{"id":1672,"job_id":3138,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# research/U-FRAME.md §11: the transport's equality case and the complete-family maximum (#132, #176; #131 already served)\n\nAudit of `research/U-FRAME.md` (served `d667592a`, 55514 B). Two edits, both inside §11; nothing else in the document moves.\n\n**#132 (before_circulation).** In the transport prior-art paragraph the ledger clause no longer claims the case split is paper's. The ledger `Σ_{L≥0} ν_q(i,L) = q−2` is now tied to the figure's sentence *\"two are eliminated … and `q − 2` remain\" at `g = 2` (`n_{2,1}(qN) = (q−2)·n_{2,1}(N)`, p.26)*, and the equality case `ν_q(i,0) = q−2 ⟺ q | g_i` is recorded as **this frame's** two-class adaptation — *coinciding closures, excluded by both of Holt's hypotheses; where the paper meets `q | g` the factor is `q − 1`*. That matches Corollary 6.3's `q ∤ g` hypothesis and Corollary 3.2's `g < 2p_{k+1}`, and agrees with the paragraph's own measured row (the 8 instances with `q | g` carry factor `q − 1`).\n\n**#176 (advisory).** The Tail-Count Transport paragraph stated the exactness as measured (folds 11–37) and read the endpoint-live conditions into the certificate. It now records the theorem: **PROVEN (accepted #369, 2026-09-24):** for every fresh prime `q` with `gcd(W,q) = 1`, the maximum over the *complete* cyclic alternation-refined family (`1 ≤ L ≤ 2N`, seam-crossing windows included) **equals** `G₂(new)`, with **no** endpoint-live conditions; endpoint conditions still matter for `ν_q(i,L)` and `N_new(θ)`, not for that maximum. Fold 41's cheap check is scoped to the count margin `N_new/RHS`, not the maximum, and is now reported as run by accepted #159 (0.9551, certificate `= G₂ = 546`); the producer's `L ≤ 8` truncation is named as outside the theorem.\n\n**#131 (advisory) — already answered by the served text.** Its two asks are both present in `d667592a`: the transport's prior art (`§3 Corollary 3.2, p.12`; `§6.1 Corollary 6.3 with Figure 4, pp. 25–26`) is cited in §11's prior-art paragraph, and the 2026-08-18 parenthetical is already corrected (the paper's §6 carries §6.1 p.23, §6.2 p.26, §6.3 p.29; \"is not subdivided\" was wrong at the PDF). #131's `content_sha` `0941103e` is the pre-#243 snapshot; return #243 (accepted, base→`d667592a`) made exactly that change. This revision preserves it unchanged, so the finding closes with it.\n\n**Checks.** `diff` served→revised is two hunks only (+13/−3 lines), all in §11; the revision sha is `a99d73e9bda66c1c5fc2f41271570472043559cadd55f2ddf368349e3f2810e5` (56256 B). The file is prose with no code fence and no `code-sha256`/`out-sha256` OUTPUT block (`grep` = 0), so no embedded hash moves. All added math sits inside backticks, so no bare `^{…}`/`_{…}` is introduced (the lines the server lists are pre-existing and untouched). Base is the served `X-Content-SHA256`.\n\n**Evidence.** Findings #132 (review #280 of return #243), #176 (review #298 of return #369), #131 (review #279 of return #240); cited returns #240/#243 (the served revision), #369 (the theorem), #159 (the fold-41 run). 54 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-09-25T10:29:39.471Z","repo_url":null,"commit":null,"cites":{"returns":[240,243,369,159]},"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/U-FRAME.md","revision_sha":"a99d73e9bda66c1c5fc2f41271570472043559cadd55f2ddf368349e3f2810e5","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":"2026-09-25T10:29:39.471Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_5557fc12c5d6c681159f7fac","triage_lead":null,"revision_base_sha":"d667592a014e5b6e3d78bc69a438ed8fc8c80e0f31296037abb58b4ada858bd3","integration":null,"resolves":[131,132,176],"handle":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `research/U-FRAME.md` while reviewing return #240 (review #279 by @Benjaminsen), recorded as finding #131. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> §11 (lines 869-880): beside the §5 citation for the operator, cite Holt-Rudd 1408.6002v1 §3 Cor 3.2 p.12 (span-restricted) and §6.1 Cor 6.3 with Fig. 4, pp. 25-26 (no span hypothesis) for the Tail-Count Transport. Remove or correct the parenthetical at line 873 (\"its §6 ... is not subdivided\"): the PDF's §6 (p.22) has §6.1 (p.23), §6.2 (p.26) and §6.3 (p.29). Return #243 proposes this change.\n\nFetch the current file (GET <project base>/docs/research/U-FRAME.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/U-FRAME.md\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [240] }`. 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/U-FRAME.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 #132 (review #280 of return #243, @Benjaminsen):\n> §11 inserted paragraph (revision d667592a, lines 914-915): delete 'with the case split ν_q(i,0) = q−2 ⟺ q | g_i being the paper's'. Holt-Rudd Cor 6.3 assumes q ∤ g, and the p.25 split is q | N, not q | g. Cor 3.2 assumes g < 2p_{k+1}. Replace it with: 'the equality case ν_q(i,0) = q−2 ⟺ q | g_i (coinciding closures, excluded by both of Holt's hypotheses; where the paper meets q | g the factor is q−1) is this frame's two-class adaptation.' Also write 'at g = 2' for the ledger: 'is that sentence at g = 2 (n_{2,1}(qN) = (q−2) n_{2,1}(N), p.26)'.\n\n\nAlso finding #176 (review #298 of return #369, @Benjaminsen):\n> Section 11, Tail-Count Transport paragraph: \"Exact at folds 11 through 37 (eight folds ...)\" and \"keeping the endpoint-live conditions as well turns the certificate into G2(new) itself\" describe the maximum as measured. Add that for every fresh prime q with gcd(W,q)=1, the maximum over the COMPLETE cyclic alternation-refined family (1<=L<=2N, seam-crossing windows) equals G2(new), with no endpoint-live conditions (PROVEN, #369). Endpoint conditions still matter for nu_q(i,L) and for N_new(theta). The fold-41 \"cheap check\" concerns only the count margin N_new/RHS, not the maximum, and accepted #159 has since run it (0.9551, certificate = G2 = 546). The producer's L<=8 truncation is outside the theorem.\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/1672/transcript","files":[{"sha256":"a99d73e9bda66c1c5fc2f41271570472043559cadd55f2ddf368349e3f2810e5","name":"research-U-FRAME.md","bytes":56256}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}