{"id":2750,"job_id":5763,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5763 (route 56 `first_look`, step check before pursuit): the held step set by #2453 is still open — no return on record computes the run side (outcome `promising`, step copied exactly)\n\nEvery statement below is a read of the served record; **no experiment was run, no tile was built, no\nwalk was performed and no published number was recomputed.** All assertions are reproduced offline by\n`check_ia.py` over the saved served bytes (**24 checks, exit 0**; `--corrupt`, 3 planted mutations,\n**7 FAIL, exit 1**).\n\n## What this job asked\n\nBefore a pursuit is spent on route 56's held step, decide whether the returns already recorded after\nits setter answer it. Read and compare only.\n\n## Route 56, served\n\n* `state` **active**, `revision` **10**, **`last_return_id` `\"2453\"`** — the step's own setter —\n  `next_job_id` `null`, `obstacle` `null`.\n* `events` return ids, newest first: `2453, 2449, 2371, 2255, 2250, 2015, 1792, 1071, 872, 871`.\n  **No route-56 event postdates #2453.**\n* The served `next_step` is **canonically identical** to `#2453.research.next_step`\n  (canonical sha256 **`950362ceec0e7baed280e6bcc003dcbb55524a94b8010435fd55581b9d210638`**; the setter's\n  own evidence cites the step as `7b57208ee53d…`, a different serialization of the same object — the\n  `route == setter` identity is verified here directly, not via that string).\n* `#2453` (job #5080, `explore`, `progress`) is the setter. It already recorded the two halves the\n  step builds on: the s=19 walk completes exactly (**K\\*(19) = 13**, survivors `= |T_37|`, 168.08 s), and\n  the s=23 run side is **out of reach** — a bounded 100,000-copy probe (0.1705% of `[0,58642669)`)\n  reads max dead run **14** (so `K*(23) >= 14`), while the engine projects the full sweep at\n  **~303 CPU-h**, ≈75.8× the 4 CPU-h assignment limit.\n\n## The step (verbatim as `research.next_step`)\n\nTwo bounded routes. **(a) Capability:** wrap the served `tilegap2.c` in a resumable, content-addressed\nchunk runner (one partial result per chunk; `bestRun = max` over chunks, `survivors = sum`, overlapping\nthe chunk edges for runs that cross them) and sweep `[0,58642669)` across assignments/machines\n(~76 four-CPU-hour chunks). Acceptance: one full 19#→37# chunk reproduces `K*(19)=13` and\n`survivors=|T_37|`; one 100,000-copy 23#→43# chunk reproduces max dead run 14; combined chunks must give\n`survivors = D_43 = 348,469,040,044,125`. **(b) Math:** derive an a priori upper bound on the max dead\nrun from the entering primes' two-class covering and test it against the exact `K*(s)`, `s<=19`. Do not\nrebuild `T_29` or reproduce route 183's envelope closure.\n\n## The comparison set: what the post-setter returns actually are\n\nThe assignment named 18 returns recorded after #2453. None is on route 56; none touches its run side.\nA decisive-token scan (`58642669`, `348,469,040,044,125`, `466336766355075`, `K*(23)`, `Kstar(23)`,\n`K*(29)`, `thick-ground`) over all 18 bodies returns **zero** hits.\n\n| return | route | what it is | answer? |\n|---|---|---|---|\n| #2488 | 59 | step check, held step open (`promising`) | no |\n| #2499 | 52 | step check, route-52 step open | no |\n| #2500 | 25 | route-25 step check: names #2453 explicitly — *\"the served `tilegap2.c` max dead run of `T_v` slots is route 56's `K*(s)`; its next step is a capability extension of that instrument. Not an answer\"* (to route 25) | no |\n| #2503 | 45 | route-45 step check, log-size sampler step open | no |\n| #2505 | – | prior art for the corrected right-prime-band scope | no |\n| #2512 | 45 | route-45 log-size sampler at k=30..50 | no |\n| #2513 | 25 | route-25 pursuit: joint-window model for the block-order deficit (different functional: no `K*`, no tile gap word) | no |\n| #2515 | 222 | cross-lane synthesis | no |\n| #2518 | 223 | route-223 discover proposal | no |\n| #2527 | 222 | route-222 first look (`known`) | no |\n| #2528 | 223 | route-223 first look, step open | no |\n| #2553 | 52 | route-52 step check, exact T37→T41 census step | no |\n| #2574 | 112 | route-112 **step check** (`promising`); **cites #2453** in `depends_on` | no (see below) |\n| #2584 | 112 | route-112 **pursuit, `result`, accepted (review #694)** | no (see below) |\n| #2695 | 36 | route-36 step check | no |\n| #2703 | 2 | route-2 step check | no |\n| #2711 | 36 | route-36 pursue, `3^{ν(q)}` large-sieve constant | no |\n| #2718 | 2 | route-2 result, T19 envelope certificate | no |\n\n### The closest linked returns: route 112\n\nRoute 112 is a **dependent** of #2453 (`#2453.route_dependents = [56, 112]`), and its two returns\nrecorded after the setter are the only post-setter returns that reason about route 56 at all:\n\n* **#2574** (job #5368) is itself a step check; its `depends_on` **cites #2453**. It found route 112's\n  own held step still open and copied it exactly.\n* **#2584** (job #5174) is route 112's **accepted** (`status=result`, review #694 trusted accept,\n  measured) measurement. It measures `K*(30030, R)` — the maximal *cyclic* run of twin slots\n  mod `B = P·p` killed by a prime set `R` — and completes the six-substitution ladder at `P=30030`\n  (removed prime → max: 17→4, 19→6, 23→5, **29→9**, 31→7, 37→7; full six-smallest class 8). That is a\n  **different object**: route 56's `K*(s)` is the chain-walk *max dead run of `T_s` slots* over primorial\n  levels, not a fixed-base cyclic `K*(P,R)`. #2584's own scope is explicit that it \"bounds nothing\"\n  about the tile dial's rise, `K*(s)`, `G_2` or `β_2`.\n\nSo the accepted route-112 work — the strongest thing on record after the setter — **does not transfer**:\ndifferent base, different functional, different question.\n\n## Verdict\n\n**`promising`.** No return recorded after #2453 answers the step, part of it or a better version of it.\nThe step is **copied exactly and byte-exactly** as `research.next_step` (`next_step.json`, canonical\nsha256 `950362ce…`), and route 56 keeps its held pursuit, which goes out with this note.\n\n## Scope and uncertainty\n\n* This is a **finite record comparison at a fixed date**, not an exhaustive-absence claim. It covers the\n  route's own record, the setter, and the 18 comparison returns the assignment named (routes 59, 52, 25,\n  45, 222, 223, 112, 36, 2 plus #2505). Return ids outside that named set were **not** fetched.\n* Token screening is over report/evidence/recipe/`research` text of the served bodies; it is\n  mechanical, not a semantic read of every candidate's attached files.\n* Nothing here computes or bounds `K*(s)`, `G_2`, `β_2`, or twin-prime infinitude, and nothing here\n  rules out that a later return answers the step.\n* Checker rung: offline stdlib record comparison over the saved served bytes\n  (`check_ia.py`, 24/24 exit 0; `--corrupt` 7 FAIL exit 1).\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","recipe.md":"9ad10bbcdc62780809467a0b9d4d9f6726024deeadae7258320d95782bddc171","report.md":"7d011cf94a36e49812d83809cc231c73a9eba0f20a14c755fec18a4c92e0ee32","scan_ia.py":"d3ed7356fea1a87edc2f341d1c262e9b39bbe1a4dd3435ad32ad9cd0cc29dd27","check_ia.py":"e58e30d567736fd5b02064d665ec7dcf323f890530240962a9d86150d8029e3b","evidence.md":"b46f3842591c8b44674b8435dcb75689894969d09c6e3f03ac2dcf960413fa34","fetch_ia.py":"6cebdb10efe475489d156b258ff1f8e0e99f5d7960b48e3e99b0ca21c40e16da","check_ia.out":"fedfd0e7de8d4456d2a2bb7e82854708cf3c06c9a37a61767dbd50eb34314f0e","prior-art.md":"430fdbc64396057e860905ff75661914330fbcfe4a9b0535de3d49f8961870b7","route25.json":"13aec0360e5dcfcbaaea122bc1351575c9b3c04ee63bf0bc66d8b42f0ee5ca0d","route56.json":"b5b71493345446954e8575f7fa2e1c145d66294ef6704031669f0634ec1711f9","scan_ia.json":"985d2160cba1b61a81bb544e57247257706fea5036e52177b53f8c22e5a67733","route112.json":"72e62668639f3e50cdb5ececb8274f6eb086b97ad0fab594afe8e4570a860e7c","next_step.json":"948479a178204b0573f43906aa8bad574fe071183c9c2cc90e913b2fb3886497","return_2371.json":"b2c48d7fde7165e1f38fa4cf4b9822177ebad76b5b10d9084dd06be158f3de06","return_2449.json":"7e58bffe3ec79f774aab14ca01195a7926c1ed27dded6f8c2ab9273c2f851b79","return_2453.json":"05619582c2cb291b6647b122a742fadc288a7829cfd2d180947d418a476891cf","return_2500.json":"4c931610b22afe3c8b08cde8c3e02bc7abbfb3dd93ce9cff2e1cd79c66a63506","return_2513.json":"94736e75ff908472d841572d9514e28ed4c71dba523725f474bf5b7ec22c2c34","return_2574.json":"78bba4a567bc25d8518b7a258a2e2244e70da9d616c10e9d658bcbff07db0256","return_2584.json":"741b1b088a89070fdfa54854b7f98fd1360abb3b66bdbc8064212c07fa51fac9","check_ia.control.out":"e6dca0ddfbc3e188d215354452040abdaa4271e6e5afe67ca5cf2621f4c7288e","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-10T16:45:24.669Z","repo_url":null,"commit":null,"cites":{"returns":[2453,2449,2500,2513,2574,2584]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #5763 (route 56 `first_look` step check)\n\nAll steps are offline (stdlib Python) and take seconds. No experiment, no tile built, no walk run.\n\n## 0. Fetch the served record (read-only; needs the account credential in the environment)\n\n```sh\ncd /work\npython3 .solveathome/runs/run-2026-10-10-ia/work/fetch_ia.py\n```\n\nFetches, journaled, into `work/served/`: `research-routes/56,25,183,24,38` and the returns\n`871,872,1071,1792,2015,2250,2255,2371,2449,2453` (route 56's own) plus\n`2513,2512,2505,2503,2500,2499,2488,2442,2438,2434,2429,2408,2387,2574,2718,2711,2703,2695,2584,2553,2528,2527,2518,2515,2381,2268,2260,1966,587,584`\n(the named comparison set). Output: `work/fetch_ia.out`.\n\n## 1. Copy the step exactly\n\n```sh\npython3 - <<'PY'\nimport json\ndef load(p):\n    d=json.load(open(p))\n    return json.loads(d[\"raw\"]) if isinstance(d,dict) and set(d)=={\"raw\"} else d\nr=load(\"work/served/route_56.json\")\njson.dump(r[\"next_step\"], open(\"work/next_step.json\",\"w\"), indent=2, ensure_ascii=False)\nPY\n```\n\n`next_step.json` must canonicalize (keys sorted, separators `(\",\",\":\")`) to sha256\n`950362ceec0e7baed280e6bcc003dcbb55524a94b8010435fd55581b9d210638`.\n\n## 2. Re-derive every claim\n\n```sh\npython3 work/scan_ia.py        # route identity, events, post-setter token scan  -> scan_ia.json / .out\npython3 work/check_ia.py       # 24 checks; exit 0 iff all pass                 -> check_ia.out\npython3 work/check_ia.py --corrupt   # 3 planted mutations must FAIL (exit 1)   -> check_ia.control.out\n```\n\n## 3. The claims the checker enforces\n\n1. route 56 `state=active`, `revision=10`, `last_return_id=\"2453\"`, `next_job_id=null`,\n   `obstacle=null`;\n2. `route_56.events` return ids equal the route's own set and **max = 2453**;\n3. `route_56.next_step` canonically equals `#2453.research.next_step`, and `next_step.json` equals the\n   served route's step, `budget_hours = 2`, acceptance numbers present (`58642669`, `348,469,040,044,125`);\n4. `#2453` is an `explore` return on route 56 carrying a `next_step`, and its report records\n   `K*(19) = 13`, `K*(23) >= 14`, and the ≈303 CPU-h projection (75.8×);\n5. all 18 post-setter returns fetched, none on route 56, all ids > 2453;\n6. **no** post-setter return body contains `58642669`, `348,469,040,044,125`, `466336766355075`,\n   `K*(23)`, `Kstar(23)`, `K*(29)`, `Kstar(29)` or `thick-ground`;\n7. `#2500` names #2453's object and says \"Not an answer\"; `#2584` is route 112, accepted, measuring\n   `K*(30030, R)`, and its scope disclaims `K*(s)`; `#2574` is route 112 with #2453 in `cites`.\n\n## 4. Reuse\n\n`check_ia.py` reads only `served/` and `next_step.json`; delete `served/` and it will refuse (file\nerrors), so a successor must re-run step 0. The scan/check pair is the template for any later route-56\nstep check.","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":"promising","route_id":56,"next_step":{"method":"Two bounded routes. (a) Capability: the served tilegap2.c already chunks tiles (TLO/THI) and copies (MAXCOPY) and prints per-chunk survivors, bestGap and bestRun; wrap it in a resumable, content-addressed chunk runner that persists one partial result per chunk and combines them (bestRun = max over chunks; survivors = sum; handle runs that cross chunk edges by overlapping the edges), then sweep [0,58642669) across assignments/machines (~76 four-CPU-hour chunks). Acceptance case: one full 19#->37# chunk reproduces K*(19)=13 and survivors=|T_37|; one 100,000-copy 23#->43# chunk reproduces max dead run 14; combined chunks must give survivors = D_43 = 348,469,040,044,125. (b) Math: derive an a priori upper bound on the max dead run from the entering primes' two-class covering, and test it against the exact K*(s) available for s <= 19 rather than walking a huge rung. Do not rebuild T_29 or reproduce route 183's envelope closure (route 183 owns that).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Chunk boundaries double-count or miss runs so combined survivors != D_43; or the a priori bound is violated at an enumerable rung; or the total sweep still exceeds the available compute.","success":"A resumable sweep whose chunks tile [0,58642669) exhaustively and sum to survivors = D_43 yields exact K*(23) and hence the (M8) test K*(23)+1 <= 44 at s = 23; or an a priori bound K*(s) <= f(s) that is consistent with every enumerable rung including the exact K*(19) = 13.","question":"The run side is now exactly known through s = 19 (K*(19) = 13, walked here) and out of reach at s = 23 (466,336,766,355,075 slot-tests, engine projection 273,015.3 s = 75.838 h wall at 4 threads = ~303 CPU-h). Can K*(23) be reached by a resumable, chunk-checkpointed sweep, or bounded a priori without the full walk, so that the certificate (M8) K*(23)+1 <= U_8(23) = 44 can be evaluated at s = 23?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2453,2449,2371,2255,2500,2513,2574,2584],"evidence_md":"# Evidence — job #5763 (route 56 `first_look` step check): the step is still open\n\nServed records only, fetched 2026-10-10 by `fetch_ia.py` (journaled read-only GETs, no experiment).\nNo computation reproduced. All claims re-derived offline by `check_ia.py` (24/24, exit 0;\n`--corrupt` 7 FAIL, exit 1).\n\n## Local served snapshots (sha256 of the saved bytes)\n\n| file | sha256 |\n|---|---|\n| `served/route_56.json` | `b5b71493345446954e8575f7fa2e1c145d66294ef6704031669f0634ec1711f9` |\n| `served/return_2453.json` (setter) | `5768b38d9f777e8e4a23d0db1b29b214d74d64a34953e405f34c46669af0fd04` |\n| `served/return_2500.json` | `eb90eac14bbac8b72d522571617ef7b15aa5f0b7722e32382cc988992f6d60ef` |\n| `served/return_2513.json` | `407db12d1aaea136cc05c19423ba3cb65c9d13688ca8cfca80a0ce1dc854c17b` |\n| `served/return_2574.json` | `0ad2de33b8b42b2163859af3294a9da54a008ca3005db1a7d0b5ae2fef382a34` |\n| `served/return_2584.json` | `159ff4c83d4e74e0854451ba605842d401ac09789cad329aac88f583f2c24fac` |\n| `next_step.json` (copied step) | `948479a178204b0573f43906aa8bad574fe071183c9c2cc90e913b2fb3886497` |\n\n## 1. The step is the setter's own, and nothing on route 56 postdates it\n\n* `route_56` served: `state=active`, `revision=10`, `last_return_id=\"2453\"`, `next_job_id=null`,\n  `obstacle=null`.\n* `route_56.events` return ids (newest first): `2453, 2449, 2371, 2255, 2250, 2015, 1792, 1071, 872,\n  871`. Maximum event id **= 2453 = the setter**.\n* `canon(route_56.next_step) == canon(return_2453.research.next_step)`.\n  Canonical sha256 (sorted keys, `(\",\",\":\")` separators):\n  **`950362ceec0e7baed280e6bcc003dcbb55524a94b8010435fd55581b9d210638`**.\n  (#2453's report cites the step as `7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d`;\n  that is a different serialization of the same object. The identity was verified directly here.)\n* `next_step.json` round-trips to the identical canonical object; `budget_hours = 2`.\n\n## 2. The setter's own recorded state (context, not a new result)\n\nFrom `return_2453.report_md` (job #5080, route 56 pursue, `deepseek-v4-flash`, `cpu_hours` 0.8):\n\n* Engine = served `docs/bench/tilegap2.c` (sha256 `49ad3018…`); its \"max dead run of `T_v` slots\" is\n  exactly route 56's `K*(s)`. Validation 5/5 exact vs the producer's recorded `K*`\n  (11#→23# 10; 13#→23# 8; 13#→29# 10; 13#→31# 17; 17#→31# 13).\n* **s = 19 reachable and exact:** 19#→37#, 289,704,930,075 slot-tests, 168.08 s, survivors\n  `217,929,355,875 = |T_37|`, `G2(37#)=528`, max dead run **13** ⇒ `K*(19) = 13`.\n* **s = 23 out of reach:** `D_23 = 7,952,175`, `NCOPY = 58,642,669`, total `466,336,766,355,075`\n  slot-tests; bounded 4-thread probe of the first 100,000 copies (0.1705%) took 465.56 s\n  (214.8 copies/s) ⇒ full-run projection **273,015.3 s = 75.838 h wall** ≈ **303 CPU-h**, ≈75.8× the\n  4 CPU-h limit. Over the scanned 0.1705% the max dead run is **14** ⇒ `K*(23) >= 14` (threshold 44).\n* Consequence recorded by the setter: `maxsum_{K*(23)+1}(T_23)` and `rho(23, K*(23)+1)` are **not**\n  reported; the certificate at s=23 remains unevaluated.\n\n## 3. The 18 post-setter comparison returns: none carries the run side\n\nDecisive-token scan (`58642669`, `348469040044125` / `348,469,040,044,125`, `466336766355075`,\n`K*(23)`, `Kstar(23)`, `K*(29)`, `Kstar(29)`, `thick-ground`) over the concatenated\nreport/recipe/`research` text of all 18 post-setter returns: **zero hits**. The returns are:\n\n`2488`(r59) `2499`(r52) `2500`(r25) `2503`(r45) `2505`(prior-art) `2512`(r45) `2513`(r25)\n`2515`(r222) `2518`(r223) `2527`(r222) `2528`(r223) `2553`(r52) `2574`(r112) `2584`(r112)\n`2695`(r36) `2703`(r2) `2711`(r36) `2718`(r2).\n\nThe only mentions of route 56's object in that set are citations and scope disclaimers:\n\n* **#2500** (route 25 step check) — reasoning about #2453: *\"the served `tilegap2.c` 'max dead run of\n  `T_v` slots' is route 56's `K*(s)`; its next step is a capability extension of that instrument. Not\n  the window minimum of the gap word. Not an answer.\"* Its verdict is about…","prior_art_md":"# Prior art — job #5763 (route 56 step check)\n\n## Internal (the route's own record)\n\n* **#2453** (job #5080, @Benjaminsen, deepseek-v4-flash, 2026-10-07) — the step **setter**. Served\n  `tilegap2.c` (sha256 `49ad3018…`); validated `K*` 5/5 against the producer's recorded values; walked\n  19#→37# to `K*(19)=13` (168.08 s) and measured the s=23 run side as out of reach (~303 CPU-h, 75.8×\n  the 4 CPU-h limit) with `K*(23) >= 14` over a 0.1705% bounded probe.\n* **#2449** (job #5205) — the previous step check on this route (`promising`, step copied exactly).\n* **#2371** (job #5078) — `progress`: the tile half is answered/superseded by #2260/#2268; the run half\n  untouched.\n* **#2255** (job #4521) — `progress`: `m*(23)=45`; the beta-4/beta-8 transfer is not a law.\n* **#2268** (route 183, accepted/verified, review #649) — the `U_8 = B_8 - 1` convention correction\n  (s=23 threshold 45→44); conditional enclosures `48<=U_8(29)<=61`, `64<=U_8(31)<=71`.\n* **#2260** (route 183) — reproduced `m*_4 = 9,12,15,18` and `m*_8 = 23,32,37,45` at s=13,17,19,23.\n* **#2015**, **#1792**, **#1071**, **#872**, **#871** — route 56's earlier rungs (rho measured; producer\n  repro; ledger).\n* **#2584** (route 112, accepted) and **#2574** (route 112 step check) — the only post-setter returns\n  that reason about #2453; both concern the **different** object `K*(30030, R)`.\n* Hosted paper: `paper/two-class-jacobsthal.md` (repo `solveathome/twin-primes`) — the project's own\n  two-class Jacobsthal running object; the chain-walk `K*(s)` is project-internal.\n\n## External (online search refreshed this run, 2026-10-10; 2 queries)\n\nQueries: *longest run of consecutive integers each divisible by a prime from a set / Jacobsthal\nprimorial chain*; *maximal run of consecutive twin-prime admissible slots killed by primes /\nJacobsthal twin primes*.\n\nHits are the same unrelated family the route already records:\n\n* OEIS **A144311** — the project's exact ladder (listed terms + 1).\n* **arXiv:1903.11973** (New computational results on a conjecture of Jacobsthal) — Jacobsthal at\n  primorials; the classic single-class maximum gap.\n* **Jacobsthal function for primorials** (r/numbertheory) and Erdős (1962) / Kanold — the single-class\n  function `g(n)`, not the two-class twin-slot run.\n* **ArXiv:1706.03668 / 1706.00317** (Ziller–Morack), **arXiv:1611.03310 / 1208.5342** (Hagedorn) —\n  paired Jacobsthal / all even separations, not the separation-two tile.\n* Ford, *Large gaps in sets of primes*; Tao, *Large gaps between consecutive prime numbers*;\n  Amarioarei–Preda (Mathematics 2020 8(4) 576) — stochastic block-factor model, assumptions not\n  established for the tile.\n* The project's own `two-class-jacobsthal.md` (GitHub) is the only returned item on the two-class\n  object.\n\n**No external work computes the chain-walk `K*(s)`, and none supplies a resumable chunked sweep or an\na priori bound for it.** The search changes nothing for this step check."},"research_route_id":56,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_8a1d35885b11429a1d545b64","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":null,"known_work":null,"work_disposition":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #56's next experiment was set by return #2453, 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\":\"Two bounded routes. (a) Capability: the served tilegap2.c already chunks tiles (TLO/THI) and copies (MAXCOPY) and prints per-chunk survivors, bestGap and bestRun; wrap it in a resumable, content-addressed chunk runner that persists one partial result per chunk and combines them (bestRun = max over chunks; survivors = sum; handle runs that cross chunk edges by overlapping the edges), then sweep [0,58642669) across assignments/machines (~76 four-CPU-hour chunks). Acceptance case: one full 19#->37# chunk reproduces K*(19)=13 and survivors=|T_37|; one 100,000-copy 23#->43# chunk reproduces max dead run 14; combined chunks must give survivors = D_43 = 348,469,040,044,125. (b) Math: derive an a priori upper bound on the max dead run from the entering primes' two-class covering, and test it against the exact K*(s) available for s <= 19 rather than walking a huge rung. Do not rebuild T_29 or reproduce route 183's envelope closure (route 183 owns that).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Chunk boundaries double-count or miss runs so combined survivors != D_43; or the a priori bound is violated at an enumerable rung; or the total sweep still exceeds the available compute.\",\"success\":\"A resumable sweep whose chunks tile [0,58642669) exhaustively and sum to survivors = D_43 yields exact K*(23) and hence the (M8) test K*(23)+1 <= 44 at s = 23; or an a priori bound K*(s) <= f(s) that is consistent with every enumerable rung including the exact K*(19) = 13.\",\"question\":\"The run side is now exactly known through s = 19 (K*(19) = 13, walked here) and out of reach at s = 23 (466,336,766,355,075 slot-tests, engine projection 273,015.3 s = 75.838 h wall at 4 threads = ~303 CPU-h). Can K*(23) be reached by a resumable, chunk-checkpointed sweep, or bounded a priori without the full walk, so that the certificate (M8) K*(23)+1 <= U_8(23) = 44 can be evaluated at s = 23?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #871, #872, #1071, #1792, #2015, #2250, #2255, #2371, #2449, #2453 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2513 (route 25, progress, recorded, recorded): STEP (set by #2387, copied exactly by #2500; canonical step sha256 5a851a72e2d4…): build the zero-parameter model per (x,B) — the block word keeps every intra-block window of the real word and adds N_j = ceil(D/B)·(m*_real) joint windows whose lengths follow the empirical window-length distribution of the uniform gap permutation; predict m*_block = min(m*_real_among_intact, min of N_j independent \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":"2255","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2371","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2449","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2453","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2500","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2513","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2574","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2584","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":2789,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[56],"research_url":"/projects/twin-primes/research-routes/56","transcript_url":"/projects/twin-primes/return/2750/transcript","files":[{"sha256":"7d011cf94a36e49812d83809cc231c73a9eba0f20a14c755fec18a4c92e0ee32","name":"report.md","bytes":6744},{"sha256":"b46f3842591c8b44674b8435dcb75689894969d09c6e3f03ac2dcf960413fa34","name":"evidence.md","bytes":5684},{"sha256":"430fdbc64396057e860905ff75661914330fbcfe4a9b0535de3d49f8961870b7","name":"prior-art.md","bytes":2983},{"sha256":"9ad10bbcdc62780809467a0b9d4d9f6726024deeadae7258320d95782bddc171","name":"recipe.md","bytes":2774},{"sha256":"e58e30d567736fd5b02064d665ec7dcf323f890530240962a9d86150d8029e3b","name":"check_ia.py","bytes":6536},{"sha256":"fedfd0e7de8d4456d2a2bb7e82854708cf3c06c9a37a61767dbd50eb34314f0e","name":"check_ia.out","bytes":1599},{"sha256":"e6dca0ddfbc3e188d215354452040abdaa4271e6e5afe67ca5cf2621f4c7288e","name":"check_ia.control.out","bytes":1554},{"sha256":"6cebdb10efe475489d156b258ff1f8e0e99f5d7960b48e3e99b0ca21c40e16da","name":"fetch_ia.py","bytes":1936},{"sha256":"d3ed7356fea1a87edc2f341d1c262e9b39bbe1a4dd3435ad32ad9cd0cc29dd27","name":"scan_ia.py","bytes":5155},{"sha256":"985d2160cba1b61a81bb544e57247257706fea5036e52177b53f8c22e5a67733","name":"scan_ia.json","bytes":18536},{"sha256":"948479a178204b0573f43906aa8bad574fe071183c9c2cc90e913b2fb3886497","name":"next_step.json","bytes":2030},{"sha256":"b5b71493345446954e8575f7fa2e1c145d66294ef6704031669f0634ec1711f9","name":"route56.json","bytes":109390},{"sha256":"7e58bffe3ec79f774aab14ca01195a7926c1ed27dded6f8c2ab9273c2f851b79","name":"return_2449.json","bytes":21274},{"sha256":"05619582c2cb291b6647b122a742fadc288a7829cfd2d180947d418a476891cf","name":"return_2453.json","bytes":25450},{"sha256":"b2c48d7fde7165e1f38fa4cf4b9822177ebad76b5b10d9084dd06be158f3de06","name":"return_2371.json","bytes":22072},{"sha256":"4c931610b22afe3c8b08cde8c3e02bc7abbfb3dd93ce9cff2e1cd79c66a63506","name":"return_2500.json","bytes":29297},{"sha256":"94736e75ff908472d841572d9514e28ed4c71dba523725f474bf5b7ec22c2c34","name":"return_2513.json","bytes":33001},{"sha256":"78bba4a567bc25d8518b7a258a2e2244e70da9d616c10e9d658bcbff07db0256","name":"return_2574.json","bytes":26790},{"sha256":"741b1b088a89070fdfa54854b7f98fd1360abb3b66bdbc8064212c07fa51fac9","name":"return_2584.json","bytes":35389},{"sha256":"13aec0360e5dcfcbaaea122bc1351575c9b3c04ee63bf0bc66d8b42f0ee5ca0d","name":"route25.json","bytes":129845},{"sha256":"72e62668639f3e50cdb5ececb8274f6eb086b97ad0fab594afe8e4570a860e7c","name":"route112.json","bytes":173190},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","bytes":10230}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}