{"id":720,"job_id":1519,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1519 — Rescue investigation: return #7\n\nRun `run_20260916_173305_986jFw`, attempt `b47aac9bb7a603b30df23b1f14ae82fb`. Explore / discovery /\nstage **rescue**, general mode, no route. Compute: `cpu_hours: 0` (no local derivation beyond reading\nserved files and hashing them). Rung: **measured** for the checks below; SOURCE-READ for every claim\nabout return #7, its review and the served documents.\n\n## 1. Verdict\n\n**The rejection of return #7 closes the ATTEMPT, not the STATEMENT.** Return #7 is the audit (job #58)\nof `paper/beta2-note.md`, \"An upper bound for the twin Jacobsthal function\". It is `rejected` by review\n#12 (`gpt-6-astra`, rung measured, verification `spot`, one trusted vote, 2026-09-11). The review's own\nheadline is decisive and is quoted verbatim in check 2:\n\n> The sieve argument is not refuted by this review.\n\nThe review also reproduces the attempt's finite work independently — all nine gap values through 23#\n(`2, 6, 12, 30, 42, 66, 108, 150, 204`), all nine censuses, and an integer-gcd check of the 41#\ncertificate at `r = 3,784,200,788,231` — and publishes its own verification files\n(`/files/66841a03…`, `/files/aac21ef2…`, `/files/b479ecfe…`). So neither the theorem nor its finite\nevidence is what failed.\n\n**What the rejection actually condemns** is (a) one false source-availability claim *in the audit's own\nreport*, (b) one label the revision introduced, and (c) two calibration overclaims in §5/§6 that the\nreview asks to be stated at their true rung. All four are localized and repairable; none reaches the\nβ₂ + ε bound, its §3 derivation, the dimension check, or the free lower bound.\n\n## 2. Layer assignment of the four required corrections\n\n| # | correction | layer | why |\n|---|---|---|---|\n| 1 | Cite `research/exponent-control.js` OUTPUT S7 instead of declaring the uncertainties unprinted; the audit report's issue 7 is **false** | **attempt** (the report's claim) — and a *locator* fix in the note | executed below; the audit's own sentence about \"both files\" is contradicted by line 506/508 |\n| 2 | New §5 label says `pₙ = 41` where the numbers are 43 → G₂ = 618 | **attempt** (introduced *by this revision*) | the served file's pair is 41 → 546 and carries no `pₙ=43` label (check 11) |\n| 3 | The control exponent must be **conjectural**, not a known answer | **statement** (§5's calibration; also in the producer script) | published record below; the producer and the note share the overclaim (check 9) |\n| 4 | §6.6's \"exponent 2 ⇔ twin primes\" must be qualified as `G₂(x#) < x′² − 2`, not `Cx²` with unspecified `C` | **statement** (prose of the pre-revision note) | the sentence is in the file the review read, before any revision (check 12) |\n\nCorrections 3 and 4 are the only statement-level items, and both are **downgrades of prose rungs**, not\ndefects of the proof: #3 changes what the *control* calibrates (the estimator's rung), #4 narrows an\nequivalence claim in §6.6. Corrections 1 and 2 are attempt-scoped, and #1 is an error the audit\nintroduced about the repository's own files.\n\n## 3. Decisive evidence, executed rather than assumed\n\nThe review left four concrete falsifiers. The first one is the cheapest and it decides the layer\nquestion, so it was run (checks 4–6):\n\n> show that S7 lacks the cited uncertainty figures\n\nIt does **not** lack them. `research/exponent-control.js`, OUTPUT S7, line 506 reads\n\n```\n//     G2     [5,37]   10  1.801   +-0.074        2.7     1.539+-0.094    0.729  (aeff 0.48->1.98)\n```\n\nand line 508 gives the h₂ corrected result `1.566+-0.058`. Every figure the report declared\nunavailable is printed by the producing script, exactly as review correction 1 says. Two consequences:\n\n1. The audit's issue-7 sentence (\"neither served source prints the uncertainties\") is **factually\n   false**, and the review is careful to separate this from the manuscript: \"the manuscript's narrower\n   statement that the `.md` file does not reprint a figure is not disproved merely by finding it in\n   `.js`\". The repair is to **cite the producer** — a locator, not a retraction.\n2. The served note is byte-identical to the original the review names\n   (`sha256 c6c23609c582c8d423fd7926449875df1dcc4e50e8f3d4b2af06b203c88584b6`, check 7), so there is\n   no drift between the file the review read and the file the server serves. The rejection is about\n   the submitted revision `b8721a0d…`, not about the served note.\n\nIndependent grounding for correction 3 (check 8), from the authoritative status record rather than from\nthe review's summary of it — Erdős problem #687, `erdosproblems.com/687`, fetched 2026-09-16, HTTP 200,\nsaved as `replies/erdos687.txt`:\n\n- status **OPEN**, \"$1000\", \"cannot be resolved with a finite computation\";\n- best known upper bound **Iwaniec [Iw78], Y(x) ≪ x²** — i.e. exponent at most 2 is proven, exponent 1\n  is not;\n- best known lower bound `Y(x) ≫ x log x / log log log x` (GPT 5.6 Pro, improving FGKMT 2018);\n- **Maier and Pomerance conjectured** `Y(x) ≪ x(log x)^{2+o(1)}` — the near-linear scale is a\n  conjecture.\n\nThat makes correction 3 exactly right, and it makes the correction local: §5's bias correction is\ncalibrated against a control whose exponent is conjectural, so the corrected estimates are conditional\non that conjecture, while the **proven** floor of 1 survives as a floor. The same overclaim lives in the\nproducer's own header comment (\"true exponent 1 + o(1)\", check 9) — which is why this is a\nstatement-level repair rather than an erratum against the revision.\n\n## 4. Changed alternatives, searched before testing\n\n- **The producer-not-reprint audit.** The changed ingredient that dissolves correction 1 is to audit\n  *the script that produced the numbers* rather than the summary document that reprints them. The\n  served corpus already contains the producer; the audit looked at `.md` and concluded about \"both\n  files\". This is the concrete alternative the review implicitly demands (\"cite the available\n  producer\"), and it is a distinct test that avoids the obstruction: the falsifier is one `grep` on\n  OUTPUT S7, and it **fails**, which is what reopens the audit's issue 7 as a locator fix.\n- **Re-priced calibration.** With the published record above, §5 can state: control exponent\n  conjectural (Maier–Pomerance), proven range `1 ≤ exponent ≤ 2` (lower bound GPT 5.6 Pro; upper bound\n  Iwaniec), and therefore the fitted 1.50–1.57 corrected centrals are conditional. This replaces the\n  note's claim that the control's exponent *is* 1, without touching the β₂ + ε theorem.\n- **Search channels, recorded honestly.** The hosted `web_search` channel returned **no results** for\n  three queries (Erdős 687 status; Maier–Pomerance / Iwaniec exponent; Jacobsthal maximum gap upper\n  bound). That is a **channel failure, never evidence of absence**. The `read_url` channel was live and\n  answered the one authoritative page (HTTP 200), which is why the status facts above are cited from\n  that page and not from a search snippet.\n- **Prior art already on record (read, not re-derived).** The department's search record\n  `research/PRIOR-ART.md` is already the owning convention for this object: G₂ is a **rediscovery** of\n  OEIS A144311 (published 2008) and the reduction \"gap bound ⇒ twin primes\" is published in stronger\n  form by Ziller–Morack Thm 4.1 (2017); Maier–Pomerance 1990 is the earliest two-classes-per-prime\n  sieve device. Nothing there changes the rejection's scope, and no part of it is re-litigated here.\n\n## 5. What is preserved (refutations and their scope)\n\n- The rejection stands for the exact revision `b8721a0d…`: do **not** integrate that file.\n- The review's credited predecessor, **return #20**, was a later audit that identified some of the same\n  problems; the review says it does \"not approve return #20's entire revision\" either. That is a\n  second, independent obligation for whoever repairs the note.\n- The scoped literature negative (\"no two-class upper bound in print\") stays *scoped to the searches\n  recorded* — the review explicitly commends that reading over a proof of absence.\n- The DH-page claims remain the author's reading (`research/dhr-verification.md` §5); the review did\n  not open Diamond–Halberstam or Halberstam–Richert 1974, and neither did this reassessment.\n- The audit's *successful* computations (nine levels, censuses, 41# certificate), the §3 derivation and\n  the free lower bound all stand, now with independent published verification files from the review.\n\n## 6. Cheapest next experiment (for the repair, not for this attempt)\n\nOne bounded `audit` return that (i) applies corrections 1 and 2 as **locator/label** edits and (ii)\ndowngrades §5's control calibration to the conjectural rung with the four published citations above,\n(iii) qualifies §6.6 to the recorded sufficient target `G₂(x#) < x′² − 2`. Falsifier: if\n`research/exponent-control.js` OUTPUT S7 is later changed so that it no longer prints line 506/508, the\nlocator fix is void. Success criterion: the revision is rejected by review only for reasons that are\nnot \"the source is unavailable\".\n\n## 7. Obligations left open (explicit)\n\n1. `research/exponent-control.js` itself carries the same \"true exponent 1 + o(1)\" overclaim as §5; the\n   producer should be corrected alongside the note, otherwise the locator fix cites a source that\n   asserts the unproven exponent. Not edited here — no served file was touched by this attempt.\n2. Return #20's revision was never approved by the review and is not adjudicated here.\n3. The web-search channel was unavailable (three empty queries); any wider prior-art claim must wait\n   for a working channel or another route.\n4. This harness exposes no token counters, so usage for this return stays **pending**, recovered once\n   through `POST /projects/twin-primes/return/<id>/transcript` under this run's headers.\n\n## 8. Files\n\n- `job1519-report.md` — this report.\n- `job1519-checks.py` / `job1519-checks.json` — 14 offline checks, all passing, re-runnable from the\n  department root as `python3 .solveathome/runs/run_20260916_173305_986jFw/work/job1519/checks.py`.\n- Evidence read (saved under `work/job1519/replies/`, fetched through the tested request path):\n  `return-7.json` (rid `q_40AvKl4pTPEP7teA`), `exponent-control.js` (rid `q_X5B5AA7Y7cVjAH27`),\n  `beta2-note.md` (rid `q_ofaRZzbRFGf5I7LJ`), `PRIOR-ART.md` (rid `q_D2aUwo6Hn4LIHG0f`), `erdos687.txt`\n  (read_url, HTTP 200).\n\nNo twin-prime claim, no novelty claim, no served file edited. The rejecting review's own rung is kept:\nmeasured for the finite checks, and every layer attribution above is marked measured or source-read.","patch":null,"cpu_hours":0,"hashes":{"job1519-checks.py":"eff7b8c6c934ea19fde40bae00ddc0d97bea25bd8225e2d64ec696ca553cc754","job1519-report.md":"215af1e99b20c4a18c0da7815cf944f2089c1cfcaac12e2155935dbadc6eba79","job1519-checks.json":"550bfd165594febb54e3e31c889f56310d6590fa9e1b8898afae18d8344723f2"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-16T15:35:55.352Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[7,20],"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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c326cb5ae203e5d0d94f8db1","run_id":"run_e772c958e678ded8f1ab467e","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Read return #7 and its search record, then search online for the method and changed alternatives before testing them. Check whether its negative conclusion closes only a statement or attempt. Use published numerical results with citations, reserving reproduction for later validation. Inspect the decisive evidence, then seek a concrete alternative. Preserve valid refutations. A promising alternative should return research.proposal with parent evidence in cites.returns, a prior-art comparison and the cheapest next experiment. If nothing changes, record the scoped obstacle and stop. This is a bounded sample; do not reproduce the whole investigation.","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/720/transcript","files":[{"sha256":"215af1e99b20c4a18c0da7815cf944f2089c1cfcaac12e2155935dbadc6eba79","name":"job1519-report.md","bytes":10720},{"sha256":"550bfd165594febb54e3e31c889f56310d6590fa9e1b8898afae18d8344723f2","name":"job1519-checks.json","bytes":3953},{"sha256":"eff7b8c6c934ea19fde40bae00ddc0d97bea25bd8225e2d64ec696ca553cc754","name":"job1519-checks.py","bytes":6721}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}