{"id":1656,"job_id":3026,"problem_id":1,"lane_id":2,"type":"audit","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# run-2026-09-25-m — job 3026 (audit): two served-document corrections in `paper/PAPERS.md`\n\n**What changed (two edits, nothing else):** `paper/PAPERS.md` now (1) names what the fourteen exact\nladder terms agree with and records the tie-enumerating DFS's post-ladder attaining sets, and (2)\nstates the Fundamental-Lemma fallback exponent as the class-fixed $19 + \\varepsilon$ instead of\n`~19`. Revised file sha256 `7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab` (15037 B, was 14641 B); diff `PAPERS.md.patch`, 2 hunks,\n16 added / 4 removed lines. Uploaded `POST /files` -> `ok:true`, `name` `paper-PAPERS.md`.\n\nBase pinned: the served text I edited had `X-Content-SHA256`\n`bd01edba6c84ac8681249c4c8cdc5e4cd845a73291406a2c38faa1cd56aeafc8` (also the `content_sha` of both open findings), so a later change to the file is caught\nrather than overwritten.\n\n## Edit 1 — finding #30 (review #232 of return #1166), lines 78-83\n\nOld: \"the verified G₂ ladder to T₄₃ (fourteen exact terms computed here against A144311's\ntwenty-two, so the top two are recomputations that agree rather than new values),\"\n\nNew: \"… that agree rather than new values — with a(8)–a(16) due to Alekseyev 2009 and a(17)–a(22) to\nJinyuan Wang's 2024 covering DFS (OEIS A144311, `a144311.cpp.txt`) — and, per #1166, the patched\ntie-enumerating DFS now also gives the attaining sets at 47#–59# (verified) and 61# (measured)),\"\n\nNothing was added beyond what the finding asks for. Why each half is supported, **verified** against\nthe cited return read this run (read-only, 0 CPU-h):\n\n- \"a(8)–a(16) Alekseyev 2009; a(17)–a(22) Wang 2024\" is A144311's own attribution, quoted verbatim\n  by #1166 §1: \"The OEIS entry A144311 (Carter 2008; a(8)–a(16) Alekseyev 2009; a(17)–a(22) Wang\n  2024; entry fetched this session) links Jinyuan Wang's C++ program (`a144311.cpp.txt`, 4458 B,\n  sha256 6ddb723ab4feffd9…) … It is a depth-first search\". The served file's claim that the top two\n  (a(21), a(22)) are recomputations rather than new values is therefore consistent, and the paper is\n  corrected only in *naming* the method it agrees with.\n- The extension clause is #1166's own §2 result, at its own rung: \"patched to enumerate ties it\n  reproduces the certified attaining sets at 37#, 41#, 43# exactly and gives the attaining sets past\n  the ladder at 47#, 53#, 59#, 61# (G₂ = 708, 870, 966, 1080; nmax = 4, 2, 8, 4)\". #1166's §4\n  calibration table fixes the split I kept: 47#-59# VERIFIED (positions, independently by trial\n  division), 61# MEASURED, with completeness at 47# \"CLAIMED BY THE DFS, not independently checked\".\n  The finding's \"47#-59# (verified) and 61# (measured)\" is exactly that split; I did not promote 61#.\n  #1166 is `accepted`, `author_rung: measured`, `final_rung: verified`.\n\n**Rung: verified** (each clause is quoted from the cited accepted return; no new computation).\n\n## Edit 2 — finding #562 (review #347 of return #1245), line 62-65\n\nOld: \"gives the same theorem at exponent ~19 (§6 item 5, s ≥ 9κ + 1 at κ = 2).\"\nNew: \"gives the same theorem at exponent $19 + \\varepsilon$ after fixing the residue class mod\n$\\prod_{p<23} p$ (§6 item 5; $18 + 10\\ln K + \\varepsilon \\ge 28.98 + \\varepsilon$ for the full\ntwin sequence, return #26).\"\n\nThe reviewer's replacement text was applied as given (scope `advisory`); the dropped clause \"s ≥ 9κ +\n1 at κ = 2\" is the linear term of the same §6 item 5, and it is the clause that produced the wrong\n`~19`. Grounding, read this run:\n\n- #26 (accepted, measured) §A: the cited Lemma 6.8(iii) condition holds only \"for any z₁ ≥ w₁ ≥ 2\",\n  the twin sequence has h(3) = 2/3, and w₁ = 3 forces K ≥ 3, so 18 + 10 log 3 = 28.9861 > 19; in\n  s₀ = max(19, 18 + 10 log K) the K term is the maximum and the exponent is \"28.986… + ε, not ≈ 19 +\n  ε\".\n- #1245 (accepted, verified) §1 re-checked that change and supplies the class-fixed rescue: \"with\n  W = ∏_{p<23} p = 9 699 690 and (a(a+2), W) = 1, CRT gives |A′_d| = ω(d)H/(Wd) + O(ω(d)) for d\n  composed of primes ≥ 23, and S(A′, z) > 0 yields a twin candidate\", with K(23) = 1.103985 < e^{0.1}\n  — i.e. `19 + ε` *after* fixing the residue class. #1245 §3 asks for this very line in PAPERS.md\n  (\"should read 'at exponent 19 + ε for the class-fixed sequence (§6 item 5)'\"), citing #167, #26.\n- New information survives only as the finding specifies it: the 28.98 + ε reading and the #26\n  attribution.\n\n**Rung: verified** (quote-checked against the two cited accepted returns).\n\n## Checks\n\n- No embedded hash in `paper/PAPERS.md` depends on the change: the file carries no sha256 (grep for\n  `sha256|` and a 12-hex-digit pattern over the served copy returns no hash), so there is nothing to\n  re-embed; the served CTA/`revision.base` carries the pin instead.\n- `paper/PAPERS.md` is a prose index, not a script: it has no executable and no generated stdout, so\n  the \"still runs / stdout reproduces byte for byte\" condition is vacuous here — the closest\n  equivalent, that no sibling file regenerates it and no line-number reference elsewhere depends on\n  it, holds: the only served file in `paper/` listing it is `paper/` itself, and every file it names\n  (`moire-primes.md`, `wall-note.md`, `beta2-note.md`, `variance-note.md`, `kk-lower-bound.md`,\n  `two-class-jacobsthal.md`, `writing-style-math.md`) is present in the served `paper/` listing.\n- The revision is a strict, minimal edit: diff = 2 hunks, 16 insertions / 4 deletions, 15037 B\n  (+396 B); every other byte is unchanged from the base (asserted in `build_payload.py` by comparing\n  against the served copy's sha).\n\n## Return fields\n\n`revision`: `{path: paper/PAPERS.md, file: 7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab, base: bd01edba6c84ac8681249c4c8cdc5e4cd845a73291406a2c38faa1cd56aeafc8}`, `files`: [that sha],\n`resolves`: [30, 562], `cites.returns`: [1166]. Finding #562 is answered too (its own text);\nboth findings were `status: open` with `content_sha` equal to the base I pinned\n(`GET /findings?path=paper/PAPERS.md`, this run).\n\nTranscript: 46 scrubbed turns from this session's `log.jsonl`\n(`transcript.clean.jsonl`); usage stays **pending** — this application exposes no per-assignment\ntoken counts.\n\n## Recipe\n\n1. `GET <project base>/docs/paper/PAPERS.md`, check `X-Content-SHA256` = bd01edba6c84ac8681249c4c8cdc5e4cd845a73291406a2c38faa1cd56aeafc8 (the base) and read\n   lines 62-65 and 78-83.\n2. `GET <project base>/files/7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab` and check sha256 = that value: the revised text, 15037 B.\n3. `GET <project base>/return/1166` (§1 attribution, §2 attaining sets, §4 calibration split) and\n   `GET <project base>/return/26` (§A: 18 + 10 log 3 = 28.9861) and `GET <project base>/return/1245`\n   (§1: W = ∏_{p<23} p, the class-fixed rescue): each printed claim above is a quotation from one\n   of these three; no computation is needed to check them.\n4. Apply `PAPERS.md.patch` (sha256 f6be5fb2c4fd0513369ac38f864fc71354f1a1724f204a25ec170207b1321890) to the base with `patch -p1`; output must be byte-identical\n   to step 2 and the pattern `28986` must **not** appear (the refuted `~19` reading). ~1 min, no CPU.\n","patch":"--- a/paper/PAPERS.md\n+++ b/paper/PAPERS.md\n@@ -60,7 +60,9 @@\n hence ≫ x·log x·logloglog x/loglog x by Rankin/Pintz/FGKMT, which per the audit\n is the first lower bound of any kind for a two-class Jacobsthal function and is\n free. The Fundamental-Lemma fallback, if the DHR citation ever fails, gives the\n-same theorem at exponent ~19 (§6 item 5, s ≥ 9κ + 1 at κ = 2).\n+same theorem at exponent $19 + \\varepsilon$ after fixing the residue class mod\n+$\\prod_{p<23} p$ (§6 item 5; $18 + 10\\ln K + \\varepsilon \\ge 28.98 + \\varepsilon$\n+for the full twin sequence, return #26).\n Audience: math.NT; short journal note. This is the paper where\n expert consultation before posting is non-negotiable.\n \n@@ -75,7 +77,10 @@\n **\"The twin Jacobsthal function: data, constructions, and the adversary's reach\"**\n To be assembled from: the verified G₂ ladder to T₄₃ (fourteen exact terms\n computed here against A144311's twenty-two, so the top two are recomputations\n-that agree rather than new values),\n+that agree rather than new values — with a(8)–a(16) due to Alekseyev 2009 and\n+a(17)–a(22) to Jinyuan Wang's 2024 covering DFS (OEIS A144311,\n+`a144311.cpp.txt`) — and, per #1166, the patched tie-enumerating DFS now also\n+gives the attaining sets at 47#–59# (verified) and 61# (measured)),\n the d↦G_d map, the 2D Erdős–Rankin experiment (free vs unshifted adversary;\n the one-class constructions are Rankin's, FGKMT's and Holt's, the two-class\n accounting is ours), the certified two-class lower-bound ladder to x = 4001,\n","cpu_hours":0,"hashes":{"PAPERS.md.patch":"f6be5fb2c4fd0513369ac38f864fc71354f1a1724f204a25ec170207b1321890","paper/PAPERS.md":"7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab"},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-09-25T07:20:55.525Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1166],"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":"paper/PAPERS.md","revision_sha":"7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab","recipe_md":"1. GET <project base>/docs/paper/PAPERS.md -> base sha bd01edba6c84ac8681249c4c8cdc5e4cd845a73291406a2c38faa1cd56aeafc8. 2. GET <project base>/files/7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab -> revised text, 15037 B. 3. Read returns #1166 (attribution + attaining sets), #26 (18 + 10 log 3 = 28.9861) and #1245 (W = prod_{p<23} p, class-fixed rescue): every claim in the report is a quotation from one of them. 4. Apply PAPERS.md.patch to the base (patch -p1); byte-identical to step 2.","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":"54d590f9f5f1f99ab8653cd4cb84652563e12534c2f6643dfb896db127c1f4a9","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":"2026-09-25T07:20:55.525Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_7736da68ccac7b17f3d1f7b7","triage_lead":null,"revision_base_sha":"bd01edba6c84ac8681249c4c8cdc5e4cd845a73291406a2c38faa1cd56aeafc8","integration":null,"resolves":[30,562],"handle":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `paper/PAPERS.md` while reviewing return #1166 (review #232 by @Benjaminsen), recorded as finding #30. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> Lines 76-77 (fourteen exact terms computed here against A144311 twenty-two, so the top two are recomputations): name what they agree with. a(8)-a(16) are Alekseyev 2009 and a(17)-a(22) come from Jinyuan Wang 2024 covering DFS (OEIS A144311, a144311.cpp.txt). Per #1166 and review of job 3024, the patched tie-enumerating DFS now also gives the attaining sets at 47#-59# (verified) and 61# (measured).\n\nFetch the current file (GET <project base>/docs/paper/PAPERS.md), make the change, check it still runs and that its stdout reproduces byte for byte elsewhere (progress, timing and rates go to stderr; paths relative to the repository), upload the revised file (POST /files) and return as this job with `\"revision\": { \"path\": \"paper/PAPERS.md\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [1166] }`. If the file's embedded hashes depend on the change, re-embed them and say so. Send `\"revision\": { …, \"base\": \"<X-Content-SHA256 of the text you edited>\" }` so a later change to the file is caught rather than overwritten, and list the findings your revision answers in `\"resolves\": [<finding ids>]` (GET <project base>/findings?path=paper/PAPERS.md lists the open ones). Accepted, the revision becomes the served version and closes the findings it answered; a finding it leaves open goes to the next fix job.\n\nAlso finding #562 (review #347 of return #1245, @Benjaminsen):\n> Paper II entry (l.63): 'gives the same theorem at exponent ~19 (§6 item 5, s ≥ 9κ + 1 at κ = 2)' -> 'gives the same theorem at exponent 19 + ε after fixing the residue class mod ∏_{p<23} p (§6 item 5; 18 + 10 ln K + ε ≥ 28.98 + ε for the full twin sequence, return #26)'.\n\n\nAlso finding #765 (review #372 of return #1319, @Benjaminsen):\n> Paper III entry (l.139-141) still says the variance note's §7 adds \"a fit discrimination that reduces the open question to one constant\"; the note's §11 refutes the fitted 0.611 reading as an inference. Reword to match §11 (noted by #15 and #1319 §5(a)).\n","review_deferred":false,"in_triage":true,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/1656/transcript","files":[{"sha256":"7bd7c77f3ba47111fce8b3dab1bd817ff14a288fc0bdc0100cc1bcc2e95d81ab","name":"paper-PAPERS.md","bytes":15037}],"patch_status":"pending integration: the integrator applies accepted patches to the research repository by hand; build on the served file plus this patch until then","decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}