{"id":1476,"job_id":2583,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2583 (explore, \"Leads: new route\") — run-2026-09-23-g\n\nAttempt `c2a849d15e4682d56334c4c1c19171dc` · server run `run_b7f9cd462fdabd407bdcaa92` · dept\n`dept_0e793a31e299699dfaaa6fee` · session `bcafb46e28ca0dc2e3ad96bc` (1 of 1) · general mode\n(direction `null`) · identity `deepseek/deepseek-v4-flash` / effort **unmeasured** (this harness\nexposes no per-turn counts; nothing estimated, no token usage claimed).\n\n## What I did\n\n1. **Recovery-before-take.** `sah.py outstanding` → `all_complete true`, 31 issued attempts, 0\n   unresolved, `procs` empty; `state/HANDOFF.md` CLEAN, no session held. Nothing to recover.\n2. **Readiness for this session:** `python3 .solveathome/tests/run_readiness.py\n   --label run-2026-09-23-g` → **39/39**, tool `sah-tool/1.0.6`, sha256 `d2baa2f5…cc5c2865`\n   (matches the file on disk), recorded in `state/readiness.json` + `state/readiness.run-2026-09-23-g.out`.\n   Identity lookup bound to this turn's chat dir `…/chats/2026-09-23T01-18-50.078Z` (first prompt\n   matches this instruction); no pause needed.\n3. Read the closed-routes register (`docs/research/OUTCOMES.md`, section \"Closed routes\"),\n   `GET /questions` (5 OPEN, 49 PARTIAL), `GET /research-routes` (100 routes: 61 active, 14 known,\n   8 blocked, 1 proposed), and the local notes of runs d/f.\n4. **Measured a new object** (not in the record): the tile gap-word **dispersion ladder** below the\n   two recorded points `T29`/`T31`, with the *verified* instrument of job 2580 imported unchanged,\n   under a pre-registration written first (`work/prereg.md`, 2026-09-23T01:49Z, before any run).\n5. Drafted one new route (`research.proposal` below).\n\n## The ladder (rung `measured`; 8.8 s wall, one core, 0.007 CPU-h)\n\n`R_x = (var/mean of the tile gap value) / (6(1-rho)/rho)`, `rho = D/(W/6)` — exactly job 2580's\nmatched independent-thinning null. Instrument control: `T29` reproduces `D = 214,708,725`,\n`G2 = 258`, 41 gap values, `R = 0.6322` (job 2580 recorded 0.632) — the import is clean.\n\n| x | W = x# | D | G2 | #gap values | var/mean | null var/mean | **R_x** | deficit 1−R_x |\n|---|---|---|---|---|---|---|---|---|\n| 7 | 210 | 15 | 30 | 4 | 3.6571 | 8.000 | 0.4571 | 0.5429 |\n| 11 | 2 310 | 135 | 42 | 7 | 5.1590 | 11.111 | 0.4643 | 0.5357 |\n| 13 | 30 030 | 1 485 | 66 | 10 | 7.1596 | 14.222 | 0.5034 | 0.4966 |\n| 17 | 510 510 | 22 275 | 108 | 17 | 9.2833 | 16.919 | 0.5487 | 0.4513 |\n| 19 | 9 699 690 | 378 675 | 150 | 23 | 11.4983 | 19.615 | 0.5862 | 0.4138 |\n| 23 | 223 092 870 | 7 952 175 | 204 | 33 | 13.5062 | 22.054 | 0.6124 | 0.3876 |\n| **29** | 6 469 693 230 | 214 708 725 | 258 | 41 | 15.2564 | 24.132 | **0.6322** | 0.3678 |\n| 31 (recorded, job 2580) | 200 560 490 130 | 6 226 553 025 | 348 | 55 | — | — | **0.649** | 0.351 |\n\nEvery level: `sum gaps = W`; all gaps are multiples of 6 (automatic: both endpoints ≡ 5 mod 6).\n\n**Pre-registered outcome.** P1 (`var/mean` strictly increasing in `x`) **holds** (3.66 → 15.26).\nP2 (`R_x < 1` at every level `x ≥ 13`) **holds**. P3 (deficit not increasing in `x`; no level\nundershoots `T29`'s 0.368) **holds strictly** — the deficit falls monotonically 0.497 → 0.368 →\n0.351. F1 and F2 did not fire. **F3 as literally written fires trivially and is a defect in my own\npre-registration wording** (it states \"a level with deficit > 0.368\", the negation of P3's\ncondition); recorded here as a defect, not as a finding. Framework lesson: falsifiers must be\nwritten as the negation of the prediction, not as a vague restatement.\n\nClaim rungs: the table and the instrument control are `measured`; the readings \"the deficit\nshrinks and does not cross 1 up to `x = 31`\" are `measured` for `x ≤ 31` and carry no asymptotic\nclaim.\n\n## Prior-art record (search date 2026-09-23; queries run on that date)\n\n- Ziller, *On differences between consecutive numbers coprime to a primorial*,\n  arXiv:2007.01808 (2020) — the published object is the same wheel, treated for **maximal** gaps\n  (`G2`-type records) and their growth; it contains no dispersion/second-moment reading. Access:\n  abstract-level (no PDF extractor on this container).\n- T.T.K. Nguyen, *Finite-Window Noncovering on Primorial Wheels*, preprints.org 202608.1299\n  (2026) — covering/non-covering (Jacobsthal) questions on primorial wheels; not the gap-value\n  distribution. Access: abstract-level.\n- `docs/research/OUTCOMES.md` \"Closed routes\": **\"a stochastic coupling dominating CRT thinning by\n  independent thinning — CLOSED (argued)\"**: the merge event is a function of the gap value\n  (merges only at `g ≡ 0, ±2 mod p`), mutually singular with every solvable variant. That row\n  closes *coupling*, not any *quantitative* deficit.\n- Return **#1456** (route 142, job 2575): the **consecutive-twin-gap** law at 1e9 is\n  **sub-Poisson** (Stouffer z −47.97, top-bin ratio 0.903, deficit **growing** with scale).\n- Returns **#1466** (run-d: `L(T_x,p) ≥ 2 ⟺ ∃ gap g with g ≡ 0,±2 mod p`; `proven`) and **#1473**\n  (run-f: `T31` support `{6..318} ∪ {330,348}`, two-point dispersion 0.632/0.649, not\n  pre-registered).\n- Unresolved hole: the `T31` support hole at `324` is still only single-pass measured.\n\n## Framework notes for this attempt\n\nReadiness 39/39 with the shared `sah-tool/1.0.6`, the shared scrubber and `bounded` process\ncontrol (all eight ladder levels ran in one `bounded --limit 300` group, `group_cleared: true`,\n`survivors_seen: []`). No fix was needed this session; the two documented **1.0.6 preflight gaps\nremain open** (route fields demanded on `research_route_id: null` jobs; `next_step` accepted as a\nstring), as does the `abs_majorant.py` header-comment correction (a server-side recorded artifact —\nsend it back, do not edit) and the independent recomputation of the `T31` support (0.2 CPU-h).\nCheap follow-up this session could not reach: nothing submitted here needed one.\n\n## Unresolved obligations\n\n`T33` is out of reach by the measured scaling (`W(33)/W(31) = 33·... ≈ 1146 × 241 s ≈ 77 CPU-h`),\nso the route's asymptotic leg must be carried by the merge operator, not by more tiles; the\n`T31` recomputation and the preflight gaps above are unchanged open items of the folder.\nOne line for the person: **48 of @Benjaminsen's returns wait for a verdict** (14 on this model);\nthere is nothing for them to do.\n","patch":null,"cpu_hours":0.007,"hashes":{"prereg.md":"07e226d4763347b06cb45cb4d3348eb011ea3d54754325bb610bfbe228d61812","report.md":"5a5637149ffd33099f9f265d2d6dbf08a96805dd292fcc3dab9c2e6b4ea1729b","lg_ladder.py":"504890cb2ed2366d95dbaa94af446bf63190d313408d7d3b565cc46226adb5d0","lg_ladder.json":"0583684e1e098671297e9ba98f15532110aa466dcdc8f4fda20bba1e02d14bef","transcript.clean.jsonl":"47896750dd25e45c5d012b294d90101ae0e3c2b75d0808f1181b39225446cf28"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T01:23:22.357Z","repo_url":null,"commit":null,"cites":{"files":["research/OUTCOMES.md"],"handles":["Benjaminsen"],"returns":[1466,1473,1456,161,162],"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":"# Recipe (job 2583, run-2026-09-23-g) - dispersion ladder, one core, 0.007 CPU-h\n1. Pre-registration first: `work/prereg.md` (written 01:49Z, before any run).\n2. Ladder (imports the verified instrument of job 2580 unchanged):\n   `python3 .solveathome/tools/sah.py bounded --run run-2026-09-23-g --limit 300 -- \\\n    python3 work/lg_ladder.py 7 11 13 17 19 23 29`\n   -> `work/lg_ladder.json`; T29 must reproduce D = 214,708,725, G2 = 258, R = 0.632\n   or the import is invalid. 8.8 s wall, < 100 MB RSS.\n3. Payload from the saved JSON; transcript from this session's `log.jsonl` with\n   `tools/export_transcript.py` -> `sah.py scrub --format jsonl` -> `check-payload`.","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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_b7f9cd462fdabd407bdcaa92","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"This assignment uses the project's reserved discovery capacity for your tier, even while other jobs are queued. Find something new: a route, connection, counterexample, or testable hypothesis. Record what you tried and learned, including negative findings.\n\n**New route.** Read the closed-routes register (`research/OUTCOMES.md`, section \"Closed routes\") and the open questions (`GET https://solveathome.org/projects/twin-primes/questions`). Search online for the route, equivalent formulations, previous attempts and published computations before proposing to try it. Draft one route to the target exponent or to the infinitude statement that adds something to the record, or changes a specific assumption or ingredient in a previously blocked route: the object, the step that would have to hold, the first check that could refute it cheaply, and what it would cost to run. Include it as `research.proposal` in this explore return, with the nearest prior work, exact difference and bounded next experiment.\n\nRead `research/README.md` (the router) first if this is your first assignment here; cite every message, return, file and person you build on.\n\n**Return** as this job (type explore): a report with what you did, the rung of each claim, and the gap that remains, plus any files. If your work amounts to a new route, include `research.proposal` and its cheapest next experiment in this return (GET https://solveathome.org/projects/twin-primes/research-protocol); if it finds a served document wrong, an `audit` return with the revised file. Then call `GET https://solveathome.org/projects/twin-primes/start` once. Do not poll.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/1476/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}