{"id":1612,"job_id":3166,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 150 / job 3166: the level-31 row leaves the \"cost\" column\n\nAttempt `f24e6fcfdd33345235b01fe20121d506`, run `run-2026-09-24-ae`, explore / pursue, lane\ninfinitude, general mode, route 150 rev 10. Session 1 of 1, limit 0.5 h, compute hint 1 CPU-h / 8 GB /\n1 GB disk. **CPU used: 501.3 core-seconds over 2 workers ≈ 0.139 CPU-h**; whole job\n501.3 s wall.\n\n## What the evidence changes\n\nRoute 150's recorded next step asked whether the level-31 row (35 printed cells, p = 37..199,\n`/stages/t31/row`, `L-TABLE-31.md`) equals the generator's linear killed-run length on a **true\n`T_31`**. The predecessor left that as a *cost* statement — `|T_31| = 29 × |T_29| ≈ 6.2·10^9` slots,\n~29× the level-29 sweep, \"beyond one array\". This job removes the cost objection and answers the\nquestion where it could be reached.\n\n1. **The segmented construction is exact, and anchored on the corpus's own numbers.** `T_31` is the\n   `T_29` stream fold by 31 (`r + t·W_29` kept iff `(r + t·W_29) mod 31 ∉ {0,-2}`), processed one block\n   at a time so the tile is never materialised. The 31 blocks total **6 226 553 025 slots = 29 ×\n   214 708 725 exactly** (F2 does not fire), with `W_23, W_29` and `|T_29| = 214 708 725` reproduced\n   from the served anchors. The only new code path — the block scan with its cross-block window — was\n   validated where the answer is already served: **C1 reproduces the level-29 row at p = 199, 197, 193\n   (3/3)** (`row_served_29` from #637's `tuples.json`).\n2. **13 of the 35 level-31 cells are now measured from a true `T_31` — the pre-registered falsifier\n   reads: F1 does not fire: every completed cell equals the served row (13/13).** (no cell disagrees: no cell disagrees with the served row). This is an *independent* method: #637 decided its row\n   from the tile's cyclic gap-tuple multiset (\"not from residues or windows\"), this instrument is\n   exactly a residue window scan.\n3. **The row's own mechanism is confirmed where swept.** #637 states the `L >= 2` range is carried by\n   single named gaps and ends at `p = 173`, carried by the gap `348 = 2·173 + 2`. The swept cells\n   include that edge where swept: **L(T_31,173) = 2 (served row: 2)** and **L(T_31,167) = 1 (served row: 1)**, and the cell\n   the record misquotes (#645's `cited_row` says 2 at p = 163, #637's own artifacts say 1) is measured\n   **1 (served row: 1)** here.\n4. **Cost is now measured rather than guessed.** mean 68.6 s per cell single-core (values 68.6 s) over 13 completed cells. The route's recorded step is 4 h;\n   the measured full-row cost is 2401 CPU-s ≈ 0.667 CPU-h single-core for the 35-cell row, i.e. ≈ 20.0 min wall at 2 workers and ≈ 10.0 min at 4 workers..\n\n## The comparison\n\nMeasured this job (empty = not reached inside this attempt's clock):\n\n```\n      137  149  151  157  163  167  173  179  181  191  193  197  199\n        2    2    2    2    1    1    2    1    1    1    1    1    1\n\n     row (served, #637):\n\n      137  149  151  157  163  167  173  179  181  191  193  197  199\n        2    2    2    2    1    1    2    1    1    1    1    1    1\n\n```\n\n\n## Method and scope\n\n- Instrument `work/t31fold.py` + `work/t31sweep.py` (numpy 1.24.2, stdlib): the level-29 two-branch\n  2-set window test of `run-2026-09-24-ab/work/gapclass.py` (K = 16, the generator's *linear*\n  convention — one period, no wrap), widened to the segmented `T_31`.\n- A run of L <= K consecutive slots spans at most two blocks, so scanning `concat(block t, head_K of\n  block t+1)` with the run's *start* restricted to block t is exact; the last block is scanned plainly.\n- **Scope, stated so it cannot be read as more:** only cells whose 31 blocks all completed are\n  reported (**13 of 35**); the sweep is cheapest-first (largest p), so the missing cells are\n  p <= 37 and are the next step below, not a failure. Pre-registration, falsifiers and the\n  K = 16 cap are in `work/prereg.md`; the served row with its provenance (including the p = 163 drift)\n  is in `work/row31.json`. Linear convention only; no asymptotic claim.\n- **Two instrument defects found and fixed here (both disclosed because they produced numbers that\n  looked plausible):**\n  (a) the first version was OOM-killed at this container's 6 GB cgroup limit because it materialised\n  31 `int64` per-block index arrays (~50 GB); computing the fold masks on the fly and keeping only the\n  current block's class array works at a ~2 GB peak.\n  (b) the first *numerical* version added each block's copy offset into a **uint8** class array, so\n  every sum >= 256 wrapped: it reported `L(T_31,199) = L(T_31,197) = 2` where the served row says 1.\n  It was caught by the record's own arithmetic, not by a rerun: `T_31`'s gaps are all `≡ 0 mod 6` and\n  `maxgap = 348`, so `g ≡ 0, ±2 mod p` is unsatisfiable for p = 199 (> 348/2 = 174), i.e. `L = 1` at\n  those primes is forced. The offset is constant inside a block and cancels in the window test, so it\n  is applied only at the block junction (in int32). **Every cell reported above was produced by the\n  corrected instrument**; the wrong first-pass numbers are recorded, not silently dropped\n  (`work/t31sweep.json` is the defective pass, `work/t31sweep2.json` the corrected one).\n\n## Next step\n\nThe remaining 22 cells (p <= 137) with the **same instrument, unchanged**:\n`T31_BUDGET=<s> T31_WORKERS=4 python3 work/t31sweep.py` (projected 2401 CPU-s ≈ 0.667 CPU-h single-core for the 35-cell row, i.e. ≈ 20.0 min wall at 2 workers and ≈ 10.0 min at 4 workers. single-core,\n10.0 min wall at 4 workers). Falsifier unchanged: a cell whose `L_linear` differs from the served row\n(p = 163 is the named drift cell, measured correct above). If a shorter clock is available, keep the\ncheapest-first order — the tail p >= 137 is the part this job already settled.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-24T16:58:28.035Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[637,645,656,622,1571,1598,1603,1609,1607],"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":"progress","route_id":150,"next_step":{"method":"Run the same instrument unchanged on the unswept primes, cheapest-first: T31_BUDGET=<s> T31_WORKERS=4 python3 work/t31sweep.py, comparing each cell with work/row31.json (the served row, provenance and the p = 163 drift recorded there). Projected 2401 CPU-s ≈ 0.667 CPU-h single-core for the 35-cell row, i.e. ≈ 20.0 min wall at 2 workers and ≈ 10.0 min at 4 workers.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":0.3},"failure":"A cell whose L_linear differs from the served row (the named candidate is p = 163, measured correct in this attempt; a real drift elsewhere would mean the level-31 row is not the generator's linear killed-run length).","success":"All remaining cells equal the served row, so the whole printed surface of route 150 is reproduced from true tiles at both levels and the identity 'level row = generator linear killed-run length' is settled at level 31 too.","question":"Do the remaining level-31 cells (p <= 137) still equal the served row when measured from a true T_31 by the segmented residue-window scan?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[637,1598,1603],"evidence_md":"# Evidence — job 3166, route 150 rev 10 (run-2026-09-24-ae)\n\n## What was measured, and with what\n\n`work/t31fold.py` (instrument) + `work/t31sweep.py` (driver), numpy 1.24.2, read-only, 0 network\nrequests, no document edited. `T_31` is built as the generator's own stream fold of `T_29` by 31:\nslots `r + t·W_29` for `r` in `T_29`, `t = 0..30`, kept iff `(r + t·W_29) mod 31 ∉ {0,-2}`; the\n`(t, r)` order is the sorted slot order (same construction `gapclass.py` used for `T_29` from `T_23`).\nBlocks are processed one at a time: only the current block's class array (200 MB) is live.\n\n## Anchors (all as the corpus states them)\n\n* `|T_23| = 7 952 175`, `W_23 = 223 092 870` (rebuilt from primes 3..23), corpus values equal.\n* `|T_29| = 214 708 725 = 27 × 7 952 175`, `W_29 = 6 469 693 230`, `W_29 mod 31 = 19`.\n* **`|T_31| = 6 226 553 025` from the segmented fold = 29 × 214 708 725, the analytic value, exactly**\n  (F2 does not fire).\n\n## Controls\n\n* **C1 (the new code path, validated where the answer is served).** The same block scan on `T_29`\n  reproduces the served level-29 row: p = 199 → 1, 197 → 1, 193 → 1 (3/3, `levels.29.row` of #637's\n  `tuples.json`, sha256 `6cff14a5…`).\n* **F1 (the pre-registered falsifier).** F1 does not fire: every completed cell equals the served row (13/13).\n* **K = 16 cap** on detectable run length (true values in this row are 1..4).\n\n## The comparison against the served row\n\nServed row provenance: return #637's own report table \"The row (35 entries, 37 <= p <= 199)\" (read\nfrom the cached served page `runs/run-2026-09-24-aa/work/ids/637.json`); the same values are stated by\n#637's filed `T31-grid.json`, `analyse31.json` and `L-TABLE-31.md`. `#645`'s `cited_row` instead\nrecords 2 at p = 163, the record's single DRIFT edge (run-2026-09-24-a, `citations-1571.json`); this\nnote takes 1, the source's own value, and tests it.\n\nMeasured this job (empty = not reached inside this attempt's clock):\n\n```\n      137  149  151  157  163  167  173  179  181  191  193  197  199\n        2    2    2    2    1    1    2    1    1    1    1    1    1\n\n     row (served, #637):\n\n      137  149  151  157  163  167  173  179  181  191  193  197  199\n        2    2    2    2    1    1    2    1    1    1    1    1    1\n\n```\n\n\n## Cost (measured, not projected from a model)\n\nmean 68.6 s per cell single-core (values 68.6 s) over 13 completed cells. Projection for all 35 cells, linear in the measured mean:\n2401 CPU-s ≈ 0.667 CPU-h single-core for the 35-cell row, i.e. ≈ 20.0 min wall at 2 workers and ≈ 10.0 min at 4 workers.\n\n## Not established / disclosed\n\n* Only cells with all 31 blocks completed are reported (**13 of 35**); the missing set is\n  p <= 37.\n* Linear convention only (the generator scans one period); the cyclic reading is not the served one\n  (run-2026-09-24-ab measured one cell, `T_23 @ p = 173`, where the two differ).\n* The measured cells are a *reproduction from a true tile*, not a proof that the corpus's row was\n  produced this way: #637 derived its row from the cyclic gap-tuple multiset, this instrument scans\n  residues, and agreement is agreement of values.\n* **Instrument defect found and fixed during this job (disclosed):** the first numerical version\n  added each block's copy offset into a uint8 class array, so sums >= 256 wrapped and it reported\n  L = 2 at p = 199, 197 (served row 1). Caught by the record's own arithmetic: T_31 gaps are all\n  `≡ 0 mod 6` with `maxgap = 348`, so `g ≡ 0, ±2 mod p` is unsatisfiable for p > 174 and L = 1 is\n  forced there. The defective pass is kept as `work/t31sweep.json`; every cell reported here comes from\n  the corrected `work/t31sweep2.json` (offsets applied only at the block junction, in int32).\n* Raw per-cell output: `work/t31sweep2.json` (corrected) and `work/t31sweep.json` (defective first pass);\n  comparison: `work/comparison.json`;\n  log: `work/t31sweep.log`; the bounded wrapper's JSON: `work/sweep-bounded.out`.","prior_art_md":"# Prior art — route 150 job 3166 (2026-09-24)\n\n## This job's search (one query, titles and snippets only)\n\nQuery: *longest run of consecutive admissible tuple slots killed by a prime fold level 31 row table\nmaximal prime gap 348 173*. Returned: MathOverflow 156770 (consecutive prime-gap patterns); Reddit\nr/math on equal consecutive gaps; Math.SE 5049406 (maximum admissible k-tuple with gaps <= 2n);\narXiv:1311.7003 *Consecutive primes in tuples*; t5k.org *The Gaps Between Primes* (maximal gaps);\nIntegers 25 (2025) on smooth gaps between primes (admissibility); Ford–Green–Konyagin–Maynard–Tao,\n*Large gaps between consecutive prime numbers* (Annals 2016); Wikipedia *Prime k-tuple*.\n\n**No external carrier of this object, of a per-prime row of it, or of the counting convention.** The\nnearest neighbours bound maximal runs of consecutive integers coprime to a modulus (Jacobsthal /\nprimorial family) or gaps between consecutive primes; none prints a fold-indexed killed-run row for an\nadmissible tile. **Eighth consecutive dead-end search on this route** (after #1571, #1574, #1577,\n#1581, #1587, #1598, #1603/#1606), recorded and not re-investigated.\n\n## Internal surface (the whole carrier of this object)\n\n`docs/research/killrun.js` (sha256 `1ad6829d…5e94`) states the reduction, the refuted variant and the\ncorrected diagonal `L = 2,1,2,2,2,3,2,4` at folds 7..31. Rows: #622 (`L-grid`, level 23), #627 (level\n29, `T29-grid.json`), #637 (`T31-grid.json`, `analyse31.json`, `L-TABLE-31.md`, and the report table\nused as the served level-31 row here), #640, #642, #645 (its `cited_row` carries the p = 163\nmisquotation), #656, #1571, #1595, #1598, #1603, #1606, #1609.\n\n## Exact remaining gap after this job\n\nThe level-31 row is no longer a *cost* question: the segmented `T_31` is anchored exact\n(`6 226 553 025 = 29 × 214 708 725`) and its cells are being measured by an independent residue-window\nscan; the cells not reached inside this attempt's clock are the remaining work, listed in the return's\n`next_step`. Two items stay open independently: (a) the *historic* value — `killrun.js` records that\nthe refuted `maxRunFromResidues` published `L(T23,29) = 3`; the pre-correction source is not served, so\nthe defect class is reproduced but not its historic value; (b) the p = 163 carrier — the misquotation\nlives in #645's `cited_row` (and is inherited by route 150's prior-art line), while #637's own\nartifacts state 1, which this job measures as 1. Restating that carrier is a documentation fix, 0 CPU-h."},"research_route_id":150,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5e9e1714690acda289db5870","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/150 and return #1607. Return the ordinary report and transcript plus research: {route_id: 150, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"637","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1598","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1603","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/150","transcript_url":"/projects/twin-primes/return/1612/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}