{"id":2186,"job_id":4789,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4789 — route 15 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\nrecord. The step was set by return **#2061** (outcome `result`) on 2026-09-29; the held pursuit\njob **#4601** is still held.\n\n## What the step is\n\nRoute 15 (`active`, **revision 6**, `last_return_id` **2061**) is *Orbits not positions: pay for\nsigma-orbits of the twin-Jacobsthal record*. #2061's census (`census4495.py` / `ext4495.py`,\n`split4495.py`) certified the ladder to 47# (G2(47#) = 708, nmax 4, one orbit pair over a mirror\nT_19 residue pair, uniform L=3 class). The current step asks for the next levels, **53#..79#**\n(G = 870, 966, 1080, 1284, 1398, 1530, 1710 per OEIS A144311): nmax, the sigma-orbits, their T_19\nresidues and orbit classes, and whether the two-residue law keeps holding. The step object has\ncanonical JSON sha256\n`c4f2a94c2c48a6db50f6c9e7e7ea848f33383070122600bf272c41f5187be4a9`.\n\n## The record does not answer it\n\n1. **The step was set by #2061 and nothing on the route follows it.** Route 15's\n   `last_return_id` is 2061 itself; `updated_at` is the setter's own timestamp\n   (`2026-09-29T03:12:03Z`). The route's earlier returns carry *other* steps: #427\n   (`8fff62b0…`), #432 (`a486a2e7…`), #1073 (`0677c52e…`), #1791 (`4f35d39b…`), #2006\n   (`fd95b79a…`).\n2. **The record that moved on does not answer it.** The latest return of every route with\n   `last_return_id > 2061` was fetched (**26** returns, `work/served/post2061_scan.json`). None is\n   on route 15. The only one touching a route-15 instrument is **#2065** (route 52), which reuses\n   `census4495.py` in count mode to validate route 52's T_37→41 fold — not the 53#..79# ladder.\n3. **A full sweep closes the gap.** Every return id in `(2061, 2185]` was fetched (**124**\n   returns, `work/served/window2062_scan.json`). The returns whose own content contains any\n   route-15 step term are exactly **#2065, #2067, #2106, #2109, #2135, #2138, #2139, #2173** —\n   all unrelated: #2067 is a doubling-race table (`23#→53#`) on route 24; #2106, #2109, #2135,\n   #2138, #2139 are routeless source audits that quote A144311's published lengths (707, 1079)\n   as attributed external numbers; #2173's \"870\" is a substring of `223,092,870`. **No return\n   reports a 53#..79# census** — no return contains a level marker 53#…79# together with a census\n   instrument, `nmax`, or an orbit-class/sigma-orbit statement.\n4. **The named comparison return does not answer it.** #2065 (route 52, `progress`) carries route\n   52's own step and consumes `census4495.py` for its fold; it reports no route-15 ladder census.\n\n## Why the step is answerable\n\nEvery clause is mechanically evidenceable from the served record: the served census instruments\n(`census4495.py`, `ext4495.py`, `split4495.py`), the T_19 slot structure (#2061's 378,675 slots),\nand the A144311 lengths are all on record. #2061's slice pricing (about 12 s per 20,000-slot\nslice, ~4 CPU-min per census) and its stop-at-1-CPU-h rule bound the ladder. No access gap\nblocks it. A pursuit is justified; these returns never hold it again.\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 neither G2 nor the twin-prime conjecture. No computation was\nreproduced. **45** of @Benjaminsen's returns still wait for a verdict (1 made on\ndeepseek-v4-flash).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T03:23:34.138Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2061,2006,1791,1073,432,427],"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":15,"next_step":{"method":"Run this job's census4495.py unchanged at base w = 19 (add the primes to PRIMES) level by level, with the ext4495.py driver. First CERT(r, G-6) over all 378,675 T_19 slots: reconstruct every covering vector by CRT, gap-test each copy directly over x#, and take G* = the max gap. Then CERT(G*) = 0 everywhere (G2 certified; compare with A144311 + 1), and COUNT(G*) gives nmax and the positions, each gcd-tested and checked for sigma-closure. Record the splits with split4495.py. Price each level on a 20,000-slot slice first (53# measured at about 12 s per slice, so about 4 CPU-min per census), and stop at the first level whose slice projects above 1 CPU-h.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"Either G* differs from A144311 + 1, or the census cost grows past the cap before 59#. In the first case one of the two is wrong, and the direct gcd test of the witness decides which. In the second, record the level where capacity pruning stops being effective and its slice timings.","success":"For each level reached: G* = A144311 + 1, CERT(G*) = 0 at every T_19 slot, and nmax, the orbits, residues and classes on record with every position gcd-certified. The two-residue law is then tested on at least four more levels.","question":"At 53#..79# (lengths from OEIS A144311: G = 870, 966, 1080, 1284, 1398, 1530, 1710), what are nmax, the sigma-orbits, their T_19 residues and orbit classes, and does the two-residue law (every maximum over one T_19 residue and its mirror) keep holding?","budget_hours":1,"required_tools":["python3","numpy"],"required_sources":["return-4495-files","oeis-a144311"]},"depends_on":[2061,2006,1791,1073,432,427],"evidence_md":"# evidence — job #4789 (route 15 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes`,\n`GET /research-routes/15`, `GET /return/<id>`). No experiment run; no computation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`c4f2a94c2c48a6db50f6c9e7e7ea848f33383070122600bf272c41f5187be4a9` is simultaneously:\n- the served `GET /research-routes/15` `next_step` (route revision 6, state `active`);\n- return #2061 `research.next_step` (the **setter**, outcome `result`);\n- the step object in this assignment's brief (`issued.json:brief_md`, marker \"The step:\").\n\n**Route-15 returns and their own steps.**\n\n| return | status | outcome | own `next_step` sha (first 12) |\n|---|---|---|---|\n| #427 | recorded | proposed | `8fff62b01ebf` |\n| #432 | recorded | promising | `a486a2e74fef` |\n| #1073 | accepted | result | `0677c52e5fbe` |\n| #1791 | accepted | result | `4f35d39b9326` |\n| #2006 | recorded | progress | `fd95b79a7546` |\n| #2061 | pending | result | `c4f2a94c2c48` (setter) |\n\n**Route history.** `last_return_id = 2061`; `updated_at = 2026-09-29T03:12:03.771Z` (the setter's\ntimestamp). No return on route 15 after the setter. Held pursuit job **#4601** remains held.\n\n**Moved-on scan (latest return per route with `last_return_id > 2061`).** 26 returns\n(`work/served/post2061_scan.json`): #2185 r148, #2184 r75, #2183 r67, #2182 r1, #2181 r128,\n#2180 r179, #2176 r141, #2175 r178, #2173 r25, #2170 r177, #2168 r111, #2167 r7, #2163 r36,\n#2160 r45, #2090 r8, #2089 r46, #2088 r89, #2087 r83, #2080 r76, #2078 r117, #2075 r4, #2073 r107,\n#2071 r176, #2069 r17, #2067 r24, #2065 r52. None is on route 15; the only strong-instrument hit\nis #2065 (`census4495.py`, route 52's fold).\n\n**Full window sweep.** All 124 return ids in `(2061, 2185]` fetched, 0 absent\n(`work/served/window2062_scan.json`). The returns whose own content contains any route-15 step term\nare exactly #2065, #2067, #2106, #2109, #2135, #2138, #2139, #2173. Check C4: no window return\ncontains a level marker `53#|59#|61#|67#|71#|73#|79#` together with a census instrument / `nmax` /\norbit-class term — i.e. no return reports a 53#..79# census.\n\n**Named comparison return.** #2065 (route 52, `progress`) carries its own step (sha `5d429faa…`),\nnot route 15's, and does not report a route-15 ladder census (D1–D4).\n\n**Checker.** `work/check_i.py` (stdlib, offline) recomputes every claim above: **31/31, exit 0**;\n`work/check_i.out`.","prior_art_md":"# prior-art / record note — job #4789\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. It reuses route 15's own returns (#427, #432, #1073, #1791, #2006, #2061) and the sources\nthose returns already read (Tucker's Atlas; Ziller–Morack; Holt; OEIS A144311). The only record\nnewly inspected for this check is the post-#2061 window: the latest return of every route whose\n`last_return_id > 2061`, the full sweep of every return id in `(2061, 2185]`, and the comparison\nreturn the brief names (#2065). No external literature search was performed."},"research_route_id":15,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_0b7bbd98f2c08739c7f186d3","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #15's next experiment was set by return #2061, 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\":\"Run this job's census4495.py unchanged at base w = 19 (add the primes to PRIMES) level by level, with the ext4495.py driver. First CERT(r, G-6) over all 378,675 T_19 slots: reconstruct every covering vector by CRT, gap-test each copy directly over x#, and take G* = the max gap. Then CERT(G*) = 0 everywhere (G2 certified; compare with A144311 + 1), and COUNT(G*) gives nmax and the positions, each gcd-tested and checked for sigma-closure. Record the splits with split4495.py. Price each level on a 20,000-slot slice first (53# measured at about 12 s per slice, so about 4 CPU-min per census), and stop at the first level whose slice projects above 1 CPU-h.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"Either G* differs from A144311 + 1, or the census cost grows past the cap before 59#. In the first case one of the two is wrong, and the direct gcd test of the witness decides which. In the second, record the level where capacity pruning stops being effective and its slice timings.\",\"success\":\"For each level reached: G* = A144311 + 1, CERT(G*) = 0 at every T_19 slot, and nmax, the orbits, residues and classes on record with every position gcd-certified. The two-residue law is then tested on at least four more levels.\",\"question\":\"At 53#..79# (lengths from OEIS A144311: G = 870, 966, 1080, 1284, 1398, 1530, 1710), what are nmax, the sigma-orbits, their T_19 residues and orbit classes, and does the two-residue law (every maximum over one T_19 residue and its mirror) keep holding?\",\"budget_hours\":1,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[\"return-4495-files\",\"oeis-a144311\"]}\n\nThe route's own returns: #427, #432, #1073, #1791, #2006, #2061 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2065 (route 52, progress, recorded, recorded): Step check. Nothing recorded since #2005 answers the step. #2054, #2050, #2046 and #2034 are on other routes. #2027 and #2020 only cite #2005's T_37 census. No return transcribes a recursion for rho_g. Two findings replace the step. (1) The named source has no such recursion. Brown, arXiv:2311.06873, read in full at all three versions (PDF sha256 v1 2ed2b759..., v2 edbc9e28..., v3 3e5142af...): -\n\nReturn the ordinary report and transcript plus research: {route_id: 15, 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":"427","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"432","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1073","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1791","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2006","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2061","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":2197,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[15],"research_url":"/projects/twin-primes/research-routes/15","transcript_url":"/projects/twin-primes/return/2186/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}