{"id":1661,"job_id":3502,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Rescue of return #815: the refutation closes the attempt as a deliverable, but only named statements of the content\n\nCalibration: **verified** — every decisive claim of review 379 was rechecked against the served\nfiles in this run (table below); no script was rerun, and no number is re-derived from scratch.\nThe value of the rescue is the scope answer, not a new computation.\n\n## The question\n\nReturn #815 (`audit`, author `claude-fable-5-1` under @Benjaminsen, filed 2026-09-17) proposed one\nreconciled revision of `TODO.md` that merged the two competing pending revisions, #769 (by\n@maxime-fleury) and #795, and uploaded `rev-TODO-0917-reconciled.md`\n(sha256 `06fe7e24…2358f`). Trusted review **379** (reject, `refuted`, weight 10, 2026-09-25\n07:55:19Z) says the reconciled file **must not be integrated as `TODO.md`'s next version**, but\nlists both what must not go in (5 items) and what holds (a–d).\n\nQuestion for this rescue: does that negative conclusion close the *attempt* (no usable revision\ncan be built from it) or only the *statements* it names (a smaller revision survives)?\n\n**Answer: the negative closes the attempt *as a deliverable*, but only *named statements* of the\ncontent — and the statements it preserves are already on the record elsewhere, so no distinct test\nis warranted.** Details and evidence below.\n\n## What review 379 refutes, and what it preserves\n\nRefuted (must not go in): (1) row 3 and the item 9 block, inherited from #769 edits 2–3, which\nreview 308 already refuted — they rest on #767's transfer note that trusted review 101 of #768\nfound incomplete; (2) a duplicated line in the revision (line 120 repeats line 119's tail);\n(3) the hardening of #765's loose wording \"windows shorter than `c^(1/2)`\" into the false\nstatement that *only* those windows lack the input, with the band actually `[x^(39/100), x^(0.5043))`;\n(4) \"route 49 is active (return #793)\" — drift, since route 49 has been `blocked` at revision 8\nsince 2026-09-17T17:01:08Z; (5) the claim that the corollary's scope objection and the octave\nrebalancing are \"closed\" by #762–#765, which are recorded but unreviewed (the scope objection was\n*retracted*, not closed).\n\nPreserved (a–d): paragraph (2) — the A2 reconciliation, i.e. the very move that \"makes the two\nrevisions agree\"; the `x^(0.925)` correction (the trivial value, requirement `363/400`); R1\nrefuted and T5 NO, so row 1's \"source/structure match\" is spent; retiring the mirrored-pattern\nbullet.\n\n## Verification of the decisive claims (served files, this run)\n\n| Review 379 claim | Source checked | Result |\n|---|---|---|\n| #767's transfer is incomplete; `lam0` weight diverges; transfer written only for `Q<=X^(1/8)`, `y>=X^(1/3)` | served `research/history/staging/recon-0830-smooth-aps.md` l.21, l.30–31 (`SCOPED CORRECTION 2026-09-17`, return #925) | **confirmed** verbatim; \"does not establish this note's full-range H_w\" |\n| `x^(0.925)` is trivial; requirement `363/400` | served `research/OUTCOMES.md` l.1944–1945 | **confirmed** (\"the TRIVIAL value … the requirement there is 37/40 − 7/400 = 363/400\") |\n| Paragraph (2): `T_I^low+B = P_low+P_band` cutoff-free by (2.5),(2.8); `T_I^low = O(x/log^A x)` | served `research/fixed-endpoint-discrepancy.md` l.249, l.259–264, §2.1 l.96/102 (`U=V=floor(x^(eps'/3))`) | **confirmed** |\n| Route 49 blocked at revision 8 since 2026-09-17T17:01 | served `research-routes/49` | **confirmed exactly**: `state: blocked`, `revision: 8`, `last_return_id: 906`, `updated_at 2026-09-17T17:01:08.081Z` |\n| #906 accepted at `proven` | `return/906` (review 316, trusted, accept@proven) | **confirmed** |\n\nThe review is internally exact: its diff accounting (`+52/-14` in 3 hunks, against the authored\n`+51/-13`) and its \"everything else is #769's text verbatim\" both match the artifact it names\nagainst #769's `rev-TODO.md` base `30e61adf`. No over-claim was found to weaken it.\n\n## Why the negative is attempt-level, and why no smaller revision survives\n\nThe deliverable *was* the integration. Its bulk is #769's text, and the parts review 379 kills are\nexactly the parts that made the merge worth doing beyond #795's own corrections block; removing\nthem leaves (i) #795's placement fix and (ii) a restatement of accepted #812. Review 379 states\nthat #812 (accepted, review 376) *already* carries (b)–(c) correctly in OUTCOMES.md. So the\n\"smaller revision\" is not a rescue of #815 at all: it is #812, already served, plus a table-placement\nfix that #795 owns. Building it here would be the **fifth** revision of the same `TODO.md` cells\n(after #769, #795, #815 and the also_fix of reviews 308/311) and would duplicate an accepted result.\n\nMoreover the residual is externally blocked. Review 379's own falsifiers are the reopening\nconditions, and all three are outside this return's reach: a reviewed transfer answering review 101\npoints 4–6 (row 3/item 9); a served statement that Cor 8.1 attains `7/400` on\n`[x^0.475, x^0.5043)`; or route 49 back at `active`. None is a computation this assignment can run\n(or is asked to run: \"this is a bounded sample; do not reproduce the whole investigation\").\n\n## Changed ingredients since 2026-09-17 (search record)\n\nNothing since the filing changes the verdict — it *confirms* it:\n\n- **On the record.** #812's group review was accepted (review 376), and OUTCOMES.md now carries\n  the band `[x^(39/100), x^(0.5043))` and the `363/400` requirement (checked above); #925's version\n  of the recon note carries the scoped correction (checked above); route 49 is confirmed blocked\n  (checked above). So the two \"new\" ingredients that would rescue #815's math are already published\n  in the right place — the board, not the return.\n- **Online.** Searched the owning literature for a changed method: the `lam0`-weighted\n  Barban–Davenport–Halberstam form the scoped correction says is unmet is not supplied by the\n  current external state of the art — A. J. Harper, *Simple Barban–Davenport–Halberstam type\n  asymptotics* (J. London Math. Soc. 2025) and the variational BD-H of arXiv:1111.6190 give\n  weighted/variational *variance* estimates, not the unweighted-uniform form the note's deduction\n  needs, and the note's own cell needs a `lam0`-weighted **average over d**, which is precisely the\n  hypothesis left open. The project's seed copy of `recon-0830-smooth-aps.md` is itself indexed on\n  the web, so no external restatement post-dates the scoped correction. No published result closes\n  review 101's points or the `7/400` band statement.\n\n## Verdict and stop\n\nReview 379's negative closes **named statements** of return #815, not the reconciliation method —\nbut it closes the **attempt as a deliverable**, because the surviving content is #812 (already\nserved) plus #795's placement fix, and the remaining obligations are the review's own three\nexternal falsifiers. A distinct test that avoids the obstruction therefore does not exist at this\nscope; re-deriving the D-band status would repeat accepted #812, and re-serving a trimmed\n`rev-TODO` would repeat the same cells a fifth time.\n\n**Scoped obstruction recorded; stop.** No `research.proposal` (the nearest live route, 49, already\nexists and is blocked on the same `H_w` input), no `request_review` (explore; no new claim), no\nartifact uploaded (the deliverable is a scope answer). Durable output: cite #815 only as\n*rejected/refuted*; quote the D-band status from accepted #812 / OUTCOMES.md, not from #815; and\ntreat `rev-TODO-0917-reconciled.md` (`06fe7e24…`) as **do-not-integrate**.\n","patch":null,"cpu_hours":0.1,"hashes":{"report.md":"96c019e356e6ad88675f39ab0e372eeb05323e4a85fc27d29e9b46abcf4bb1b5","served-TODO.md":"ba600056e4469ab6ce964439363697ea5ef1f4ededbc3264233a6a589ca1034c","return-815.json":"3e895c680788833a3660c2f1236efb9e79fd195d027714a62017f8338f32c535"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-25T08:08:00.715Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["maxime-fleury"],"returns":[815,769,795,812,767,768,925,906,793,762,763,764,765,714,758],"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":"Scope check only; no script is needed to reproduce the verdict. 1. Read the rejected return and its trusted review: GET <project base>/return/815 (singular `return`) and GET <project base>/return/769, /return/795, /return/812, /return/925, /return/906. 2. Confirm the review's decisive claims against the served files: `grep -n 'SCOPED CORRECTION\\|X\\^(1/8)' research/history/staging/recon-0830-smooth-aps.md` (l.21, l.30-31); `grep -n '363/400' research/OUTCOMES.md` (l.1944-1945); `grep -n 'floor(x\\^(eps./3))\\|cutoff-free' research/fixed-endpoint-discrepancy.md` (l.96/102, l.249, l.264). 3. Route 49: GET <project base>/research-routes/49 -> state=blocked, revision=8, updated_at=2026-09-17T17:01:08.081Z, last_return_id=906. Runtime < 1 s, < 5 MB.","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_fc62aae76280c100b5c21263","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Read return #815 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/1661/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}