{"id":1521,"job_id":2865,"problem_id":1,"lane_id":null,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Triage of route 147: proceed — the slice already has a served witness of the target phenomenon, and the arithmetic expects 2–3 more\n\n**Verdict: `promising`, proceed with the priced pass.** Route 147's contribution (#1516) proposes the\nonly deficit-capable slice at `P=30`, `p in {7,11,13}`, `2.5e7 < Mp <= 3e8` (5536 rows, ~0.5 CPU-h).\nThree things make it a bet rather than a sweep: the served census **already contains a `d=2` witness in\nthat exact cell family**, the slice's own rate extrapolates to ~2–3 further `d>=2` rows, and a null\nresult would be *sharp* rather than empty. No new computation is run in this triage; every input is a\nserved or local artefact.\n\n## 1. The filter is confirmed by the served census, not assumed\n\nReproduced exactly from the served 15747-row census (`out/full_census_summary.out`): rise histogram\n`-2:1, -1:5, 0:9729, 1:4276, 2:1578, 3:137, 4:21`; 686 hard rows (`p <= 2A`) and 15061 easy; **6\ndrops, all in the hard regime, all at `P=30`**.\n\n| # | P | p | R | A | B | d | hard | p <= A |\n|---|---|---|---|---|---|---|---|---|\n| 1 | 30 | 11 | [7,13,17,23] | 12 | 11 | 1 | yes | yes |\n| 2 | 30 | 11 | **[7,13,19,23]** | 12 | **10** | **2** | yes | **yes** |\n| 3 | 30 | 11 | [7,17,19,23] | 12 | 11 | 1 | yes | yes |\n| 4 | 30 | 13 | [7,11,19] | 9 | 8 | 1 | yes | no |\n| 5 | 30 | 13 | [7,17,19,23] | 12 | 11 | 1 | yes | no |\n| 6 | 30 | 17 | [7,13,19,23] | 12 | 11 | 1 | yes | no |\n\nRow 2 is the point: **`d=2` already exists, at `P=30`, `p=11`, `R=[7,13,19,23]`, and it satisfies the\nincrement's necessary condition `p <= A` (11 <= 12)**. Row 6 (`p=17 > A=12`) is the control on the\nother side: it drops `d=1` and the filter correctly excludes it from being deficit-capable. So the\nroute's filter is not an assumption about the data — the data's only `d=2` row sits inside the slice\nfamily, and its only counterexample sits outside the filter.\n\n## 2. The investment arithmetic\n\nThe served census contains **2200** rows at `P=30` with `p in {7,11,13}` and `Mp <= 2.5e7`\n(`out/price_p30_target.out`), carrying **5 drops** (3 at `p=11`, 2 at `p=13`) and **1** of magnitude\n`>= 2`. The proposal extends the same `P`, the same `p`-set and the same `|R|` classes to\n`2.5e7 < Mp <= 3e8`: **5536 new rows** (two already-served categories aside). Under exchangeability\nwithin the cell family:\n\n- expected drops in the pass: `5536 x 5/2200 ~= 12.6`\n- expected rows with `d >= 2`: `5536 x 1/2200 ~= 2.5`\n- price: ~0.5 CPU-h, per-row setup dominated (measured per-R-set cost, 6000 of 6330 `|R|=4` sets in\n  753 s).\n\nHalf a CPU-hour for an expected ~12 drops and ~2–3 second-witnesses of a phenomenon the corpus has\nseen exactly once is a clear proceed.\n\n## 3. The falsifier is informative, which is why this is worth doing\n\nPre-registered: if the pass returns **0 rows with `d >= 2` while returning >= 5 drops of `d = 1`**,\nthe larger-`Mp` regime is *structurally different*, not merely sparser — the exchangeable reading is\nrefuted and the deficit phenomenon becomes a small-modulus accident rather than a regime property.\nThat is a sharper statement than \"the sweep found nothing\", and it is only available because the\nslice is pre-filtered to where `d >= 2` is arithmetically possible.\n\n## 4. Not claimed\n\nThat any further `d >= 2` row exists: the extrapolation in §2 is the only non-exact step, and it is\nlabelled heuristic. Nothing here is about `G_2`, `beta_2` or twin-prime infinitude, and no claim from\n#1516 is strengthened beyond the census reproduction. The pass's rows are candidates, and a `d >= 2`\nfinding would be a finite computation, not a theorem.\n","patch":null,"cpu_hours":0.1,"hashes":{"report.md":"303137743511500a4de259b7d33734cbd7f6ca164d96e9cdf37de71483e86133","evidence.md":"e7eab11bb8336b5f58ebe8854e2fa9460d90468616029a27b062aa655953dcab","price_p30_target.out":"40c0d363b78bdceefd3b72b6e0131a676350c5f396358e84d52f3993d5864e1f","full_census_summary.out":"ce82eee8b605f141b3735496b6c54353cafaec8015f7d1e458e546462c8e9d4d"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T06:30:18.671Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1516,1384,1365,1267],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-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":"high","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":147,"next_step":{"method":"Run the census instrument over exactly those 5536 rows (plus the 12 served |R|=5 rows), recording (P, R, A, p, B, d) per row, and report the full d histogram with every d >= 2 row and its witness.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Zero rows with d >= 2 while at least 5 rows drop by 1: the exchangeable reading is refuted and the deficit is a small-modulus accident, which is a sharper negative than an empty sweep.","success":"About 12 drops and at least one row with d >= 2, i.e. a second witness that the deficit is a regime property of the P=30 cell family.","question":"Do the 5536 new P=30 rows with p in {7,11,13} reproduce the served rate of drops (about 5 per 2200) and of d >= 2 (about 1 per 2200)?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[1516,1384],"evidence_md":"# Evidence — triage of route 147\n\n## Inputs (served or local; nothing recomputed)\n\n- Served 15747-row census, reproduced in `research/triage-117/out/full_census_summary.out`:\n  histogram `-2:1, -1:5, 0:9729, 1:4276, 2:1578, 3:137, 4:21` (sum 15747), 686 hard (`p <= 2A`) and\n  15061 easy, 6 drops all hard, all at `P=30`.\n- The six drops with `(P, p, R, A, B, d, p<=A)` are printed there; the `d=2` row is\n  `P=30, p=11, R=[7,13,19,23], A=12, B=10`.\n- `out/price_p30_target.out`: `P=30` rows with `p in {7,11,13}` and `Mp <= 3e8` = 7736, of which 2200\n  are inside the served `Mp <= 2.5e7` census and **5536** are new at `2.5e7 < Mp <= 3e8`.\n- `out/deficit_capable.out`: the `d >= 2` filter `p <= A` empties the re-scoped `P >= 210` cells\n  (1389 R-sets, 1619 hard rows, 0 with `p <= A`), so the slice in §2 is the only remaining ground.\n- Constants: 7736 total rows, `sum(Mp) = 7.550e11`; price basis 6000 `|R|=4` R-sets in 753 s\n  (`out/deficit_capable_P30.out`).\n\n## Arithmetic (all of it)\n\n- served small-`p` subset: 2200 rows, 5 drops, 1 of magnitude 2.\n- new slice: 5536 rows.\n- expected drops `= 5536 * 5/2200 = 12.58`; expected `d>=2` `= 5536 * 1/2200 = 2.52`.\n- price ~0.5 CPU-h.\n\n## Calibration\n\n- **Verified** (exact reproduction): the histogram, the hard/easy split, the six drops and their `A`,\n  `B`, `d`, and the `p <= A` column; the 2200/5536 split. These are read off the served census\n  reproduction and the local enumeration, and the reproduction matches the published counts exactly\n  (`diff 0` on every bucket).\n- **Heuristic** (the only inference): the exchangeability of the small-`Mp` and large-`Mp` halves of\n  the same `(P, p, |R|)` family behind the 12.6/2.5 expectations.\n- **Measured**: the per-R-set cost behind the price.\n- **Not claimed**: existence of further `d >= 2` rows; any asymptotic or twin-prime statement.\n\n## Reproduce\n\n```\ncd research/triage-117\n$V full_census_summary.py            # exact census reproduction -> out/full_census_summary.out\n$V price_p30_target.py               # 2200 served / 5536 new split -> out/price_p30_target.out\n$V deficit_capable.py                # the p <= A filter over the re-scoped cells\n```","prior_art_md":"Corpus, served: #1516 (this route's contribution and price), #1384 (the route-117 triage whose re-scoped sweep is being triaged here), #1365 (the census whose counts are reproduced), #1267 Theorem 3 (the `d <= floor(2A/p)` bound the filter comes from). All of the triage's numbers are read off those served artefacts; nothing is recomputed. External: paired-Jacobsthal / covering-run computations (Ziller-Morack, arXiv:1706.03668, h2 to p=73) compute the same two-class object at larger primes but not the rise `B - A` under adding one prime to a fixed P=30 tile at the moduli this slice reaches, so cited prior work does not cover the proposed contribution and `known` would be wrong. The remaining gap is exactly the measured pass: whether the larger-Mp half of the same cell family keeps the small-Mp drop rate."},"research_route_id":147,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_9cda8e25020f0955d5df6681","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/147 and return #1516. Return the ordinary report and transcript plus research: {route_id: 147, 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":"1384","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1516","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/147","transcript_url":"/projects/twin-primes/return/1521/transcript","files":[{"sha256":"303137743511500a4de259b7d33734cbd7f6ca164d96e9cdf37de71483e86133","name":"report.md","bytes":3602},{"sha256":"e7eab11bb8336b5f58ebe8854e2fa9460d90468616029a27b062aa655953dcab","name":"evidence.md","bytes":2171},{"sha256":"ce82eee8b605f141b3735496b6c54353cafaec8015f7d1e458e546462c8e9d4d","name":"full_census_summary.out","bytes":1017},{"sha256":"40c0d363b78bdceefd3b72b6e0131a676350c5f396358e84d52f3993d5864e1f","name":"price_p30_target.out","bytes":566}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}