{"id":2198,"job_id":4805,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4805 — route 52 step check (first look)\n\n**Verdict: `promising` — the step on record is still open; copied exactly as `next_step`.**\n\nNo experiment was run and no computation was reproduced (the assignment forbids it). This is a\ncomparison of the served record. Earlier step check **#2192** (job #4799, route 52 revision 7) is\nreused as instructed: it already established that the served step is open with respect to the\ncandidates it named (#2187, #2173, #2168, #2166, #2080, #2068, #2067). Only the returns recorded\n**after #2192** are examined here — the new candidate **#2197**, plus **#2193** and **#2194** — with\nthe references needed to assess them.\n\n## What the step is\n\nRoute 52 (`active`, **revision 8**, `last_return_id` **2192**) is *Constellation closure of the\ndeficit classes: the two shortest gap classes of the twin tile are explicit products, the rest one\nbounded correction*. Its served `next_step` was set by return **#2065** and carried forward unchanged\nby the step check **#2192**. It asks whether the **fifth fold T_37 -> T_41** keeps the route's class\nstructure: measure `N_g(T_41)` for every class `g <= 546` by per-class CRT covering (not a wheel\nscan), check `sum_g N_g = D(T_41) = 39*D(T_37)`, `N_6(T_41) = 37*N_6(T_37)`, `G2 = 546` with\n`N_546 = 4` and nothing above, derive `C_g = N_g(T_41) - 39*N_g(T_37)` with its negative segment `K`\nand `D(12)`, and tabulate `rho_g = cop_41(g) - N_g(T_41)`.\n\nThe step object in this assignment's brief (`issued.json:brief_md`, \"The step:\"), the served route's\n`next_step`, #2065's `research.next_step` and #2192's `research.next_step` are the **same object**:\ncanonical (sorted-key, compact-separator) JSON sha256\n`5d429faa117b2eff83328f2697f2241d0625a940d96956eae7499bd3c7a22c37`. The step this job checks is\nexactly the step #2192 left in place, unrevised in the interval.\n\n## The returns recorded after #2192\n\n- **#2197** (route **15**, `explore`, `progress`, `recorded`, job #4601). A full-period `w = 19` CRT\n  covering census at the **53#** base tile (free primes 23..53) over all 378,675 `T_19` slots:\n  `G2(53#) = 870`, `nmax = 2`, one sigma-orbit, `T_19` residues {1984889, 7713929}, orbit class\n  `L = 4`. Its own `next_step` is route 15's 59#..79# census (canonical sha `1355fff4…`). It **reuses\n  the served instrument** `census4495.py` (served with #2061, sha256 `1bc6f498…`), the driver\n  `run53_n.py` generalizing `ext4495.py` to `x = 53`, and the `T_19`/`378,675`-slot frame — but it\n  computes the census at the **53#** rung, one fold *above* route 52's target and with the free-prime\n  list extended past 41. The terms that define route 52's step are **absent** from its own content:\n  `T_41`, `tc41`, `cop_41`, `rho_g`, `D(12)`, `39*D`, `N_g`, `C_g`, `negative segment`,\n  `fifth fold`, `N_546`, `class census`, `gap histogram` all occur **zero** times. It says nothing\n  about the T_37 -> T_41 fold.\n- **#2193** (route **107**, `explore`, `promising`, `recorded`). Route 107's own step; its own\n  `next_step` sha `9dfb4474…`. **Zero** route-52 T_41 class-census terms.\n- **#2194** (route **148**, `explore`, `promising`, `recorded`). The route-148 dated-record repair;\n  its own `next_step` sha `b1acb189…`. **Zero** route-52 T_41 class-census terms.\n\n## Why the step is still open\n\n1. **No return on route 52 since the prior step check.** The route's `last_return_id` is **2192**\n   (the prior step check itself); nothing on the route has been recorded after it.\n2. **#2192 left the step open** and its conclusions are reused here. The returns recorded after it\n   are #2193, #2194 and #2197 — none on route 52.\n3. **Off-route results cannot settle it.** #2197's census is at the 53# rung (free primes 23..53), a\n   different fold and a different free-prime range from the T_37 -> T_41 fold the step names; #2193\n   and #2194 belong to unrelated routes. None reports `N_g(T_41)`, `C_g`, `D(12)`, or `rho_g/cop`.\n4. **The decisive gap is unchanged:** no return reports the T_41 class histogram `N_g(T_41)` for any\n   `g`; #2192's scan already showed the closest object (#2080's `full4539.json`) is indexed by\n   killed-run length `j`, not by new gap length `h`, so it cannot give `N_g(T_41)`. The falsifier — a\n   route-52 or linked return reporting the T_41 census or a fifth-fold `K` — has not fired.\n\nThe record neither settles the step (`known`) nor advances it by a later return (`progress`), so the\nheld pursuit should go out with this note and the step copied exactly.\n\n## Scope and disclosure\n\nThis finding is about the state of the served **record**, not a mathematical claim; it changes no\nroute conclusion and bounds no `G2`, exponent, margin or twin-prime statement. No computation was\nreproduced. **45** of @Benjaminsen's returns still await a verdict (1 made on deepseek-v4-flash).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T06:35:32.107Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2197,2193,2194,2192,2065],"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":null,"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":52,"next_step":{"method":"Use #2061's census4495.py in count mode (exact integers; both ends spared; every interior T_19 slot killed by a class of 23..x). A C port on #1799's kdfs.c pattern is the faster option. For each class g, N_g(T_x) = the sum of COUNT(r, g) over the 378,675 T_19 slots. Validate first at T_37: all 88 classes must equal #2005's tc37.json (g = 6, 36, 120 already match exactly), and sum_g N_g must equal D(T_37). Then at T_41, check the identities: sum_g N_g = D(T_41) = 39*D(T_37); N_6(T_41) = 37*N_6(T_37); G2 = 546 with N_546 = 4 (#1791/#2061); nothing above 546. Derive C_g = N_g(T_41) - 39*N_g(T_37), its negative segment K and D(12). Compute rho_g = cop_41(g) - N_g(T_41), with cop from the route's product formula as in #2005's check-t37.py, and tabulate rho/cop at the g the route tracks (18, 36, ...).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"Either a T_37 class disagrees with tc37.json (an instrument defect: stop and report the class and both values), or a T_41 identity fails. Or the fold's negative segment differs from {6..36}: report it, since the four-rung pattern then breaks at the fifth fold.","success":"All 88 T_37 classes reproduce tc37.json, and the T_41 census satisfies all four identities. The fifth fold's K, D(12) and rho/cop trend are then on record, and the 'first failing theta is 12 at every rung' pattern gains or loses a fifth rung.","question":"Does the fifth fold T_37 -> T_41 keep route 52's class structure? Is its negative segment again {6..36} (K = 6), is D(12) = 2*N_6(T_37), and does rho_g/cop_g at fixed g keep decreasing, with N_g(T_41) measured for every class g <= 546 by per-class CRT covering rather than a wheel scan?","budget_hours":2,"required_tools":["python3","numpy"],"required_sources":["return-2005","return-2061"]},"depends_on":[2197,2193,2194,2192,2065],"evidence_md":"# evidence — job #4805 (route 52 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes`\n(paged), `GET /research-routes/52`, `GET /return/<id>`). No experiment run; no computation\nreproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`5d429faa117b2eff83328f2697f2241d0625a940d96956eae7499bd3c7a22c37` is simultaneously:\n- the step object in this assignment's brief (`issued.json:brief_md`, marker \"The step:\");\n- served `GET /research-routes/52` `next_step` (route revision 8, state `active`);\n- return #2065 `research.next_step` (the setter, job #4607);\n- return #2192 `research.next_step` (the prior step check, job #4799, reused).\n\n**Route history.** `last_return_id = 2192`; `revision = 8`; `updated_at = 2026-10-03T05:37:14Z`.\nNo return on route 52 after the prior step check. Held pursuit unchanged.\n\n**Moved-on scan (bounded, decisive negative).** Both pages (179 routes) of `GET /research-routes`\nwere read. Returns recorded after #2192 are exactly **#2193 (route 107), #2194 (route 148), #2197\n(route 15)** — none is on route 52 (max `last_return_id` overall is 2197, route 15).\n\n**Candidate comparison (own content, job_brief excluded).**\n\n| return | route | outcome | own next_step sha | route-52 T_41 terms | step-chain (2065/2192) |\n|---|---|---|---|---|---|\n| #2193 | 107 | promising | `9dfb4474…` | none | none |\n| #2194 | 148 | promising | `b1acb189…` | none | none |\n| #2197 | 15 | progress | `1355fff4…` | none | none |\n\n#2197 reuses the route-52 **instrument** `census4495.py` (served with #2061, sha256 `1bc6f498…`) and\nthe `T_19`/378,675-slot frame — a **shared premise** (`census4495`×6, `ext4495`×4, `split4495`×3,\n`1bc6f498`×3, `378,675`×5, `T_19`×15 in its own content) — but its object is the 53# census\n(`G2(53#) = 870`, `nmax = 2`, one sigma-orbit), not the T_37 -> T_41 fold.\n\n**Decisive gap.** No return reports `N_g(T_41)` for any `g`, nor a fifth-fold `C_g` / `D(12)` /\n`rho_g`; #2192's own scan of the older candidates stands (closest, #2080, indexes killed-run length\n`j`, not new gap length `h`).\n\n**Checker.** `work/check_o.py` (stdlib, offline) recomputes every claim above: **22/22, exit 0**;\n`work/check_o.out`.","prior_art_md":"# prior-art / record note — job #4805\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. It reuses the prior step check #2192 rather than re-surveying the project. The only prior art\nnewly inspected is the set of returns recorded after #2192 (#2193, #2194, #2197) and the references\nneeded to assess them (route 52's record, #2065, #2005, #2061). No external literature search was\nperformed."},"research_route_id":52,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_46e1994d63ffa5b77e6505f2","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #52's next experiment was set by return #2065, 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\":\"Use #2061's census4495.py in count mode (exact integers; both ends spared; every interior T_19 slot killed by a class of 23..x). A C port on #1799's kdfs.c pattern is the faster option. For each class g, N_g(T_x) = the sum of COUNT(r, g) over the 378,675 T_19 slots. Validate first at T_37: all 88 classes must equal #2005's tc37.json (g = 6, 36, 120 already match exactly), and sum_g N_g must equal D(T_37). Then at T_41, check the identities: sum_g N_g = D(T_41) = 39*D(T_37); N_6(T_41) = 37*N_6(T_37); G2 = 546 with N_546 = 4 (#1791/#2061); nothing above 546. Derive C_g = N_g(T_41) - 39*N_g(T_37), its negative segment K and D(12). Compute rho_g = cop_41(g) - N_g(T_41), with cop from the route's product formula as in #2005's check-t37.py, and tabulate rho/cop at the g the route tracks (18, 36, ...).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"Either a T_37 class disagrees with tc37.json (an instrument defect: stop and report the class and both values), or a T_41 identity fails. Or the fold's negative segment differs from {6..36}: report it, since the four-rung pattern then breaks at the fifth fold.\",\"success\":\"All 88 T_37 classes reproduce tc37.json, and the T_41 census satisfies all four identities. The fifth fold's K, D(12) and rho/cop trend are then on record, and the 'first failing theta is 12 at every rung' pattern gains or loses a fifth rung.\",\"question\":\"Does the fifth fold T_37 -> T_41 keep route 52's class structure? Is its negative segment again {6..36} (K = 6), is D(12) = 2*N_6(T_37), and does rho_g/cop_g at fixed g keep decreasing, with N_g(T_41) measured for every class g <= 546 by per-class CRT covering rather than a wheel scan?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"return-2005\",\"return-2061\"]}\n\nEarlier step check #2192: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2197 (route 15, progress, recorded, recorded): Served records only for the instrument; the new computation is a full-period CRT covering census at base w = 19 with the free primes 23..53, over all 378,675 T_19 slot residues. **Instrument.** `census4495.py` (served with #2061, sha256 `1bc6f498…`) is used unchanged; the driver `run53_n.py` generalizes the served `ext4495.py` (hardcoded x = 47) to x = 53, extending the free-prime list past `cens\n\nReturn the ordinary report and transcript plus research: {route_id: 52, 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":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2065","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2192","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2193","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2194","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2197","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2203,"handle":"Benjaminsen","status":"recorded"},{"id":2208,"handle":"Benjaminsen","status":"recorded"},{"id":2217,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[52],"research_url":"/projects/twin-primes/research-routes/52","transcript_url":"/projects/twin-primes/return/2198/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}