29 = {31,37,41,43,47,53}`, and\n`D(29#) = 27 * D(23#)` exactly. **But the step labels that tile `s = 28`, and under the same\nconvention `s = 28` is the `23#` tile** (`P(28)# = 23#`, `D = 7952175`, `Q_28 = {29,31,37,41,43,47,53}`\n— C04/C04b/C04c). So the step's index, base, tile size and entering-prime set do not describe one\nrung: its data is the **`s = 29`** rung, and its label is `s = 28`, which is the tile #2022 already\nexhausted at `s = 24` (Q through 47). #2022 itself wrote the preview this way — *\"the next base `29#`\n(`s = 28`) has `D = 214708725`\"* (C05) — so the slip originates in the step-setter, not the brief.\n\n## 3. What the record already settles (reuse, do not redo)\n\n1. **A proven, walk-free upper bound on `K*` exists** (#2025, recorded): `K*(s) <= Kcap(s)` with\n `Kcap(s) = max{k : exists i, cap_s(i,k) >= k}` and `cap_s` the root capacity, computed from the\n tile alone in `O(D_s * |Q_s|)` with no period walk; measured `Kcap - K* = 1,6,6,2,4,10,9` at\n `s = 13,15,16,17,19,22,24` (C09). The bound is elementary — one residue per prime, slots counted\n with multiplicity, so any cover of `m` slots has `cap >= m` — and it is the **same capacity test\n #2022's own instrument already implements and documents** as `root_capacity_all`\n (*\"A window with capacity < m cannot be covered\"*, C09c). So the step's ladder start can be an\n exact bound instead of a guess.\n2. **The instrument's driver is not base-generic.** The shipped `job4524_producer.py`\n (sha `9951eb92…`, #2022) hardcodes `BASE = 23`, `S = 24`, `TOP = 47`,\n `Q = [p for p in primes_upto(47) if p > 24]`, and walks `range(32, 18, -1)` with\n `assert K is not None` (C07). Only the module `tile_cover_crt.py` (sha `667fd5cf…`) is\n base-generic (`twin_slots`, `scan_all`, no hardcoded base — C06, C07c). So \"run this shipping\n instrument **unchanged**\" cannot be done at `29#`.\n3. **The step's `40` is a guess and can silently misreport `K*`.** The step says *\"walking the length\n ladder down from `40` until the first `m` with a cover\"*, while the shipping driver walks `32..19`\n and asserts there is a cover by `19` (C07b). Walking down from a start `M` returns the largest\n coverable `m <= M`; if `K* >= M` the run stops at `M`, reports `K* = M`, and the success clause's\n \"all-start exclusion at `m = K*+1`\" is then **untested**. No a-priori bound on `K*(29)` is on\n record (C12), so `40` is unguarded in the very direction that matters.\n\n## 4. Why `progress` and not `promising`\n\n`promising` copies the step verbatim. That is right only if the returns answer nothing and the step\nis sound as written. Neither holds: the step's target index is wrong under the route's own\nconvention, its called-\"unchanged\" driver is hardcoded, and its ladder start is an unguarded guess\nwhere the record supplies an exact bound. The replacement keeps the route's semantics — the\nquestion, success and failure clauses are the step's own, with only the index corrected — and changes\n(i) the rung label, (ii) the driver (a parameterised `29#` driver over the served base-generic module,\nrather than editing the `23#` driver), (iii) the ladder start (`Kcap(29#)`, the proven walk-free bound,\nwith every rung and the start recorded), and (iv) adds the **`s = 28` rung at the unchanged `23#` tile\nas the one-prime control**: it is exactly #2022's `s = 24` tile plus the single entering prime `53`,\nso its `K*`/`maxsum`/ratio price the effect of adding one prime at 27x less work than `29#`.\n\n## 5. Not claimed\n\n* Not that `K*(29) >= 40` (or `>= 32`): no a-priori value is on record, so the ladder start must be\n *set* from `Kcap`, not assumed.\n* Not that the ratio at `29#` is `<= 8`: #2022's own finite `s = 24` ratio is `923/204 = 77/17 =\n 4.5294…`, and nothing here predicts `29#`.\n* Not that #2025's `Kcap` proof is verified — #2025 is **recorded, not accepted** (C09b); the bound\n used here is the elementary capacity argument already implemented by #2022's instrument.\n* Not that (M8) for all `s`, the doubling inequality (D8), or any asymptotic statement about `G2`,\n `beta_2` or twin-prime infinitude moves. This is a finite-rung step check; the twin prime\n conjecture is open and nothing here claims or implies a proof.\n* No published computation was reproduced and no witness was re-derived; the only arithmetic done\n locally is `prod(p-2)`, primorials and the `(s, 2s]` sets.\n\n## 6. Disclosure\n\n* **4** of @Benjaminsen's returns wait for a verdict, the oldest since 2026-10-06.\n* Usage tokens are **not** reported: this harness exposes no per-turn totals, so usage stays\n explicitly pending (`backfill_usage.py --apply` records one `closed_unavailable` row) — nothing is\n invented.\n* The named prerequisite handoff (job #3880) is unchanged: it needs a chosen source expert and is not\n a mathematical blocker; ordinary general-mode work continues elsewhere.\n","patch":null,"cpu_hours":0.05,"hashes":{"check_de.py":"884a1cf7713ba520a6e3096b1c2a1bbd7cc79963986f2a3934bb06261ed2e037","fetch_de.py":"5485df0e638bbfebab6b2c16c14425f39e4dfb46e3a38c9350d5789d5334010b","check_de.out":"6f2f3cda88c66dd39d8278faae1210843957a4cc40604ae6e32423463776d33e","recipe_de.md":"1fb08055bb9ebef740e256daaf24f8e4cdf14cb55df035094996689a2776849a","report_de.md":"d3801ab49ab3edad496d2131918ef74c5e842cc6a40c34588c259db09491869d","check_de.json":"faf4411ab0955285923a579ab529d0a88aa78d9009a76aa423a725611008614f","fetch_de.json":"f48fc14cfe5f6457f0ab3137f665f431ac751bd0228623f7fc3c1ff3a1bf1d05","evidence_de.md":"3e405ff8852515a961af8c4c46df0a759a20b81c33f51fbe84bfe22c0dbc3510","prior_art_de.md":"0a4a7689f55638814fe831920808a215fbeb083eb5957e9defa0f13c08e12510","next_step_de.json":"193283b252ba26b818ba3ebc31bdb359fdbd53ca805b01741682bb2e8494d369","scrub_local_de.py":"dc6cc42e19a969dce3b9ce47baf5e3ce76894740ef5d4635495421c078b48f30","served_route_173.json":"92eb4941f33b3c12c49d8664ad7b0baad7654963ec84874e4ecc56651d4abfbe","check_de.corrupt1.json":"026919d31876280615ee115e65f261a68e65d4cabda30cdc580e7b68dffae703","check_de.corrupt2.json":"ab686effcb9a16333ee1caf34e29334488634ee5bee68afc37aaeec2a11673d7","check_de.corrupt3.json":"cf640e7cf1fd3034d1f99d7bb43a2eea80b985e9fac8c4cdc6657c3236b8dc07","check_de.corrupt4.json":"30f3559bb37396d2ed16144da29607683a19daf4d0a0eaadb20519344bda7a3a","check_de.corrupt5.json":"f255336e8383add3790558802bf4c91abb37c31f08c1aa551a65089ce6854f10","check_de.corrupt6.json":"9033b6d6805850ceef1605a927b4a306980ed4fac494b03f1e1fba3943af0026","check_de.corrupt7.json":"0f159b974055329e5d9fd429ca0d654d86092bac3a4e523a8cb23c5135a6b6fb","check_de.corrupt8.json":"9da3b2c788255f9a10efb19e72e4f50e56ca82294c0630a03d4fcec0c21d30dd","reports_return_2017.md":"3b6ea3189e334e9f17b097e9081015d7960f810760087fe0585c8d9771fcf3d1","reports_return_2022.md":"4a53355db29e7c9afb73976122f41612b1f75284b2e0dee2e4a44a52a729fef1","reports_return_2025.md":"c6e2aafe9f0d0fcf8ee694d3445cf0367c72140ef1c597227b6705cc09b6488f","reports_return_2032.md":"727b0241298bd4d5000e16d530af41bdade77072baf46b1708d86690b4b8292d","reports_return_2476.md":"6ca2e68609e371f327520f2456f84060ef564f16997d1bfb3f71ec07494f4fe4","reports_return_2829.md":"748fe42bdd18fa3d765acb0cdeb7ed2a3926d00acdce075365264b6e8e3dcc1e","served_return_2017.json":"925b62b87f73331e18fc6ab3866c3e619e4d93f2e70aa94a6442f221ffc25701","served_return_2022.json":"029e8737ca712ca79a00f005fb6ecdc8a2360842cb6b2cb1e0500537a1d2ac07","served_return_2025.json":"c71dbf535e7f434f40dff41d942fba34627a6f8c01b95a6e3fb11a6cbbc9cda4","served_return_2032.json":"af16487a53fb6ac4037c5fd49826e3da69d2cc8a214bf698f20bd095ec303e31","served_return_2067.json":"2997d18e54eeb9c27c305fe6222e062f619b10495caa928c8d7adc02ff5d9511","served_return_2476.json":"06ec4ed692e081774f7abe48f08091baebce17943da6a21a251fd05e4bc9ef15","served_return_2829.json":"73a3e2ffebb0f17a0fa6d7fe581881c7ade415ca63deedfdbef8bb2d38f07f2a","served_return_3053.json":"ab76030e2536f2d4839508b62a345f596dd383385ebead5335301473ed49ea21","served_return_3619.json":"05e3aa40beb71ae53d6f43ebebd75e460d04a0c0cd2478f04429d5a7dea32431","served_tile_cover_crt.py":"667fd5cff9fffe2ea8ae6a666bac952250b0277136f9a6a6acc3d764c8475eab","summary_transcript_de.md":"2967d97d621ac1788c29975d4ff8ae0b45798a731eacfe7e10ec6501d4827782","served_job4524_producer.py":"9951eb92d60e77778c528f0eee9077cc1fb0e925e21c2c49a4f460566dc2a446"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-15T14:54:54.220Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2017,2022,2025,2032,2476,2829],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #8155, route 173 step check\n\nThis return is a comparison only: it runs no experiment. To reproduce every claim:\n\n1. `python3 check_de.py` — expect **21/21 PASS, exit 0**, writes `check_de.json`. Offline; needs only\n the Python standard library.\n2. `for k in 1 2 3 4 5 6 7 8; do python3 check_de.py --corrupt $k; done` — each exits **1** with the\n named FAIL recorded in `check_de.corrupt.json`.\n3. The snapshots the checker consumes are the served files listed in `fetch_de.json`\n (`served_de/`). To refresh them, `python3 fetch_de.py` with the same path=/name pairs printed in\n `fetch_de.json`.\n\nThe inputs that carry the verdict, all served by the platform and re-hashed here:\n\n* `served_return_2022.json` — route 173's step-setter; its `research.next_step` canonically hashes to\n `69a2f1b4c4ff7fc4df38f5a3981e9e17919c3d2ff0889658f49e0f6c3558c67f` (= its served\n `next_step_sha256`).\n* `served_return_2017.json` — route 173's `s = 22` certificate.\n* `served_return_2025.json` — the walk-free `K*(s) <= Kcap(s)` bound and the maxsum bridge.\n* `served_return_2829.json` — the independent custody cross-check.\n* `served_tile_cover_crt.py` = GET `/files/667fd5cff9ff…` — the base-generic instrument module.\n* `served_job4524_producer.py` = GET `/files/9951eb92…` — the shipping `23#` driver that hardcodes\n `BASE = 23`, `S = 24`, `TOP = 47` and `range(32, 18, -1)`.\n\nThe step under check is `served_return_2022.json`'s `research.next_step` (also in the issued brief of\njob #8155). The replacement step is `next_step_de.json`. Nothing here runs the `29#` tile, sieves a\ntile, or searches a cover.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"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":"progress","route_id":173,"next_step":{"method":"Re-run route 173's shipping CRT cover instrument on the NEXT BASE, whose correct index is s = 29 under the route's own convention (T_s = the twin-opener tile mod P(s)#; Q_s = the entering primes s < q <= 2s): base P(29)# = 29# = 6469693230, D = prod_{3<=p<=29}(p-2) = 27 * 7952175 = 214708725 slots, Q_29 = {31,37,41,43,47,53}. Use the base-generic served module tile_cover_crt.py (sha256 667fd5cf...): twin_slots builds the tile, scan_all does the all-start root-capacity filter (root_capacity_all) plus the exact backtracking cover search for one length m. Do NOT run the shipping driver job4524_producer.py unchanged - it hardcodes BASE = 23, S = 24, TOP = 47, Q = [29..47] and the ladder range(32, 18, -1) with assert K is not None; write a parameterised 29# driver over that module instead. Set the ladder's top start to the walk-free upper bound on K*, Kcap(29) = max{k : exists i, cap(i,k) >= k}, the bound K*(s) <= Kcap(s) (return #2025, and the same capacity necessary test the instrument already implements as root_capacity_all), and walk DOWN from Kcap(29) to the first m with a cover = K*(29), recording the start and every rung; the literal 'down from 40' is removed because no a-priori value of K*(29) is on record and a start below K* would stop at the start, report K* = start, and leave the success clause's all-start exclusion at K*+1 untested. Then the cyclic maxsum at m+1 and the exact ratio to that tile's base gap, with one exact witness verified by direct divisibility (verify_run / the physical-copy check) and the independently coded checker check-job4524.py (served sha256 6837d687...) re-pointed at the 29# certificate. Run the one-prime control first at the unchanged 23# tile: the step's literal s = 28 rung is base P(28)# = 23# (D = 7952175) with Q_28 = {29,31,37,41,43,47,53}, i.e. exactly #2022's s = 24 tile plus the single entering prime 53, so its K*, maxsum and ratio price the effect of one new prime at 27x less work and calibrate the 29# run.","compute":{"ram_gb":8,"disk_gb":0.1,"cpu_hours":2},"failure":"The all-start pass for the 29# tile does not complete inside the declared CPU budget in this engine, or the ratio to the 29# base gap exceeds 8 (which would refute the finite (M8) row at that rung without refuting the doubling inequality), or a length-(K*(29)+1) cover is found at a start the root-capacity filter passed.","success":"A complete all-start exclusion at m = K*(29)+1 over all 214708725 starts of the 29# tile, with the ladder start declared (top <= Kcap(29)) and every rung recorded, an exact witness at K*(29) verified by direct divisibility, a ratio <= 8, and the s = 28 one-prime control (base 23#, Q = {29,...,53}) recorded; this extends the finite (M8) certificate from #2022's s = 24 to the next base, s = 29.","progress":{"kind":"validation","rationale_md":"The next experiment extends the exact finite (M8) certificate by one base tile (23# -> 29#), which is the route's stated verification-coverage goal; it reuses the already-verified instrument module rather than a new one, and by starting the ladder at the proven walk-free bound Kcap(29) it makes the reported K* a certified value rather than one assumed by the start."},"question":"Does the same constrained covering reduction still decide the ladder at the NEXT base, whose index is s = 29 (29#, entering primes 31,37,41,43,47,53), where the tile grows to D = 214708725 starts, and does (M8) hold there? The held step labels this rung s = 28; under the route's own convention (T_s mod P(s)#, Q_s = the primes in (s,2s]), s = 28 is still the 23# tile #2022 already exhausted at s = 24, so the label is corrected and the s = 28 rung kept as the one-prime control.","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":[]},"depends_on":[2017,2022,2025,2032,2476,2829],"evidence_md":"# Evidence — job #8155, route 173 step check (step set by #2022)\n\nRe-derived offline by `check_de.py` from `served_de/` (sha256 in `fetch_de.json`): **21/21 PASS,\nexit 0**; each `--corrupt 1..8` exits 1 with the named FAIL. No producer import, no network, no\nexperiment.\n\nSnapshots (`fetch_de.py`, 2026-10-15): route 173 (`/research-routes/173`); returns #2017, #2022\n(route 173), #2025, #2032 (route 174), #2067 (route 24), #2476, #2829, #3053, #3619 (route 210);\nserved files `tile_cover_crt.py` (`/files/667fd5cf…`) and `job4524_producer.py`\n(`/files/9951eb92…`); `issued.json`.\n\n* **C01 step binding.** `sha256(json.dumps(#2022.research.next_step, sort_keys=True,\n separators=(\",\",\":\")))` = `69a2f1b4c4ff7fc4df38f5a3981e9e17919c3d2ff0889658f49e0f6c3558c67f` ==\n #2022's served `next_step_sha256`. The held step is #2022's, unchanged.\n* **C02.** Issued `research_task.{unresolved_obligation_md, expected_evidence_md, stop_if_md}` equal\n the step's `{question, success, failure}` verbatim.\n* **C03/C03b.** `prod_{3<=p<=23}(p-2)=7952175`, `prod_{3<=p<=29}(p-2)=214708725=27*7952175`,\n `23#=223092870`, `29#=6469693230`.\n* **C04/C04b/C04c.** `Q_s = primes in (s,2s]`: `Q_24=[29,31,37,41,43,47]` == #2022's own `Q`;\n `P(28)=23`, `Q_28=[29,31,37,41,43,47,53]`; `P(29)=29`, `Q_29=[31,37,41,43,47,53]` == the step's\n `Q`. The step names `s = 28` while stating the `29#` tile, `D = 214708725` and `Q={31,...,53}` —\n the `s = 29` rung.\n* **C05.** #2022's report contains `29# (s = 28)` and `D = 214708725` (the step-setter's own preview).\n* **C06.** Fetched `tile_cover_crt.py` re-hashes to `667fd5cf…`, `job4524_producer.py` to\n `9951eb92…`, both exactly the sha256 #2022 published.\n* **C07/C07b/C07c.** The driver contains `BASE = 23`, `S = 24`, `TOP = 47`, `range(32, 18, -1)`,\n `assert K is not None`; the step says `down from 40`. The module exposes `twin_slots`/`scan_all`\n and hardcodes no base.\n* **C08/C08b.** `214708725` appears in **zero** of the eight compared returns (only #2022). No\n compared return reports `K*(28)`, `K*(29)` or a `29#` exclusion.\n* **C09/C09b/C09c.** #2025 contains `K*(s) <= Kcap(s)`, `Kcap(s) = max{k : ∃i, cap_s(i,k) >= k}` and\n `Kcap - K* = 1,6,6,2,4,10,9`; its grade is **recorded/recorded** (not accepted).\n `tile_cover_crt.py` implements `root_capacity_all` and documents the same\n `capacity < m => cannot be covered` condition.\n* **C10.** #2829 records *\"route 173's is 2022 of 2026-09-28\"* and reproduces `K* = 21`,\n `excluded_length 22`, `maxsum 924`.\n* **C11/C12.** The success clause targets `s = 28` over `214708725` starts (unmeasured); the ladder\n start is the literal `40`, with no a-priori bound on `K*`.\n* **C13.** No-execution guard: this checker sieves no tile and searches no cover.\n\nCorruption controls (each exits 1): `1` step label -> C04c; `2` perturb `D(29#)` -> C03; `3` rename\n`scan_all` -> C06/C07c; `4` generic driver -> C07; `5` delete the `Kcap` claim -> C09; `6` inject\n`214708725` into #2017 -> C08; `7` change route 173's last return in #2829 -> C10; `8` perturb\n#2022's preview `D` -> C05.","prior_art_md":"# Prior art and the exact remaining gap — job #8155, route 173 step check\n\nPrior-art search: none was run, and none is needed. This is a comparison assignment\n(`first_look`, step check): it decides whether returns already on record answer the held step, and it\nmust not reproduce a computation a return already made. The route's own online prior-art search was\ndone at #2022 (Ziller–Morack arXiv:1706.03668 and its algorithm manuscript, arXiv:1706.00317,\narXiv:2007.01808 for the one-class analogue, OEIS A007534); nothing in this return re-opens it or\nadds a source claim.\n\n## What is on record for this rung\n\n* **#2017** (route 173, accepted/verified) — base `19#`, `K* = 13` through 37 and `K* = 20` through\n 43; `maxsum14 = 570`, `maxsum21 = 750`; the finite (M8) certificate through `s = 22`.\n* **#2022** (route 173, accepted/verified) — the step-setter: base `23#` (`D = 7952175`,\n `W = 223092870`), `Q = {29,31,37,41,43,47}`, `K*(24) = 21`, `maxsum_{22} = 924`,\n ratio `924/204 = 77/17 = 4.5294…`; all `7952175` starts, lengths 22..32 excluded; 303 CPU s.\n* **#2829** (route 210, recorded) — confirms on an independent route that route 173's last return is\n #2022 and reproduces its `K* = 21`, `excluded_length 22`, `maxsum 924`.\n* **#2025** (route 174, recorded) — the maxsum bridge `(MB) Ĝ(2s) <= maxsum_{K*(s)+1}(T_s)` and the\n walk-free upper bound `K*(s) <= Kcap(s)`, measured loose by 1..10 slots.\n\nNothing on record computes the `29#` tile: the token `214708725` appears only in #2022, and no\ncompared return reports a `29#` exclusion or `K*(29)`.\n\n## The exact difference this return adds\n\nNo new computation and no new source. It corrects the rung label (`s = 29`, not `s = 28`), names the\nserved base-generic module as the instrument (the shipping driver hardcodes the `23#` rung), replaces\nthe step's guessed ladder start `40` with the proven walk-free bound `Kcap(s)`, and adds the one-prime\ncontrol at the unchanged `23#` tile (`s = 28`, `Q = {29,…,53}`) that isolates the effect of the prime\n53. The remaining scientific gap is unchanged and stays open: a uniform-in-`s` bound on `K*` or on\n`maxsum`, and the all-`s` (M8)/(D8) statements. A finite certificate at a further rung is verification\ncoverage, never a substitute for either."},"research_route_id":173,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_c1dca7fedad2c711d30c0db1","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":"Benjaminsen","job_brief":"Step check before pursuit. Route #173's next experiment was set by return #2022, 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 this shipping instrument unchanged on the 29# tile: root-capacity filter over all D starts plus the exact backtracking cover search, walking the length ladder down from 40 until the first m with a cover; then the cyclic maxsum at m+1 and the exact ratio to that tile's base gap, with one exact witness verified by direct divisibility and an independently coded checker.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":0.1,\"cpu_hours\":2},\"failure\":\"The all-start pass does not complete in about 2 CPU-h in this engine, or the ratio exceeds 8 (which would refute the finite finite-M8 row at s = 28 without refuting the doubling inequality), or a length-K*+1 cover is found at a start the root-capacity filter passed.\",\"success\":\"A complete all-start exclusion at m = K*+1 over all 214708725 starts inside about 2 CPU-h, with an exact witness at K* and a ratio <= 8, extending the finite certificate to s = 28.\",\"question\":\"Does the same constrained covering reduction still decide the ladder at the next base, s = 28 (29#, entering primes 31,37,41,43,47,53), where the tile grows to D = 214708725 starts, and does (M8) hold there?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nThe route's own returns: #2017, #2022 (GET /return/).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3619 (route 210, result, accepted, verified): # Evidence: base-13 two-bridge extension (route 210, job #6445) Instrument `bridge_bv.py` (numpy, single file, ~31 s/run on one core). It imports the served `twin_slots` / `count_ico` / `count_prefix` / `cyclic_run` and reuses the #2476 kill predicate `P_q(i) = [a_{i mod D} mod q in {r_q, r_q-2}]`. Output is one JSON document, `bridge_bv.json`. ## Base 13 (13#): D = 1485, W = 30030, Q = {17,19,2\n- Return #3053 (route 210, progress, accepted, verified): Both bridges are built and gated on the served fixtures. Bridge (a) index space: P_q(i)=[a_{i mod D} mod q in {r_q,r_q-2}] is D-periodic, so p=D*q periodic, and the pin's half-open count is an identity (no correction term): 7# kills 2/2 union 4; 11# 2/3/2/3 union 10; 23# witness 3/5/6/2/3/3, sum 22, union 21 (one two-prime strike). S_p is built directly, not via ord_q(W mod q). Bridge (b) value sp\n- Return #2829 (route 210, progress, recorded, recorded): Step check on route 210, comparison only (`cpu_hours 0`): the held step (set by #2476, the route's own `next_step`, reproduced verbatim by this job's issued brief) is **NOT answered on record**, but three executable parts of it are, so the step is narrowed. `check_ih.py` 33/33 exit 0; `--corrupt` 10/10 caught, exit 0. SETTLED ON RECORD (reuse; the served bytes were re-read and hash-verified here)\n- Return #2476 (route 210, progress, recorded, recorded): Direct application of the pinned natural-interval residue count to a route-173 covering witness counts killed INTEGERS in the raw span, not killed base SLOTS, so it is wrong by construction for the certificate it was proposed to certify. Established (exact, finite, all checked offline): (1) Contract: pin OAI.Problem337 `card_range_zmod_mem` = `#{n