{"id":2183,"job_id":4785,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4785 — route 67 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 **#2157** (job #4755) is reused as instructed:\nit already established that route 67's step is open with respect to the eighteen returns it named\nand the live route history. Only the **three new** candidates listed for this job — **#2173**,\n**#2168**, **#2166** — are examined here, plus the references needed to assess them.\n\n## What the step is\n\nRoute 67 (`active`, revision 10, `last_return_id` 2157) is *The longest-run statistic L(T_x,q)\nbounds the support of the Tail-Count Transport correction term in the fold inequality*. Its served\n`next_step` was set by return **#2020** (job #4523). It asks whether `R_loose(T37,q) <= 3` holds for\nevery prime `37 <= q <= G2(T37)+2 = 530` at the producer's T37 fold tile\n(`D = 217,929,355,875`, `G2(T37) = 528` measured by #2005, replacing Tucker's provisional\n`W(37) >= 462`), i.e. whether the four-term bound and the idle `LMAX = 8` truncation persist; with\nthe controls `q = 41` (`L = 3`, `R_loose = 3`, from #159) and `q = 43`.\n\nThe step object in this assignment's brief (`issued.json:brief_md`, \"The step:\"), the served route's\n`next_step`, #2020's `research.next_step` and #2157's `research.next_step` are the **same object**:\ncanonical (sorted-key, compact-separator) JSON sha256\n`b5043165c1214b37794f19c72341012d0d695c49edbcd8017f620d2a5d7f1fde`. The step this job checks is\nexactly the step #2020 set, unrevised in the interval.\n\n## The three new candidates\n\n- **#2173** (route **25**, `explore`, `progress`, `recorded`). Route 25's *arrangement control* at\n  `x = 31` and `x = 37`: #592's streaming gap-permutation on the served T31/T37 gap histograms\n  (`#2005`). It answers the `x = 31` half and scopes the `x = 37` half as a measured cost obstacle.\n  Its own `next_step` is to run the permutation sampler on `tc37.json` (canonical sha\n  `bb71c48ebac637dadefefbc5003190694e03f437eb320c060853b64c3c7a9cbd`). It **reuses the T37 tile and\n  the `D`/`G2` gates** (hence the `T37`, `tc37`, `217,929,355,875` tokens) but computes a\n  permutation/min-window statistic of the gap histogram, **not** the ordered loose-run maximum\n  `R_loose`: the terms `R_loose`, `loose-run`, `LMAX`, `rl31`, `bit-sliced`, `qualify mask` and\n  `tail-count transport` are **absent** from its own content.\n- **#2168** (route **111**, `explore`, `progress`, `recorded`). The corrected F1 whole-block\n  reduction/application map for route 111 (Fouvry–Radziwiłł); its own `next_step` is route 111's\n  §VI refinement (canonical sha\n  `001654ccc60c429f76a167c5392be2025025a28ebb4def140c247915304be332`).\n- **#2166** (route **111**, `explore`, `inconclusive`, `recorded`). The strict whole-block\n  applicability diagnostic for route 111's F1 derivation; carries no `next_step`.\n\nNone of them answers route 67's step:\n\n- Each belongs to a different route (25, 111, 111) and carries its own step, or none.\n- Each contains **zero** route-67 loose statistic. Substring counts over\n  `finding + report_md + human_md + recipe_md + research.evidence_md + research.prior_art_md +\n  research.next_step + research.obstacle` for the term set (`R_loose`, `loose-run`, `loose census`,\n  `LMAX`, `rl31`, `bit-sliced`, `qualify mask`, `tail-count`, `tail-count transport`,\n  `fold inequality`, `killed-slot`, `loose support`) are **all 0**.\n- Neither cites nor depends on route 67's step chain (2020, 2157, 4529, 4785).\n- None runs a loose-run census, extends `rl31.c`, or reports `R_loose(T37,q)` for any `q`.\n\n## Why the step is still open\n\n1. **No return on route 67 since the step check.** The route's own `last_return_id` is 2157 (the\n   `promising` step check that copied `b5043165…` forward); nothing on the route has been recorded\n   after it.\n2. **#2157 left the step open** and its conclusions are reused here; #2173/#2168/#2166 are the only\n   returns recorded after #2157 that were eligible for comparison, and all three are off-route.\n3. **Off-route results cannot settle it.** A route-25 permutation control on the same T37\n   histogram, a route-111 application map, and a route-111 whole-block diagnostic say nothing about\n   the ordered loose-run maximum `R_loose(T37,q)` over the 88 primes.\n4. **The decisive gap is unchanged:** the only T37 loose values on record remain #159's two quoted\n   fields at `T37/41` (`L = 3`, longest qualifying gap run `= 3`); no return reports `R_loose(T37,q)`\n   for any `q != 41`. The falsifier — a route-67 or linked return reporting `R_loose(T37,q)` for\n   some `q != 41` — has not fired.\n\nThe record neither settles the step (`known`) nor advances it by a later return (`progress`), so the\nheld pursuit (job #4529) 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":"2026-10-03T02:24:55.770Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2173,2168,2166,2157,2020],"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":67,"next_step":{"method":"Extend rl31.c by one streamed fold (T29 in memory, folds by 31 and 37 streamed; about 2.5e11 fold steps). Replace the per-prime loop with a bit-sliced loose-run counter (one 128-bit qualify mask per gap value; B_k = B_{k-1} & mask), so cost is independent of the number of primes -- this is required, not optional: the naive per-prime loop over the whole T37 tile was measured at under 8,192 of 117,950 segments per 60 s per process, i.e. ~1.5-2 h wall for all 88 primes on 8 sharded processes (~16 h serialised). Gates: D = 217,929,355,875; the word sums to 37#; max gap = 528 = G2(T37), now MEASURED (return #2005, tcensus.c, 8 threads, 12 min 4 s) rather than Tucker's provisional W(37) >= 462, so the sweep range is 37 <= q <= 530, i.e. 88 primes, not 58. Run refined state machines only at the controls q = 41 (#159: L = 3, R = 3 at T37/41) and q = 43.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"Some q with R_loose >= 7 (the truncation could bite), R_loose = 4..6 (the four-term bound fails while the truncation stays idle), or a gate or control mismatch.","success":"R_loose(T37, q) <= 3 for every prime 37 <= q <= 530, and the q = 41 fields equal #159's (L = 3, R_loose = 3).","question":"Does R_loose(T37, q) <= 3 hold for every prime 37 <= q <= G2(T37) + 2 = 530, where G2(T37) = 528 is now MEASURED by #2005 (Tucker's provisional W(37) >= 462 is superseded), so the four-term bound and the idle LMAX = 8 truncation persist at the tile of the producer's fold-41 run?","budget_hours":3,"required_tools":["cc","python3"],"required_sources":["return-159","return-1244"]},"depends_on":[2173,2168,2166,2157,2020],"evidence_md":"# evidence — job #4785 (route 67 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /return/<id>`,\n`GET /research-routes/67`). No experiment run; no computation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`b5043165c1214b37794f19c72341012d0d695c49edbcd8017f620d2a5d7f1fde` is simultaneously:\n- the step object in this assignment's brief (`issued.json:brief_md`, marker \"The step:\");\n- served `GET /research-routes/67` `next_step` (route revision 10, state `active`);\n- return #2020 `research.next_step` (the setter, job #4523);\n- return #2157 `research.next_step` (the prior step check, job #4755, reused).\n\n**Candidate comparison (own content, job_brief excluded).**\n\n| return | route | outcome | own next_step sha | route-67 loose terms | cites/dep on 2020/2157/4529/4785 |\n|---|---|---|---|---|---|\n| #2173 | 25 | progress | `bb71c48e…` | none | none |\n| #2168 | 111 | progress | `001654cc…` | none | none |\n| #2166 | 111 | inconclusive | none | none | none |\n\n#2173 does reuse the T37 tile and the `D`/`G2(T37)` gates of #2005 (`T37`×1, `tc37`×3,\n`217,929,355,875`×2 in its own content) — that is a **shared premise**, not an answer: its object is\nthe arrangement/permutation min-window statistic of the gap histogram, while route 67's step is the\nordered loose-run maximum `R_loose`.\n\n**Route history.** `last_return_id = 2157`; no return on route 67 after the prior step check.\nDecisive gap: no return reports `R_loose(T37,q)` for any `q != 41`; #159's `T37/41` fields\n(`L = 3`, `R_loose = 3`) remain the sole T37 loose values on record.\n\n**Checker.** `work/check_f.py` (stdlib, offline) recomputes every claim above: **21/21, exit 0**;\n`work/check_f.out`.","prior_art_md":"# prior-art / record note — job #4785\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. It reuses the prior step check #2157 rather than re-surveying the project. The only prior\nart newly inspected is the three candidates #2173/#2168/#2166 and the references needed to assess\nthem (#2157, #2020, and the served route 67 record). No external literature search was performed."},"research_route_id":67,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_e8585900142e2dc73f07db6b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #67's next experiment was set by return #2020, 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\":\"Extend rl31.c by one streamed fold (T29 in memory, folds by 31 and 37 streamed; about 2.5e11 fold steps). Replace the per-prime loop with a bit-sliced loose-run counter (one 128-bit qualify mask per gap value; B_k = B_{k-1} & mask), so cost is independent of the number of primes -- this is required, not optional: the naive per-prime loop over the whole T37 tile was measured at under 8,192 of 117,950 segments per 60 s per process, i.e. ~1.5-2 h wall for all 88 primes on 8 sharded processes (~16 h serialised). Gates: D = 217,929,355,875; the word sums to 37#; max gap = 528 = G2(T37), now MEASURED (return #2005, tcensus.c, 8 threads, 12 min 4 s) rather than Tucker's provisional W(37) >= 462, so the sweep range is 37 <= q <= 530, i.e. 88 primes, not 58. Run refined state machines only at the controls q = 41 (#159: L = 3, R = 3 at T37/41) and q = 43.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"Some q with R_loose >= 7 (the truncation could bite), R_loose = 4..6 (the four-term bound fails while the truncation stays idle), or a gate or control mismatch.\",\"success\":\"R_loose(T37, q) <= 3 for every prime 37 <= q <= 530, and the q = 41 fields equal #159's (L = 3, R_loose = 3).\",\"question\":\"Does R_loose(T37, q) <= 3 hold for every prime 37 <= q <= G2(T37) + 2 = 530, where G2(T37) = 528 is now MEASURED by #2005 (Tucker's provisional W(37) >= 462 is superseded), so the four-term bound and the idle LMAX = 8 truncation persist at the tile of the producer's fold-41 run?\",\"budget_hours\":3,\"required_tools\":[\"cc\",\"python3\"],\"required_sources\":[\"return-159\",\"return-1244\"]}\n\nEarlier step check #2157: 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 #2173 (route 25, progress, recorded, recorded): **Evidence for job #4612 (route 25 arrangement control, x = 31).** **Served inputs (read-only, journaled).** `GET /projects/twin-primes/research-routes/25` and returns 592, 1850, 1851, 2005, 2068, 2080, 2153 saved under `work/served/`. Histograms fetched by sha256: - `tc31.json` sha256 `f9e512149366a1d8…`, D = 6,226,553,025, P = 200,560,490,130, Ghat = 348 — matches the hash named in the issued\n- Return #2168 (route 111, progress, recorded, recorded): Assigned obstruction: #2166's strict whole-block applicability diagnostic reports no hit at the known D-prime control (1/3,41/240), so its no-hit at target (1/3,11/60) is not certified; \"reduction/application map unresolved\". Finding: it is a SCOPED OBSTRUCTION of the instrument. check4572.py tests only the raw main-Theoreme exponent inequalities (C.1-C.5) and BFI I / Fouvry Lemma 5-6 conditions \n- Return #2166 (route 111, inconclusive, recorded, recorded): The F1 derivation is unresolved. An exact finite whole-block applicability diagnostic at six nu_i=1/6 and six mu_i=0 reports no named input hits at (1/3,s-1/3), s=1/2,121/240,61/120,31/60. It tests C.1-C.5, BFI I Theorems 1-3/5, and Fouvry Lemmas 5-6, all whole-block partial sums, both modulus labels/collapsed labels and disjoint L,N groups, granting other coefficient hypotheses. But (1/3,41/240) \n\nReturn the ordinary report and transcript plus research: {route_id: 67, 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":"2020","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2157","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2166","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2168","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2173","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2187,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[67],"research_url":"/projects/twin-primes/research-routes/67","transcript_url":"/projects/twin-primes/return/2183/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}