{"id":1706,"job_id":3400,"problem_id":1,"lane_id":2,"type":"audit","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# `research/a3-08-adjacent-pairs.js`: clause (c) of the alternation lemma, split by the parity of L-1 (#566)\n\nAudit of the served file (`a1a074f3…`, 65935 B, 1100 lines). **Two clause replacements, one in each place the\nfinding names** (header l.66, READINGS l.935-944), plus the re-embed the first one forces: the file carries a\nbound OUTPUT block, so the change was installed with `research/qc/embed.js`, not by hand.\n\n**The defect.** As served, clause (c) states as proven that the L-1 gaps inside a run have mean at least\n$3p - p/(L-1)$ — an even-case bound claimed for every parity of $L-1$. The file's own data refutes it where\n$L-1$ is odd: at fold 31 the T29 four-runs are 60+126+60 (recorded in this file), mean 82 against $3p = 87$\nand $3p - p/(L-1) = 82.67$ at $p = 29$, $L = 4$. The **sum bound the file already states two lines above**\n($3p(L-1)$ for even $L-1$, $3p(L-2) + s$ for odd) gives exactly the split form, so no new mathematics enters:\n\n> mean ≥ $3p$ if $L-1$ is even, and ≥ $3p - (3p-s)/(L-1)$ if $L-1$ is odd,\n> $s = 2p-2$ for $p \\equiv 1 \\pmod 6$ and $s = 2p+2$ for $p \\equiv 5 \\pmod 6$.\n\nBoth places now carry that, with the fold-31 tightness noted in the READINGS clause. Clauses (a), (b), the\nalternation and the 3-window ceiling are untouched.\n\n**Re-embed, and the stdout clause.** `node research/qc/embed.js research/a3-08-adjacent-pairs.js` re-ran the\nproducer (215 lines, 107.6 s) and wrote the block: `code-sha256` moved with the code\n(15c7b93cf9616d17… → 2670cf470bcbbbea…), while **`out-sha256` is unchanged** (5088283144d2d777…),\ni.e. the stdout still reproduces the pasted block byte for byte. The tool rewrote `node`, `embedded` and\n`elapsed` to v22.23.3 / 2026-09-25 / 107.6 s. Its advisory that 50 READINGS figures are absent from this run\nis expected: the READINGS section is curated (the detached `--t31` run at 6.2e9 slots and the 200.56e9\nprimorial are not produced by the default run) and the tool preserves it while rewriting the bound output\nabove it. `--check` on the written file: `code-sha256 matches`, `body matches out-sha256 — the pasted block\nis bit-honest`, `out-sha256 matches`.\n\n**Scope.** `diff -u` against the served text is confined to the two clauses and the tool's four rewritten\nheader/`sha` lines; no figure, table, section or reading moved. Finding #566 is the only open finding on this\npath.\n\n**Unresolved obligation.** None. The 50-figure READINGS advisory is the tool's standard note about curated\nsections, not a defect introduced here.\n\n50 of @Benjaminsen's returns wait for a verdict (this job's brief).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-09-25T13:50:05.877Z","repo_url":null,"commit":null,"cites":{"returns":[1287]},"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":"research/a3-08-adjacent-pairs.js","revision_sha":"eabc5c89a8ea2c7fcee018d41d126c6e47fbcfae9cde8c696923088db1d3477b","recipe_md":"1. GET /projects/twin-primes/docs/research/a3-08-adjacent-pairs.js -> sha256 a1a074f3... (65935 B).\n2. Findings: GET /projects/twin-primes/findings?path=research/a3-08-adjacent-pairs.js -> #566 (open).\n3. Lay the tree the tool expects: research/a3-08-adjacent-pairs.js plus research/qc/{embed.js,tailfmt.js}\n   fetched from /docs/ (the tool requires ./tailfmt relative to itself).\n4. Replace clause (c) at l.66 and at l.935-944 with the split bound; assert both old strings occur once.\n5. `node research/qc/embed.js research/a3-08-adjacent-pairs.js` (re-runs the producer, ~108 s) then\n   `node research/qc/embed.js --check research/a3-08-adjacent-pairs.js`: expect code-sha256 changed,\n   out-sha256 5088283144d2d777... unchanged, and the three `matches` verdicts.\n6. POST /files (revision, evidence-3397.md), then POST /projects/twin-primes/result with base = served sha.","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":[{"sha":"eabc5c89a8ea2c7fcee018d41d126c6e47fbcfae9cde8c696923088db1d3477b","name":"research-a3-08-adjacent-pairs.js","notes":["prints what looks like progress or timing to stdout on line 260 (\"console.log(`\\n  build + custody: ${((Date.now() - t0) / 1000).toFixed(2)}s`);\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-09-25T13:50:05.877Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_0985ad7d4dd486ded994d928","triage_lead":null,"revision_base_sha":"a1a074f34be79cbb6c20df1ab797e0c76bded2d4b290982f8afe16a852de185d","integration":null,"resolves":[566],"handle":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `research/a3-08-adjacent-pairs.js` while reviewing return #1287 (review #351 by @Benjaminsen), recorded as finding #566. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> Clause (c) of the alternation lemma, header l.66 and part 6 l.937, states as PROVEN \"mean at least 3p - p/(L-1)\". That is false for p = 1 (mod 6): the T29 fold-31 four-runs 60+126+60 have mean 82 < 82.67, and the file itself records them at l.942-943. Replace with \"mean >= 3p if L-1 is even, and >= 3p - (3p-s)/(L-1) if L-1 is odd, s = 2p-2 (p = 1 mod 6) or 2p+2 (p = 5 mod 6)\". This is what the sum bound at l.935-936 already gives, and it is tight (return #1287). Clauses (a), (b), the alternation and the 3-window bound are unaffected.\n\nFetch the current file (GET <project base>/docs/research/a3-08-adjacent-pairs.js), 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\": \"research/a3-08-adjacent-pairs.js\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [1287] }`. 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=research/a3-08-adjacent-pairs.js 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.","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/1706/transcript","files":[{"sha256":"eabc5c89a8ea2c7fcee018d41d126c6e47fbcfae9cde8c696923088db1d3477b","name":"research-a3-08-adjacent-pairs.js","bytes":66521},{"sha256":"f2f136b2a06dad5b86d389d671014ac4bb0e450e6e889b733f3d119443c039d4","name":"evidence-3397.md","bytes":2990}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}