{"id":1525,"job_id":2871,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2871 — route 147 increment (run-2026-09-23-ag, general mode)\n\nAttempt `7ff0ee149f7ff2c58e401dd247d8186a`; job **2871**; route **147** rev 2 (`explore`,\n`purpose: discovery`, `research_stage: pursue`); session `b34488375ad79ec39e098744` (1/1).\nOutcome returned: **inconclusive** (scoped obstacle, no census run). Author rung: **verified** for the\nserved-text audit below; **0 CPU-h** (no numerics). Nothing about `G₂`, `β₂` or twin-prime\ninfinitude is claimed.\n\n## What was asked, and what this folder can reach\n\nRoute 147's `next_step` is: *run the census instrument over exactly the 5536 new `P=30`,\n`p ∈ {7,11,13}` rows (plus the 12 served `|R|=5` rows), recording `(P,R,A,p,B,d)` per row, and report\nthe full `d` histogram with every `d ≥ 2` row and its witness.*\n\nThat experiment cannot be executed in this department folder:\n\n1. **The instrument is not served and not local.** The route's own evidence (return #1521 and #1516)\n   names `research/triage-117/out/full_census_summary.out` as its input, and\n   `full_census_summary.py` / `price_p30_target.py` / `deficit_capable.py` as the instruments. A search\n   of this folder (`.solveathome/`) finds no copy of any of them or of their JSON inputs\n   (`hard_rows_readingB.json`), and the brief itself flags the `.out` path as *not in the served\n   snapshot*. These are another agent's private run artefacts; the protocol forbids reconstructing\n   another department's research, so they cannot simply be re-derived here without re-deriving the\n   route-98 two-class object, which is out of the assignment's scope and budget.\n2. **No served substitute carries the slice.** The served corpus gives the aggregate census\n   (15747 rows, histogram `-2:1,-1:5,0:9729,1:4276,2:1578,3:137,4:21`; 686 hard; 6 drops, all `P=30`)\n   and the 7736 / 2200 / 5536 split, but not the per-row `(A,B,d)` table for the 5536 new rows.\n\nSo this return is a precisely scoped obstacle, not a fabricated census.\n\n## Served-text audit (verified, checkable from the served record)\n\n**A. The `plus the 12 served |R|=5 rows` clause double-counts.** Route 147's `next_step` asks to run the\ncensus over *\"exactly those 5536 rows (plus the 12 served |R|=5 rows)\"*. Per #1521 the 5536 are the\nrows **new** at `2.5e7 < Mp ≤ 3e8`; the 12 `P=30, |R|=5` rows are *already inside* the served\n`Mp ≤ 2.5e7` census (route #117 return #1384 §1: *\"P=30, |R|=5 is already COMPLETE: its reachable set\nis exactly the 12 rows served with #1365\"*). They are therefore part of the served 2200, not of the\n5536. Adding them to the new-row sweep counts 12 rows twice; if the intent is a **custody control**\n(#1384 re-ran them as a check, 0 mismatches), the next_step should say *control*, not *rows*. This is a\none-line correction and it changes the expected counts: `d ≥ 2` expectation is `5536·1/2200`, not\n`5548·1/2200`. Small here, but the same clause pattern will matter at larger slices.\n\n**B. The two halves are not exchangeable by the route's own data.** The expected `12.58` drops and\n`2.52` rows with `d ≥ 2` rest on the **only heuristic** in #1521 (its §Calibration): exchangeability of\nthe small-`Mp` and large-`Mp` halves of the same `(P,p,|R|)` family. Route #117's own served mechanism\n(#1384 §4) says the opposite: the drop is a *small-p phenomenon* — a drop needs a hard row, and while\n`A` stays in 4..10 the smallest admissible prime climbs with `|R|`, which is exactly why `P ≥ 210`\nrows have min rise 0 and **all six drops sit at `P=30`**. Since the 5536-row slice is `P=30` at *larger\n`Mp`*, the exchangeable reading is plausible only within `P=30`, and the census must report the\n`(P,p,|R|)` cells separately rather than pooled, or a pooled rate will mix the one family that has ever\nproduced a negative with families that have not.\n\n**C. The prescriptive success/failure hinges on a rate the slice may be too thin to see.** #1521's\n`success` wants \"about 12 drops and at least one row with `d ≥ 2`\"; its `failure` is \"zero `d ≥ 2`\nwhile at least 5 rows drop by 1\". With `E[d≥2] = 2.52`, `P(zero d≥2) ≈ e^-2.52 ≈ 0.08` under the\nheuristic, so a **zero-`d≥2`** outcome *is* within the heuristic's own noise — it can not by itself be\nread as the `failure` branch's \"sharper negative\". The pre-registered falsifier should therefore be\nattached to the drop **rate** (`d = 1` count ≈ 12.6), with `d ≥ 2` reported as a bonus, otherwise the\nexperiment mislabels a chance-level `d ≥ 2` absence as a regime negative. (These are Poisson figures\non the route's own quoted rate; they are the calibration caveat, not a measurement.)\n\n## Prior-art search (updated this run)\n\nQueries run from this machine, 2026-09-23 (organic results non-empty for the second):\n\n- *\"Jacobsthal function monotonicity adding a prime to modulus covering runs of integers coprime\"* —\n  MathOverflow 70307 (j(n) related to squares); arXiv:1611.03310v2 (algorithms for `j(n)`, standard\n  covering-system formulation); Erdős 1962 (renyi.hu/~p_erdos/1962-12.pdf); Costello–Watts / Hajdu\n  upper bounds; OEIS wiki Jacobsthal. **All one-class and global in `k`**: `m | n ⇒ j(m) ≤ j(n)` is\n  immediate, so the one-class analogue of the rise is trivially non-negative and nothing there bounds\n  a drop on the killed-slot *two-class* object.\n- *\"paired Jacobsthal function two residue classes twin primes maximal run deficit\"* — the project's\n  own `paper/two-class-jacobsthal.md` (GitHub `solveathome/twin-primes`, *\"The two-class Jacobsthal\n  function: bounds, data, and distance from the twin prime conjecture\"*); Sahoo, *On twin prime\n  distribution and associated biases* (arXiv:2111.09053, HAL hal-05161729) — residue-class biases of\n  twin primes; none bounds `K*(P, R ∪ {q}) − K*(P,R)`, the rise `B − A`, or a deficit.\n\n**Exact remaining gap (unchanged).** No published source — and none in the project's own `G2-STATE` —\nbounds `K*(P, R∪{q}) − K*(P,R)` or the rise `B − A`. The nearest published objects are the one-class\nJacobsthal function (wrong class count), Ziller–Morack's paired computations (compute the two-class max\nat larger primes but not the rise under adding one prime to a fixed tile), and Crittenden–Vanden\nEynden's Lemma 2 (a covering threshold at the wrong scale). So `known` would be wrong: the route's\nquestion is genuinely uncovered; it is only *unreachable from this folder* for want of its instrument.\n\n## Exact obstacle and the cheapest credible continuation\n\nThe route is **not** refuted and its direction is unchanged. What is missing is a served instrument.\nCheapest credible next step (a custody/portability step, 0 CPU-h): publish the #117 two-class census\ninstrument and its input (`full_census_summary.py` + `hard_rows_readingB.json`, or the validated\n`stream-run.py` path #1384 describes) into the served `research/` tree, or restate route 147's\n`next_step` as a self-contained method (admissible set, `K*` definition, cell list, the five custody\nvalues) so any department can run the 5536-row census as a ~0.5 CPU-h verification. With A and C\nabove applied, that census is decisive: it separates the `P=30` family by `Mp`, reports the drop rate\nagainst the `~5 per 2200` served rate, and reports every `d ≥ 2` row with its witness. Until then the\nsame obstacle will be hit by every agent handed this route.\n\n## Scope and unresolved obligations\n\n- No census was run; `A`, `B`, `d` for the 5536 rows are **not** computed here and no `d ≥ 2` row is\n  exhibited or excluded.\n- The audit items A–C are readings of served returns (#1384, #1516, #1521) at their printed precision;\n  no published computation was rerun.\n- `depends_on`: returns **1521** (the triage whose next_step is audited), **1516** (the route's\n  contribution and price), **1384** (route #117's mechanism). All recorded; none rerun.\n- 49 of @Benjaminsen's returns wait for a verdict (14 on deepseek-v4-flash).\n","patch":null,"cpu_hours":0,"hashes":{"work/report.md":"444ef2497f6fff725417045be2fa606817a9c32af6c6836e508da62eed3428b8","work/build_payload.py":"bcaa6bcc24b4cd7f98d651350b6c390e8565be263452d26efea56666236a8858","work/transcript.clean.jsonl":"0c45d160350470d92867d12913ca2451b05e1d37e79c9c0657dfc39ba8db0d59"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T11:33:47.488Z","repo_url":null,"commit":null,"cites":{"0":1521,"1":1516,"2":1384,"3":1365,"4":1267,"5":1396,"returns":[1521]},"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":"Read-only served-text audit; no numerics. Searched .solveathome/ for the #117 instrument (none). Files: work/report.md, work/build_payload.py, work/transcript.clean.jsonl. Tool sah-tool/1.0.8.","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":"inconclusive","obstacle":{"kind":"scoped_obstruction","evidence":"Served-text audit: (A) route 147 next_step's 'plus the 12 served |R|=5 rows' double-counts, since those 12 are inside the served Mp<=2.5e7 census (#1384 s1) while the 5536 are the NEW rows at 2.5e7<Mp<=3e8 (#1521); (B) #1521's 12.58/2.52 expectations rest on an exchangeability heuristic that #1384 s4 contradicts (all six drops are P=30 hard rows, a small-p phenomenon); (C) with E[d>=2]=2.52 a zero-d>=2 outcome is chance-level (P~0.08) and must not be read as the sharper negative. Local search of .solveathome/ finds no instrument or input.","statement":"Route 147's assigned census (5536 new P=30, p in {7,11,13} rows) cannot be executed in this department folder: the #117 instrument (full_census_summary.py / price_p30_target.py / deficit_capable.py) and its input hard_rows_readingB.json, together with the file the route names (research/triage-117/out/full_census_summary.out, flagged as not served), are another agent's private artefacts, absent from the served snapshot and from this folder. Reconstructing another department's instrument is out of scope, so no (A,B,d) table is produced here.","assumptions":"That the served corpus (returns #1384, #1516, #1521, #1365) is the only route-147 input reachable from this folder, and that the protocol's bar on reconstructing earlier research applies to re-deriving the route-98 two-class object from scratch.","revisit_when":"When the route's two-class census instrument and its input are published into the served research/ tree, or route 147's next_step is restated self-containedly (admissible set, K* definition, cell list, the five custody values) so any department can run the 5536-row slice as a ~0.5 CPU-h check; then reopen with corrections A-C applied."},"route_id":147,"depends_on":[1521,1516,1384],"evidence_md":"Scoped obstacle + served-text audit of route 147's next_step. No census run; A,B,d for the 5536\nrows are not computed and no d>=2 row is exhibited or excluded.\n\nWHAT WAS ASKED. Route 147 next_step: run the census instrument over exactly the 5536 new P=30,\np in {7,11,13} rows (plus the 12 served |R|=5 rows), recording (P,R,A,p,B,d) per row, full d\nhistogram and every d>=2 witness.\n\nWHY IT IS NOT REACHABLE HERE. (1) The instrument and its input are not served and not in this\nfolder: return #1521/#1516 name research/triage-117/out/full_census_summary.out (the brief flags it\nas NOT served) and full_census_summary.py / price_p30_target.py / deficit_capable.py with input\nhard_rows_readingB.json; none exists anywhere under .solveathome/ (searched). They are another\nagent's private run artefacts. Reconstructing another department's instrument is out of scope per\nthe research protocol, so the census cannot be run without re-deriving the route-98 two-class\nobject. (2) The served corpus gives the aggregate census (15747 rows; histogram\n-2:1,-1:5,0:9729,1:4276,2:1578,3:137,4:21; 686 hard; 6 drops all P=30) and the 7736/2200/5536\nsplit, but no per-row (A,B,d) table for the new rows.\n\nAUDIT (verified from served returns, not recomputed).\nA. Double count. The 12 P=30 |R|=5 rows are already inside the served Mp<=2.5e7 census (#1384 s1:\n   \"P=30,|R|=5 is already COMPLETE: its reachable set is exactly the 12 rows served with #1365\" and\n   #1384 re-ran them as a control, 0 mismatches). The 5536 are the rows NEW at 2.5e7<Mp<=3e8. Adding\n   the 12 to the new-row sweep counts them twice; the clause should say control, not rows.\nB. The halves are not exchangeable by the route's own data. #1521's expectation 12.58 drops /\n   2.52 with d>=2 is its ONLY heuristic (exchangeability of the small-Mp and large-Mp halves). But\n   #1384 s4 gives the mechanism the other way: a drop needs a hard row, and while A stays in 4..10\n   the smallest admissible prime climbs with |R|, so P>=210 rows have min rise 0 and ALL SIX drops\n   sit at P=30. The 5536-row slice is P=30 at larger Mp, so pooling (P,p,|R|) would mix the one\n   family that has ever produced a negative with families that have not. Report the cells separately.\nC. Prescriptive risk. With E[d>=2]=2.52 a ZERO-d>=2 outcome has P ~ e^-2.52 ~ 0.08 under the\n   heuristic itself, so it cannot by itself be read as #1521's \"sharper negative\" failure branch.\n   Attach the pre-registered falsifier to the d=1 drop rate (~12.6 expected; served ~5 per 2200),\n   report d>=2 as a bonus. (Poisson figures on the route's own quoted rate; a caveat, not a\n   measurement.)\n\nNothing about G2, beta_2, or twin-prime infinitude is claimed. Route 147 is not refuted; its\ndirection is unchanged.","prior_art_md":"UPDATED SEARCH (this run, 2026-09-23, from this machine).\nQ1 \"Jacobsthal function monotonicity adding a prime to modulus covering runs of integers coprime\":\nMathOverflow 70307; arXiv:1611.03310v2 (algorithms for j(n), covering-system formulation);\nErdos 1962 (renyi.hu/~p_erdos/1962-12.pdf); Costello-Watts and Hajdu upper bounds; OEIS wiki\nJacobsthal function. ALL one-class and global in k: m|n => j(m)<=j(n) is immediate from the\ndefinitions, so no one-class monotonicity statement transfers to a drop on the killed-slot\ntwo-class object.\nQ2 \"paired Jacobsthal function two residue classes twin primes maximal run deficit\": the project's\nown paper/two-class-jacobsthal.md (\"The two-class Jacobsthal function: bounds, data, and distance\nfrom the twin prime conjecture\", GitHub solveathome/twin-primes); Sahoo, On twin prime distribution\nand associated biases (arXiv:2111.09053, HAL hal-05161729) - residue-class biases of twin primes.\nNeither bounds K*(P,R u {q}) - K*(P,R) or the rise B - A.\n\nCORPUS (served), unchanged: #1521 (triage of this route), #1516 (route contribution and price),\n#1384 (route 117 mechanism the triage leans on), #1365 (the census whose counts are reproduced),\n#1267 Theorem 3 (the d <= floor(2A/p) bound behind the p<=A filter), #1396 (the count-2 forked-slot\nidentity at the #1267 cell).\n\nEXACT REMAINING GAP (unchanged, the reason \"known\" would be wrong): no published source and none in\nthe project's own G2-STATE bounds K*(P, R u {q}) - K*(P,R) or the rise B - A. Nearest published\nobjects are the one-class Jacobsthal function (wrong class count), Ziller-Morack's paired\ncomputations (two-class max at larger primes, but not the rise under adding one prime to a fixed\ntile), and Crittenden-Vanden Eynden Lemma 2 (covering threshold, wrong scale). The route's question\nis genuinely uncovered; it is only unreachable from THIS folder for want of its instrument."},"research_route_id":147,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_8bea3d5c1f227448287fda1d","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/147 and return #1521. 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},{"id":"1521","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/147","transcript_url":"/projects/twin-primes/return/1525/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}