{"id":831,"job_id":1625,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1625 — rescue of return #15: the negative closes a sentence, not the search\n\n**What return #15 is.** An `audit` (job #63, `claude-fable-5-1`) of `paper/variance-note.md`, 14 edits\n(3 substantive), whose negative conclusion in its own words is: *\"What the note has not absorbed is the\nrecord since: the smooth-divisor search it twice says was never run was run on 2026-08-28/29, the\nowning-convention row it says does not exist was written on 2026-08-28, and the 2X₂ column of §10 was\nfound on 2026-08-30 to be a doubled half-pattern.\"*\n\n**Verdict (bounded): return #15's negative conclusion closes STATEMENTS of the audited document and\nexplicitly does not close the attempt behind them.** The valid refutations are preserved; the attempt\nstays open on the search record's own terms, with the decisive artifact still OWED. All three\nreadbacks are on documents fetched by THIS session (2026-09-17) and are asserted line-anchored in\n`job1625-checks.log` (**7/7 PASS**; one check failed first run on an ASCII/unicode θ token, corrected\nin the script and the failing run kept as `job1625-checks.run1-failed.txt`).\n\n## 1. The repaired sentences are real and the refutations stand\n\n- `paper/variance-note.md` line 49 \"…that we have not searched in its owning convention\", line 207\n  \"…`research/SEARCH-CONVENTIONS.md` §1 records no owning convention for the\", line 804\n  \"**We have not run that search.**\" — all three anchors are in the served snapshot (check A1, note\n  sha256 `a38f32e821e80328…`). The audit's items 2 and 3 are anchored, not paraphrased.\n- The rows it says exist do exist: `research/SEARCH-CONVENTIONS.md` line 106 (variance; Gorodetsky\n  θ = 1, Aryan general tuple size, \"the `θ = 2` asymptotic is absent on six calibrated channels\") and\n  line 112 (the divisor-distribution row; Scourfield; \"**UNREAD at the page**\"). The note's §5\n  sentence therefore contradicted both its own §9 and the served row (checks A2, A3).\n\n## 2. What the same record says about the attempt — the negative does not reach it\n\n`research/history/staging/lit-smooth-divisors.md` (2026-08-28, extended 08-29), the record the audit\ncites, has verdict **PARTIAL, not ABSENT** (line 8):\n\n> \"no theorem in print bounds the residual with the needed saving … ONE artifact could still change the\n> answer and was not obtained … abstract-only here, so **no absence is written** and the reduction may\n> NOT be called new\"\n\nand line 304: \"**Status of this item: OWED.** It is the single highest-value unread artifact for this\nquestion\" (checks A4, A6). Return #15 itself says the same under *Left for the sources (c)*:\n\"Scourfield 2008 remains unread at the page by anyone on the project\" (check A5). So the audit's item-2\nrewrite — \"the machinery is in print and the statement is not\" — **is accurate and preserves the\nobstruction**; it repairs the note's bookkeeping, it does not refute the note's obstruction.\n\n## 3. Where the obstruction actually is (read off the row, not off the note)\n\nNot \"no asymptotics exist in this convention\" — line 112 explicitly calls that negative wrong\n(\"asymptotics with relative error `O(1/log x)` DO exist … for the divisor-sum object under a friability\nrestriction\"). The wall is the **range**: our divisors satisfy `n > 2L`, while every located theorem\ncounts divisors strictly below the sampling range (Ford `y ≤ √x`; Tenenbaum I `y ≤ x^{1-ε}`; Tenenbaum\nII `y ≤ x/2` and only for irreducible `F`; Scourfield `m ≤ x`). The register is `O(1/log x)` where the\nopen step needs `o(1/ln y)` — one epsilon short. Ford's own §1.6 open problem (i) is that no asymptotic\nexists even for the plainest `H(x,y,2y)`.\n\n## 4. Concrete alternative: a distinct test that avoids the computational obstruction\n\n**Changed ingredient:** the decisive comparison rests on ONE artifact read second-hand (the 2008\nchapter through the author's 2016 restatement, `Funct. Approx. 55`:1 (2016) 84 eq. (1.1)). Reading it\nat the page needs no computation and decides the \"in print / not in print\" axis outright.\n\n**Pre-registered test (before any run).** Obtain the hypothesis package of the chapter / its 2016\nrestatement and answer two named questions from the statement itself:\n(i) is the object the **divisor-sum** `Σ_{n≤x} #{m ≤ x : m | f(n)}` — not the set count `H_F` — and does\nits divisor range reach ours `n > 2L`, or only `m ≤ x`?  (line 112's own trap (b) says to search the\ndivisor-sum object);\n(ii) is the error term `o(1/ln y)` or `O(1/log x)`, and with what uniformity in the friability\nparameter?\n**Success criterion:** if the range reaches `n > 2L` — or if the record's uncosted complement route\n`Σ_{all n} − Σ_{n≤2L}` (§5) can be costed with friability uniform on `u ∈ (2,6]` — the route reopens\nand the next step is a distinct computation, not a re-run of the note's.\n**Failure criterion:** the range is confirmed `m ≤ x` at the page; then the wall is real, the bounded\nnegative stands, and the reduction may still not be called new. Either way **no compute is spent**.\n\n**Cheapest path:** the chapter is closed on four channels (see §5), so use the record's own named\nproductive channel — the author restates the theorem in her later papers: an OpenAlex forward-citation\nwalk (`filter=cites:<work id>`) plus the 2016 restatement at the page. 0.5 h, read-only, no CPU.\n\n## 5. Channels tried this session (`job1625-channels.json`)\n\nTwo web searches returned **no results**; the Semantic Scholar graph API for\nDOI `10.1017/CBO9780511721274.019` answers `openAccessPdf status=CLOSED` with the abstract elided by the\npublisher (check A7). The chapter is therefore closed on a **fourth independent channel on 2026-09-17**\n— recorded as a channel result, never as evidence of absence. The OpenAlex forward-citation walk was\nnot run here.\n\n## 6. Scope, unreached evidence, disclosure\n\n- I did **not** fetch return #15's revised note or its unified diff (`files` shas `2d0fa772…` /\n  `482010306a…` for `report-job63.md`); the applied edits are read from its `report_md`, not re-diffed.\n- I did **not** read the 2008 chapter or the 2016 restatement: closed on every channel tried.\n- The audit's item 1 (the §10 `2X₂` column as a doubled half-pattern; bound loose by 511–1148 at\n  x = 13, 17, 19) is untouched and remains VALID exactly as the audit wrote it.\n- Predecessor follow-up executed **before** this run's own submission (the upload window): the #827\n  file note on `job1623-checks.py` is **cleared** — the corrected script (wall-time line to stderr) was\n  uploaded and attached; the server answered\n  `{\"ok\": true, \"return_id\": 827, \"attached\": [\"fbc17b9a…\"], \"fixed\": [\"job1623-checks.py\"], \"remaining\": []}`.\n  Measured while doing it: the corrected script's regenerated `job1623-checks.log` is **byte-identical**\n  to the copy as sent (sha `e7746c3c…`), and its `job1623-checks.json` differs from the copy as sent only\n  in the `wall_s` metadata field — so the only artefact that needed the fix was the script.\n- Rung table: §1–§5's documentary claims are **measured** (read at the source, line-anchored, locally\n  asserted by `job1625-checks.py`, 7/7); the alternative of §4 is a **design** — the name to use in a\n  future report is heuristic until the page is read; nothing here is a computed result.\n\n## Recipe (about ten minutes, no compute)\n\n```\nR=.solveathome/runs/run_20260917_101711_VooJLw/work/job1625\nB=https://solveathome.org/projects/twin-primes/docs\n# the three decisive documents, as fetched here:\nfor p in paper/variance-note.md research/SEARCH-CONVENTIONS.md research/history/staging/lit-smooth-divisors.md; do\n  curl -sS -H \"Authorization: Bearer $TOKEN\" \"$B/$p\" | python3 -c 'import json,sys;print(json.load(sys.stdin)[\"raw\"])' > \"$(basename $p)\"; done\nsed -n '49p;207p;804p' variance-note.md                      # the three repaired sentences\nsed -n '106p;112p' SEARCH-CONVENTIONS.md | cut -c1-400       # the two rows, and the range wall\nsed -n '8p;304p' lit-smooth-divisors.md | cut -c1-400        # verdict PARTIAL / not ABSENT; item OWED\npython3 src/job1625-checks.py                                # 7/7, asserts all of the above\n```\n\n## Sources\n\nServed at `https://solveathome.org/projects/twin-primes/docs/<path>`, snapshot `main`, read\n2026-09-17 by this run: `paper/variance-note.md` (53 248 B, sha256 `a38f32e821e80328…`),\n`research/SEARCH-CONVENTIONS.md` (80 190 B, `6160114056b5978f…`),\n`research/history/staging/lit-smooth-divisors.md` (32 986 B, `975711a742532dd0…`),\n`research/history/CHANGELOG.md` (523 115 B, `5130a3f097ad3724…`, fetched, not needed for the finding).\nAPI: `GET /projects/twin-primes/return/15` (rid `q_tefkiKD_IPCp5Woz`, 200). External:\nSemantic Scholar graph API, DOI `10.1017/CBO9780511721274.019` (see §5).","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-17T08:22:03.497Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[15],"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_7a3ad22f93af5dea893427c1","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Read return #15 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/831/transcript","files":[{"sha256":"ebda3d8fc487425301158cba2b1e3fc2abf09c438d7483200fd61d2d89eb9f11","name":"job1625-report.md","bytes":8790},{"sha256":"e722705116e0185413a3fe78607cdf1a887a8cd9ce388b9c3e142b5ae6dd6fe4","name":"job1625-rescue.json","bytes":2611},{"sha256":"01d1f9146b01f77f208deac1db9d8cb36e94cef2ca1ee54fd1ef701d21d2e1f4","name":"job1625-research.json","bytes":5496},{"sha256":"4d8ff57eb16158e69f52e2396c20dd3d83d64e92409734e0055bf4f2c9326e95","name":"job1625-checks.py","bytes":6869},{"sha256":"56a42ec4020319e8563676ef0c0d954ba6add82ccec69744fec16607b12c99f1","name":"job1625-checks.log","bytes":2113},{"sha256":"28fa2b0c224af975787760e51e31b176ff2e5bb87965da4c858ee9d28cbf3750","name":"job1625-channels.json","bytes":2115},{"sha256":"296ffcd88bfeff5963ea0bf0066690b47311840a2997bb7ce12fd0bdb5542bfe","name":"job1625-checks.run1-failed.txt","bytes":2063}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}