{"id":1712,"job_id":3497,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Findings #771, #772, #775 on `research/centered-discrepancy-measurement.md`\n\n**One line.** The note no longer says the truncation subtraction separates or isolates the parity\nobject: the subtracted remainder is stated as a mix of `S-C2 x` and the classical BV residual `B`\nat random-sign size that a census cannot split; the ledger tolerance becomes `1.1e-4 x` for j>=31;\nitem 3 and section 4 are restricted to j>=31; item 8 identifies `T1_main` as (7) with the b-range\ncut; and item 3 gains the `delta_trunc` statement with the `|B|/x` bounds.\n\n**Revised file.** `f584cf7dbae0101fa839469513c6712717bf78dabeba3481bff054e8038cca5f`, 12303 B, base `c8e8dc2d55baf66914a859d3424b596649c7358fa2b0ce7cbd715789d2aed6ed`\n(re-fetched and re-hashed immediately before the upload). Four hunks: the `verdict:` ledger line,\nand items 3, 7, 8 and section 4. No embedded `sha256` block, so none was re-embedded.\n\n**#771.** The claim was in three places, not two - item 3 (`It is isolated by subtracting that\ncomputable term`), item 7 (`does separate the parity object ... and the separated object is the\nsize of the random-sign control`), and the `verdict:` ledger line (`with it subtracted, D_y is at\nrandom-sign size at every j>=30`). All three now say the remainder is a mix of `S-C2 x` and `B`\nthat cannot be split; item 7 keeps the do-not-rerun verdict and gains the size comparison\n(B larger at j=30, 36, 37, 38 and 0.18-0.73 of `S-C2 x` elsewhere). `1e-4` -> `1.1e-4` with\n`|B|/x = 1.02e-4 at j=31`; `on this range` -> `for j>=31` in item 3 and `at every reachable scale`\n-> `for j>=31` in section 4, since the identification fails at j=30 and j<=29.\n\n**#772.** `the finite form of (8)` -> `that is (7) with the b-range cut at [d,b^2]<=x, of which (8)\nis the b->infinity limit (the two differ by 2.5e-5 x at j=30)`.\n\n**#775.** Item 3 now carries the deterministic truncation: at j>=31 all but about 1e-4 x of\n`T1-C2 x` is `delta_trunc=(x/2) sigma(x,y)-C2 x`, `sigma` over odd squarefree `d<=y` with\n`[d,b^2]<=x`, computable without primes (`t1main.c`, item 8), with `|B|/x<=1.02e-4` at j=31..38 and\n`5.8e-4` at j=30. Its item 7 and section 4 instructions coincide with #771's narrowing and are\napplied in the same edits.\n\n**Scope and evidence.** Four hunks, eight anchored replacements, each asserted to occur once and\nthe served sha asserted first; `diff -u` is the whole change. The `parity:`/`question:` lines, the\nfalsifier readings, the control block, the `delta_trunc/x` table, the cost section and every\nproof-status statement are unchanged. `resolves [771, 772, 775]`, `cites.returns [172, 171]`.\n\n**Unresolved obligations.** None for this job. 38 of @Benjaminsen's returns wait for a verdict;\nthis session cannot decide the ones made on its own model and there is nothing for the person to do.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-09-25T15:20:30.872Z","repo_url":null,"commit":null,"cites":{"returns":[172,171]},"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/centered-discrepancy-measurement.md","revision_sha":"f584cf7dbae0101fa839469513c6712717bf78dabeba3481bff054e8038cca5f","recipe_md":"1. GET /docs/research/centered-discrepancy-measurement.md -> sha256 c8e8dc2d... (11505 B),\n   re-checked before the upload.\n2. GET /findings?path=research/centered-discrepancy-measurement.md -> three open findings:\n   #771, #772, #775 (all three are in this job's brief).\n3. work/edit_bn.py: eight anchored replacements (each asserted unique), served sha asserted first;\n   revised sha f584cf7d... Four hunks.\n4. POST /files (revision + evidence-3497.md); POST /projects/twin-primes/result with base = the\n   served sha re-fetched in step 1.","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":"2026-09-25T15:20:30.872Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_eda2d6f9a2531600f1bff869","triage_lead":null,"revision_base_sha":"c8e8dc2d55baf66914a859d3424b596649c7358fa2b0ce7cbd715789d2aed6ed","integration":null,"resolves":[771,772,775],"handle":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `research/centered-discrepancy-measurement.md` while reviewing return #172 (review #374 by @Benjaminsen), recorded as finding #771. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> Do not say the correction separates or isolates the parity object (#172 item 7 \"does separate the parity object from the classical convergence\"; item 3 \"It is isolated by subtracting that computable term\"). D_y + delta_trunc = (S - C2 x) - B - P - E_pp - E_even, and B = T1 - T1_main (the BV error of T1, still classical) is as large as S/x - C2 at j>=30: larger at j=30,36,37,38 and 0.18-0.73 of it elsewhere (#171 analysis.out section D). Say instead that the subtraction removes the deterministic part of T1's error and leaves a mix of S - C2 x and B at random-sign size, which a census cannot split; the do-not-rerun verdict stands. Also: the ledger verdict \"to within 1e-4 x for j>=31\" should read 1.1e-4 (|B|/x = 1.02e-4 at j=31); restrict item 3 \"on this range\" and section 4 \"at every reachable scale\" to j>=31 (the identification fails at j=30 and at j<=29).\n\nFetch the current file (GET <project base>/docs/research/centered-discrepancy-measurement.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\": \"research/centered-discrepancy-measurement.md\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [172] }`. 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/centered-discrepancy-measurement.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 #772 (review #374 of return #172, @Benjaminsen):\n> Item 8: T1_main is (7) with the b-range cut at [d,b^2]<=x, not \"the finite form of (8)\"; (8) is its b->infinity limit (difference 2.5e-5 x at j=30, #171 section F).\n\n\nAlso finding #775 (review #375 of return #171, @Benjaminsen):\n> §3 item 3, after \"comparable to x/log^2 x with oscillating sign on this range\": add that at j>=31 all but about 1e-4 x of T1 - C2x is the deterministic truncation delta_trunc = (x/2) sigma(x,y) - C2x, where sigma sums -mu(d)mu(b) log d / phi([d,b^2]) over odd squarefree d<=y and [d,b^2]<=x. It is computable without primes (return #171, t1main.c). The remainder B = T1 - T1_main has |B|/x <= 1.02e-4 at j=31..38 and 5.8e-4 at j=30. Item 7 and §4: keep the conclusion but narrow the reason. The deterministic part is separable, but D~_y = D_y + delta_trunc = (S - C2x) - B - E_pp still contains the classical BV residual B at the same size as S - C2x (both about 1e-4 x at j>=30). It therefore does not isolate the parity object, and a larger run still has no decision attached.\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/1712/transcript","files":[{"sha256":"f584cf7dbae0101fa839469513c6712717bf78dabeba3481bff054e8038cca5f","name":"research-centered-discrepancy-measurement.md","bytes":12303},{"sha256":"ea032a7528221aab35f14ed9de42f7f2ec3a77e2e4eb48a334572642dfe4a6c5","name":"evidence-3497.md","bytes":3058}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}