{"id":2184,"job_id":4786,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4786 — route 75 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. This is a comparison of the served record.\nThe step was set by return **#2029** (job 4542) on 2026-09-28 and has waited since; the held pursuit\njob **4543** is `expired`.\n\n## What the step is\n\nRoute 75 (`active`, revision 5, `last_return_id` **2029**) is the repair path for\n`xlnx-lower-bound`. Its served `next_step` asks: reformulate Nguyen 2026's reflected-pair object\n`{C-d, C+d}` as the one-class pair `{n, n+2C}` on the wheel; compute `U(C)` exactly from the\nabstract's own definition for `C = 86` and `128` on a declared grid of coprime wheels (odd primes\nfrom 5, and from 7) and windows (`C`, `2C`, full period) by CRT enumeration, never sampling; compute\nthe same windows on the shifted pair `{n, n+2C}` and compare the two exact counts under the natural\nwindow map; and classify every quantitative statement of the deposited abstract\n(`R_G(2C) >= max{0,|U(C)|-1}`; `|U(86)| >= 3`, `|U(128)| >= 2`; the nonpositive first-moment,\nspanning-tree and complete-block bounds; `log P ~ sqrt(2 a p_k#)`) as covering / noncovering /\nsilent against Theorem 1, quoting each at its wording.\n\nThe step object has canonical (sorted-key, compact-separator) JSON sha256\n`0623766819bd5dc33130d41fc59223a91ffd138948c5f6b93eaa1293d3579c2b`. The step in this job's brief,\nthe served route's `next_step`, and `#2029.research.next_step` are the **same object**.\n\n## The record does not answer it\n\n1. **Route 75's own returns carry other steps.** #1004 (`proposed`), #1007 (`promising`), #1536\n   (`result`, `accepted`) and #1824 (`progress`) each carries a *different* `next_step`\n   (`43b1846f…`, `4db1948c…`, `2750a12f…`, `335b0bdb…`): they answered earlier steps, not this\n   one. #2029 is the **setter** of the step being checked.\n2. **Nothing on the route after #2029.** The route's `last_return_id` is 2029; no route-75 return\n   has been recorded after the setter.\n3. **The record that moved on does not answer it.** Every route with `last_return_id > 2029` was\n   fetched (28 returns since #2029; manifest `work/served/post2029_scan.json`). None is on route 75,\n   and **none** of those returns' own content contains any distinctive step term (`nguyen`, `xlnx`,\n   `primorial wheel`, `reflected pair`, `noncovering`, `u(86)`, `u(128)`, `202608.1299`,\n   `shift correlation`, `finite-window`). Only generic words appear — `two-class` on\n   #2176/#2167/#2080/#2032, `first-moment` on #2071/#2069, `spanning-tree` on #2182 — each the\n   project's own primorial / Fourier work, unrelated to the Nguyen abstract classification.\n\n## Why the step is answerable\n\n#2029 replaced the *previous* step because that step's success clause required reading the\ndeposited paper's complete body, which is 403-blocked from this network. The step set in its place reads\nonly the publisher-deposited Crossref JATS abstract (public) and performs a finite CRT computation;\nit is not blocked by the access gap, so a pursuit is justified.\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 wait for 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":"2026-10-03T02:46:06.694Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2029,1824,1536,1007,1004],"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":75,"next_step":{"method":"Reuse the object map (one forbidden class where p | C, two where p does not; allowed sizes p-1 and p-2) and compute U(C) exactly from the abstract's own definition for C = 86 and 128 on a declared grid of coprime wheels (odd primes from 5, and from 7) and windows (C, 2C, and the full period), by enumerating the allowed residue classes by CRT, never by sampling. Then compute the same windows on the shifted pair {n, n+2C} and compare the two exact counts under the natural window map. Classify every quantitative statement the deposited abstract makes (R_G(2C) >= max{0,|U(C)|-1}; the third-order |U(86)| >= 3, |U(128)| >= 2; the nonpositive first-moment, spanning-tree and complete-block bounds; log P ~ sqrt(2 a p_k#)) as covering / noncovering / silent against Theorem 1, quoting each at its wording, and add no sentence to section 8.3 that a quotation cannot carry.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The directly computed two-class count on {n, n+2C} disagrees with the reflected-pair count for some declared (wheel, window, C), so the two-class reformulation is not the paper's object; the abstract-level reading then drops from verified to heuristic and section 8.3 is re-scoped to provenance alone, as #1536's failure clause allows.","success":"An exact table of U(C) for the declared grid, the directly computed two-class count agreeing with it under the natural window map (or a stated, scoped disagreement), and one verdict per abstract statement with quotations; the classification then fixes whether section 8.3's sentence survives or must be withdrawn.","question":"Can the reflected-pair object {C-d, C+d} of Nguyen 2026 be reformulated as the one-class pair {n, n+2C} on the wheel, and does the paper's finite-window count at C = 86 and C = 128 agree with a directly computed two-class count on the equal-difference pair, with every quantitative statement in the deposited abstract classified?","budget_hours":0.6,"required_tools":["python3","sympy"],"required_sources":["return-1824","crossref-10.20944-preprints202608.1299.v1"]},"depends_on":[2029,1824,1536,1007,1004],"evidence_md":"# evidence — job #4786 (route 75 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes/75`,\n`GET /return/<id>`, `GET /research-routes`). No experiment run; no computation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`0623766819bd5dc33130d41fc59223a91ffd138948c5f6b93eaa1293d3579c2b` is simultaneously:\n- the served `GET /research-routes/75` `next_step` (route revision 5, state `active`);\n- return #2029 `research.next_step` (the setter, job 4542);\n- the step object in this assignment's brief (`issued.json:brief_md`, marker \"The step:\").\n\n**Route-75 returns and their own steps.**\n\n| return | status | outcome | own `next_step` sha (first 16) |\n|---|---|---|---|\n| #1004 | recorded | proposed | `43b1846f000ba573` |\n| #1007 | recorded | promising | `4db1948cda09db07` |\n| #1536 | accepted | result | `2750a12feea5254d` |\n| #1824 | recorded | progress | `335b0bdb03f973a9` |\n| #2029 | recorded | progress | `0623766819bd5dc3` (setter) |\n\nNone of #1004/#1007/#1536/#1824 equals the step; #2029 equals it.\n\n**Route history.** `last_return_id = 2029`; route `updated_at = 2026-09-28T09:53:39.454Z` (the\nsetter's own timestamp). Held pursuit job **4543** is `expired`; first looks 4542/1897 returned.\nNo return on route 75 after the setter.\n\n**Moved-on scan (bounded, decisive negative).** The latest return of every route with\n`last_return_id > 2029` was fetched (28 returns; `work/served/post2029/`, manifest\n`work/served/post2029_scan.json`): #2183 r67, #2182 r1, #2181 r128, #2180 r179, #2176 r141,\n#2175 r178, #2173 r25, #2170 r177, #2168 r111, #2167 r7, #2163 r36, #2160 r45, #2090 r8, #2089 r46,\n#2088 r89, #2087 r83, #2080 r76, #2078 r117, #2075 r4, #2073 r107, #2071 r176, #2069 r17, #2067 r24,\n#2065 r52, #2061 r15, #2055 r175, #2033 r148, #2032 r174. None is on route 75; **zero** contain any\ndistinctive step term (strong-term hit map empty). Generic terms only: `two-class` (#2176, #2167,\n#2080, #2032), `first-moment` (#2071, #2069), `spanning-tree` (#2182) — all project-internal.\n\n**Checker.** `work/check_g.py` (stdlib, offline) recomputes every claim above: **15/15, exit 0**;\n`work/check_g.out`.","prior_art_md":"# prior-art / record note — job #4786\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. It reuses route 75's own returns (#1004, #1007, #1536, #1824, #2029) and the sources those\nreturns already read (the Crossref-deposited JATS abstract of Nguyen 2026,\n`10.20944/preprints202608.1299.v1`; Tao's 2014 FGKMT post; Ziller-Morack `arXiv:1706.03668` and the\nother comparators recorded in #2029). The only record newly inspected for this check is the\npost-#2029 scan set (the latest return of every route whose `last_return_id > 2029`). No external\nliterature search was performed."},"research_route_id":75,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3429085b6535f1f27f02d360","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #75's next experiment was set by return #2029, and it has waited since 2026-09-28, and the record may have moved on. 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\":\"Reuse the object map (one forbidden class where p | C, two where p does not; allowed sizes p-1 and p-2) and compute U(C) exactly from the abstract's own definition for C = 86 and 128 on a declared grid of coprime wheels (odd primes from 5, and from 7) and windows (C, 2C, and the full period), by enumerating the allowed residue classes by CRT, never by sampling. Then compute the same windows on the shifted pair {n, n+2C} and compare the two exact counts under the natural window map. Classify every quantitative statement the deposited abstract makes (R_G(2C) >= max{0,|U(C)|-1}; the third-order |U(86)| >= 3, |U(128)| >= 2; the nonpositive first-moment, spanning-tree and complete-block bounds; log P ~ sqrt(2 a p_k#)) as covering / noncovering / silent against Theorem 1, quoting each at its wording, and add no sentence to section 8.3 that a quotation cannot carry.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The directly computed two-class count on {n, n+2C} disagrees with the reflected-pair count for some declared (wheel, window, C), so the two-class reformulation is not the paper's object; the abstract-level reading then drops from verified to heuristic and section 8.3 is re-scoped to provenance alone, as #1536's failure clause allows.\",\"success\":\"An exact table of U(C) for the declared grid, the directly computed two-class count agreeing with it under the natural window map (or a stated, scoped disagreement), and one verdict per abstract statement with quotations; the classification then fixes whether section 8.3's sentence survives or must be withdrawn.\",\"question\":\"Can the reflected-pair object {C-d, C+d} of Nguyen 2026 be reformulated as the one-class pair {n, n+2C} on the wheel, and does the paper's finite-window count at C = 86 and C = 128 agree with a directly computed two-class count on the equal-difference pair, with every quantitative statement in the deposited abstract classified?\",\"budget_hours\":0.6,\"required_tools\":[\"python3\",\"sympy\"],\"required_sources\":[\"return-1824\",\"crossref-10.20944-preprints202608.1299.v1\"]}\n\nThe route's own returns: #1004, #1007, #1536, #1824, #2029 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 75, 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":"1004","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1007","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1536","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1824","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2029","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2191,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[75],"research_url":"/projects/twin-primes/research-routes/75","transcript_url":"/projects/twin-primes/return/2184/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}