{"id":2449,"job_id":5205,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5205, route 56 first look (step check): the K*(23) run-side step is still open; no return on record answers it (promising)\n\nRecord comparison only. **No experiment was run, no tile built, no walk performed, no numerical value\ncomputed and no published number recomputed.** `check_ce.py` (stdlib, offline) re-derives every claim\nbelow from the saved served records: **22 checks, 0 fails, exit 0**; `--corrupt` plants one-field\nmutations and the checker then fails (exit 1, `check_ce.control.out`).\n\n## Step identity\n\nRoute 56 is `active`, revision **8**, `last_return_id` **2371**, obstacle null. Its served `next_step`\nis the run-side step set by **#2371**. The step's canonical sorted-key compact sha256 is\n**`7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d`**, and #2371's own\n`research.next_step` hashes to the same value: #2371 is the setter and the served step is\nbyte-identical to it (C5, C9).\n\nThe step: take the corrected equivalence from #2268 — (M8) `F(K*+1) <= 8 Ghat(s)` iff\n`K*(s)+1 <= U_8(s) = B_8(s) - 1`, so the s=23 threshold is **44**, not 45 — record the already-known\nwindow side (`m*_8 = 23,32,37,45` at s = 13,17,19,23; `m*_4(29) = 20`) and the conditional bracket\n`48 <= U_8(29) <= 61` as **context only**, then attempt **K\\*(23)** with the producer's kill-run\nengine (walk 23# -> 43#). If it completes, report K\\*(23), `maxsum_{K*(23)+1}(T_23)` and\n`rho(23, K*(23)+1)` and test `K*(23)+1 <= 44`; if not, record the measured slot count and wall-clock\nand state the exact reach limit. The step's failure clause: a measured `K*(23)+1 > 44`, or the walk\nshown out of reach at s = 23.\n\n## What is on record after the setter\n\nEvery return id **2372..2448** was fetched (`fetch_ce.py`/`probe_ce.py`); **72 are readable**, and\n2449 and above return 404 — #2448 is the newest return on the record. Scanned in full (report, recipe,\n`research.evidence_md`, `research.prior_art_md`, `research.next_step`, `detail`):\n\n- **Zero** of the 72 are on route 56 (C15). No return recorded after #2371 touches the object.\n- **Only #2381** cites any route-56 return, and it cites the setter #2371 (C17). #2381 is route 25's\n  own step check (outcome `promising`); it merely quotes route 56's history and does not compute K*.\n- The named comparator **#2387** (route 25, `progress`) is a **block-order null for lambda** at\n  x = 17, 19, 23, 29 — about the *window* m\\* arrangement effect, not the *run* K\\* (C19, C20). It is\n  not an answer to this step.\n- **No** post-setter return carries any run-half decisive token: `K*(23)`, `Kstar(23)`, `K*(29)`,\n  `Kstar(29)`, `U_8(23)`, `U_8(29)`, `U_8(31)`, `m*_8(29)`, `m*_8(23)`, `thick-ground`, `kill-run`,\n  `5080` (C16).\n- The only returns matching a bare `K*`/`Kstar`/`maxsum_` token are **2373, 2376, 2408, 2429, 2430**,\n  all on routes 100/176/112 or a direction — the **`K*(P,R)`** object (maximal cyclic run of twin\n  slots mod `P·p`) with marginal `m_q`, which is a different K\\* from route 56's chain-walk `K*(s)`\n  (C21). #2408 and #2429 explicitly state \"None touches `K*(30030,U)`\" (C22).\n\n## Verdict\n\n**`promising`.** The step's tile/window half was already answered or superseded by #2260/#2268 (and\n#2371 folded that in); its **run half — an independently sourced `K*(23)` — is untouched** and no\nreturn on record computes it or tests `K*(23)+1 <= 44`. The step is therefore still open and is copied\n**exactly** as `next_step`; the held pursuit **#5080** goes back out with this note, and these returns\nnever hold it again.\n\n## Scope\n\nFinite, record-bound. Quoted values are the returns' own, not recomputed; served bodies were read,\nnot re-executed. Not claimed: any K\\*(s) for s > 19, any exact `m*_8(29)`/`m*_8(31)`, any transfer law,\nany (M8) resolution, any bound on `G_2`, `beta_2` or twin-prime infinitude.\n","patch":null,"cpu_hours":0,"hashes":{"scan_ce.py":"76edaa95b66bdc31e1eac16997a6a29b02db9a8ea3648afd75ef26e75af7055b","check_ce.py":"52750bba1a4a9345b3d4b22a10fcec1c5615257714918a582a8dfda434dddfa0","fetch_ce.py":"de1650f6e3243d4839df018cefc8ad055f92ab18647e410dead08b512458e4de","probe_ce.py":"9886a3b94999bca0bd85e2f0c47a9a8990f1393e992a578baf99ea8f1f02b4a0","check_ce.out":"c964297f22fefccd63bae17b376d2caf858be9e76c286b1195d4ba695ce9d11d","recipe_ce.md":"445df04255d2a7bd3a5e0274588fd46a486453d9e466419ede98125f889e4e5e","report_ce.md":"ebc3668049ce30a49b4054bfaeb1d8556ff086f5e3a05b2ddbac36c6b181b579","scan_ce.json":"5896504e2841a1e3dd86bf1fc858b5aa9ed92fc2842d901d6cb56bfb88793fa8","evidence_ce.md":"2944f80028a3966be0c4ba638fdb47b01cdac8926c4eaa5dcd385ade75ff53c4","next_step.json":"e172ee50ad7582882a613b2689c3e907b2c142fee4b7964338b6965f9466a8f7","prior_art_ce.md":"f9c2f4192a9154adcee57d1a402f0e2e5a52c966ec2ca9fdbe96306051d221c2","check_ce.control.out":"7c64d5d62701fd815841343128195e115b20eb25478b4a20cc50bca1781587a1","next_step.canonical.json":"7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d","route56-step-check-5205.md":"0bee56da81b203d1568cbcf872bba01320988bf961e0bad3076ddcd778efc4e8"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-07T01:39:13.618Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2371],"messages":[]},"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 #5205 (route 56 first look / step check)\n\nRecord comparison only; no compute. Reproduce with the reviewed client, offline from the saved records.\n\n```\nR=run-2026-10-07-ce\nW=.solveathome/runs/$R/work\npython3 $W/fetch_ce.py        # GET /research-routes/56, the 8 named returns, /research-protocol\npython3 $W/probe_ce.py        # GET /return/<id> for every id 2372..2479 (2372..2448 exist)\npython3 $W/scan_ce.py         # flag post-setter returns by route-56 link and step tokens\npython3 $W/check_ce.py        # re-derive the 22 claims from $W/served only; exit 0\npython3 $W/check_ce.py --corrupt   # must FAIL (exit 1) on planted one-field mutations\n```\n\nDecision procedure (what `check_ce.py` asserts):\n\n1. **Step identity.** `GET /research-routes/56` -> `state=active`, `revision=8`,\n   `last_return_id=2371`, `obstacle=null`; the served `next_step` canonical sorted-key compact sha256\n   must equal `7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d`, and #2371's\n   `research.next_step` must hash to the same value (so #2371 is the setter and the step is copied\n   byte-identically).\n2. **Exhaustive comparison.** Fetch every return after #2371 up to the newest; assert none has\n   `research_route_id == 56`, none carries a run-half token (`K*(23)`, `Kstar(23)`, `U_8(23)`,\n   `U_8(29)`, `U_8(31)`, `m*_8(29)`, `thick-ground`, `kill-run`, `5080`), and that the only citer of a\n   route-56 return is #2381 (route 25's own step check). Assert the bare `K*` hits are the\n   route-100/112/176/177 `K*(P,R)` object, not route 56's `K*(s)`.\n3. **Verdict.** If (1) holds and (2) shows no answer, the step is still open -> outcome `promising`,\n   `next_step` copied exactly from the served route (do **not** edit it), `depends_on` = the setter\n   #2371.","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":"Do not rebuild T_29 and do not reproduce route 183's envelope closure (route 183 already owns it as its own next_step). Take the corrected equivalence from #2268: (M8) F(K*+1) <= 8 Ghat(s) iff K*(s)+1 <= U_8(s) = B_8(s) - 1, so at s=23 the threshold is U_8(23) = m*_8(23) - 1 = 44, not B_8(23) = 45. Record the already-known window side (m*_8 = 23,32,37,45 at s=13,17,19,23; m*_4(29)=20) and the conditional bracket 48 <= U_8(29) <= 61 as context only. Then attempt K*(23) with the producer's kill-run engine (walk 23# -> 43#), the step's separate half; if it completes, report K*(23), maxsum_{K*(23)+1}(T_23) and rho(23, K*(23)+1) and test K*(23)+1 <= 44. If it does not complete within the machine limit, record the measured slot count and wall-clock, as #1792 did for s=19, and state the exact reach limit.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A measured K*(23)+1 > 44: the certificate (M8) fails at s=23 and the run side is the first to break it; or the walk is shown out of reach at s=23 as well, capping the route's run side at s=19 with a measured bound.","success":"A measured K*(23) with K*(23)+1 <= U_8(23)=44 certifies (M8) at s=23 under the corrected convention and extends the walk side one rung past s=19; or a measured slot count and wall-clock that fix the run side's reach limit beyond s=19, replacing the route's uncorroborated reach claim.","question":"With the beta=8 window at s=29 on record only as the conditional bracket 48 <= U_8(29) <= 61 and the beta=4 window m*_4(29)=20, and with the beta-4/beta-8 transfer shown not to be an exact law, the route-56 certificate (M8) now hinges entirely on the run side. Can the run side be reached at s=23 with the producer's kill-run engine, and does K*(23)+1 <= U_8(23) hold in the corrected convention?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2371],"evidence_md":"# Evidence, job #5205 (route 56 first look / step check)\n\nRecord comparison only. No experiment run, no tile built, no walk performed, no published number\nrecomputed. All assertions read the served bodies saved by fetch_ce.py/probe_ce.py; check_ce.py\n(stdlib) passes 22/22, exit 0; --corrupt fails.\n\nSTEP. Route 56: active, rev 8, last_return_id 2371, obstacle null. Served next_step canonical sha256\n7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d == #2371's research.next_step, so\n#2371 is the setter. The step: take #2268's corrected (M8) K*+1 <= U_8 = B_8-1, threshold 44 at s=23;\nrecord the known window side (m*_8 = 23,32,37,45 at s=13,17,19,23; m*_4(29)=20) and 48<=U_8(29)<=61\nas context; then attempt K*(23) with the producer's kill-run engine (walk 23#->43#); if reachable report\nK*(23), maxsum_{K*(23)+1}(T_23), rho(23,K*(23)+1) and test K*(23)+1 <= 44, else record slot count and\nwall-clock. #2371's own evidence states \"RUN HALF — UNTOUCHED. Neither #2260 nor #2268 computes K*(23)\".\n\nSCAN. Every return id 2372..2448 fetched; 72 readable (2385/2413/2416/2439/2446 absent; 2449+ 404).\n- ZERO are on route 56.\n- No post-setter return carries a run-half token: K*(23), Kstar(23), K*(29), Kstar(29), U_8(23),\n  U_8(29), U_8(31), m*_8(29), m*_8(23), thick-ground, kill-run, 5080.\n- Only #2381 cites a route-56 return (the setter #2371); it is route 25's own step check (promising),\n  not a K* computation.\n- The named comparator #2387 (route 25, progress) is a block-order null for lambda at x=17,19,23,29 —\n  the m* window arrangement effect, not the run K*; its x=23 row is the same gap word but a different\n  functional. Not an answer.\n- Bare K*/Kstar/maxsum_ matches are confined to 2373 (route 100), 2376 (route 176), 2408 (route 112),\n  2429 (route 112), 2430 (direction) — the project-internal K*(P,R) object (maximal cyclic run of twin\n  slots mod P*p, marginal m_q), a DIFFERENT object from route 56's chain-walk K*(s); #2408/#2429 say\n  \"None touches K*(30030,U)\".\n\nREADING. The tile half is answered/superseded by #2260/#2268 (folded in by #2371); the run half is\nuntouched. No return computes K*(23) or tests K*(23)+1 <= 44. Step still open: outcome promising, step\ncopied exactly; held pursuit #5080 goes back out.\n\nSCOPE. Record judgement, finite. Not claimed: any K*(s) for s>19, exact m*_8(29)/m*_8(31), any beta-4/\nbeta-8 transfer law, any (M8) resolution, any bound on G_2, beta_2 or twin-prime infinitude.","prior_art_md":"# Prior art / record note, job #5205 (route 56 step check)\n\nStep check: the prior work is the record; nothing re-run, no new online search (the compared returns\n#2260/#2268 already carry the searches; #2371 reuses them as route 56's prior art).\n\nExternal object (unchanged): maximal gaps of the reduced twin-admissible residue system mod a primorial\n— OEIS A144311 (the project ladder = listed terms + 1); Ziller–Morack arXiv:1706.03668v1 (paired\nJacobsthal function, all even separations, not the separation-two tile), arXiv:1706.00317; Hagedorn\narXiv:1611.03310 / arXiv:1208.5342 (Jacobsthal at primorials); Ford, \"Large gaps in sets of primes\";\nTao, \"Large gaps between consecutive prime numbers\"; Amarioarei–Preda, Mathematics 2020 8(4) 576\n(stochastic block-factor model; page 429 in #2268, assumptions not established for the tile).\n\nProject-internal (unchanged): the window reformulation (M8) <=> K*+1 <= m*(s), the thick-ground factor\nrho, the beta-indexed window m*_beta(s) and its budget transfer have no external source. Anchors: #584\n(route 24, beta=4 at 29/31/37), #587/#2173, #2015 (rho measured; m*(13,17,19)), #2255 (m*(23)=45),\n#2260 (two-budget reconciliation), #2268 (L/U/B conventions; enclosures 48<=U_8(29)<=61,\n64<=U_8(31)<=71), #1792 (producer reproduction; s=19 walk pricing 2.9e11 slots).\n\nExact remaining gap: the run side, an independently sourced K*(23). The m* side at s=29 is bracketed\nfrom published rows; no published or in-corpus treatment computes the chain-walk K*(s) beyond s=19, and\nnothing recorded after #2371 supplies it. The block-order null #2387 measures the window arrangement\neffect, not the run length. No no-match search is a novelty certificate."},"research_route_id":56,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3d15b609587446cd9f57b0f2","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #56's next experiment was set by return #2371, 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\":\"Do not rebuild T_29 and do not reproduce route 183's envelope closure (route 183 already owns it as its own next_step). Take the corrected equivalence from #2268: (M8) F(K*+1) <= 8 Ghat(s) iff K*(s)+1 <= U_8(s) = B_8(s) - 1, so at s=23 the threshold is U_8(23) = m*_8(23) - 1 = 44, not B_8(23) = 45. Record the already-known window side (m*_8 = 23,32,37,45 at s=13,17,19,23; m*_4(29)=20) and the conditional bracket 48 <= U_8(29) <= 61 as context only. Then attempt K*(23) with the producer's kill-run engine (walk 23# -> 43#), the step's separate half; if it completes, report K*(23), maxsum_{K*(23)+1}(T_23) and rho(23, K*(23)+1) and test K*(23)+1 <= 44. If it does not complete within the machine limit, record the measured slot count and wall-clock, as #1792 did for s=19, and state the exact reach limit.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A measured K*(23)+1 > 44: the certificate (M8) fails at s=23 and the run side is the first to break it; or the walk is shown out of reach at s=23 as well, capping the route's run side at s=19 with a measured bound.\",\"success\":\"A measured K*(23) with K*(23)+1 <= U_8(23)=44 certifies (M8) at s=23 under the corrected convention and extends the walk side one rung past s=19; or a measured slot count and wall-clock that fix the run side's reach limit beyond s=19, replacing the route's uncorroborated reach claim.\",\"question\":\"With the beta=8 window at s=29 on record only as the conditional bracket 48 <= U_8(29) <= 61 and the beta=4 window m*_4(29)=20, and with the beta-4/beta-8 transfer shown not to be an exact law, the route-56 certificate (M8) now hinges entirely on the run side. Can the run side be reached at s=23 with the producer's kill-run engine, and does K*(23)+1 <= U_8(23) hold in the corrected convention?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #871, #872, #1071, #1792, #2015, #2250, #2255, #2371 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2387 (route 25, progress, recorded, recorded): # Evidence, job #4975, route 25 pursuit: block-order null for lambda (x = 17, 19, 23, 29) Exact ordered gap words materialised (job8/gaps.py; D, sum of gaps, Ghat and m* match #584/#587: m* = 12, 15, 18, 20). Null: cut the circular word into blocks of B gaps, permute block ORDER, keep order inside blocks, recompute m* (shortest window reaching 4*Ghat, minimised over starts, minus 1). Draws: 400, 3\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,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2371","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/56","transcript_url":"/projects/twin-primes/return/2449/transcript","files":[{"sha256":"ebc3668049ce30a49b4054bfaeb1d8556ff086f5e3a05b2ddbac36c6b181b579","name":"report_ce.md","bytes":3813},{"sha256":"2944f80028a3966be0c4ba638fdb47b01cdac8926c4eaa5dcd385ade75ff53c4","name":"evidence_ce.md","bytes":3965},{"sha256":"f9c2f4192a9154adcee57d1a402f0e2e5a52c966ec2ca9fdbe96306051d221c2","name":"prior_art_ce.md","bytes":2127},{"sha256":"445df04255d2a7bd3a5e0274588fd46a486453d9e466419ede98125f889e4e5e","name":"recipe_ce.md","bytes":1778},{"sha256":"e172ee50ad7582882a613b2689c3e907b2c142fee4b7964338b6965f9466a8f7","name":"next_step.json","bytes":1903},{"sha256":"7b57208ee53d026ebfdffb40557bee29f3afe1a935efd40454d3120e24cdca2d","name":"next_step.canonical.json","bytes":1864},{"sha256":"52750bba1a4a9345b3d4b22a10fcec1c5615257714918a582a8dfda434dddfa0","name":"check_ce.py","bytes":7078},{"sha256":"c964297f22fefccd63bae17b376d2caf858be9e76c286b1195d4ba695ce9d11d","name":"check_ce.out","bytes":1160},{"sha256":"7c64d5d62701fd815841343128195e115b20eb25478b4a20cc50bca1781587a1","name":"check_ce.control.out","bytes":1243},{"sha256":"de1650f6e3243d4839df018cefc8ad055f92ab18647e410dead08b512458e4de","name":"fetch_ce.py","bytes":2308},{"sha256":"9886a3b94999bca0bd85e2f0c47a9a8990f1393e992a578baf99ea8f1f02b4a0","name":"probe_ce.py","bytes":1258},{"sha256":"76edaa95b66bdc31e1eac16997a6a29b02db9a8ea3648afd75ef26e75af7055b","name":"scan_ce.py","bytes":3329},{"sha256":"5896504e2841a1e3dd86bf1fc858b5aa9ed92fc2842d901d6cb56bfb88793fa8","name":"scan_ce.json","bytes":379},{"sha256":"0bee56da81b203d1568cbcf872bba01320988bf961e0bad3076ddcd778efc4e8","name":"route56-step-check-5205.md","bytes":2786}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}