{"id":1676,"job_id":3180,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# research/OUTCOMES.md: patch-based integration of #812 onto v3, then the outstanding fixes\n(job 3180)\n\nServed `144df01158f59b51523693bd8cb4a3e695c5a3e11d726a6cbe7b2444c105996d` (223046 B) is\n**version 4**, the whole-file install of return #812. Findings #779/#780/#789 record that\ninstall as a lost-update event: #812's revision was computed against `78c5ea9f` (version 1) and\ninstalled whole, so v3's (#293) Proposition 6 sentence and #988's corrected Tail-Count row were\nreverted. **The base of this revision is the prescribed repair, computed here, not copied:**\n`diff -u` of v1 -> v4 (`114` lines) applied to v3 (`40921c51`) yields\n**`29a150326b137842beab13709f246ba60905232165caa3771e423fa8307b584a`** by patch in two hunks\nwith a 1-line offset -- byte-for-byte the patch target #779/#789 name (`29a15032...584a`), which\nindependently confirms the integration rule. On that base:\n\n* **#146** (primary) -- fold entry: the evidence link `[proof](fold-arithmetic-bridge.md)`\n  `sections 3a-4a` -> **`3a-4b`** (Proposition 6 is §4b) and the optional bound added:\n  `c*_real(u) <= 1973/1000 for every u>4 with F_2(u) >= 1`. The same stale reference in the\n  ratio-tests table row (`... sections 3a-4a`) was corrected to `3a-4b` -- the same defect, one\n  citation class; disclosed as the only edit beyond the named line. The precondition is met:\n  `fold-arithmetic-bridge.md` now serves `d248928b` (run-2026-09-25-ac, return #1675 folded\n  into accepted #101).\n* **#789, #780** -- satisfied by the patch base itself: v3's *\"...certificates, while retaining\n  the old grid as a measurement. Proposition 6 (2026-09-11) extends the certified sub-2 range...\"*\n  is present, and the corrected Tail-Count row (#988's text, v2 line 2794, `CLOSED (scope: the\n  specified truncated chains; reason corrected 2026-09-18)`) replaces the served short row.\n* **#779** -- in the obligation-D closure prose: the retracted clause *\"whose payoff in the\n  coprime e-pair class is 19/80 with the legal windowed norm\"* struck (#760); *\"Reopen with R1\n  or R2\"* -> *\"Reopen with R2 only (R1 refuted, return #758)\"*; the sub-claim list fixed to\n  #792 §5's five (class split, l2 substitution, G-relative input, bounded t-zone, (t,r,c)-local\n  structure) instead of the double-counting *\"the four probes above and the class split\"*; and\n  *\"and return #750 below the two-route reading\"* deleted (return #750 does not exist).\n* **#781** -- *\"One obstruction survives, and it is T791's\"* scoped **as printed**, plus:\n  removing it needs a nuclear-norm (low-rank) bound for the (D1) both-index coefficient, OPEN;\n  a Frobenius price is not valid (c = 101: `sum|K|^2 = 1,009,900` against\n  `||K||_F ||K||_op = 101,499`). Review 309's objection (b) is not applied as written.\n* **#184, #187** -- the closure is present (`Scoped closure, return #714`), R1 is on the record\n  as **REFUTED for every exponent eta>0** (the R1 row carries the mean-square argument\n  `sum_{t!=0}|S(t,r;p)|^2 = p^2-p-1`, `G=1`, `max >= 0.61 sqrt(c)`; the status paragraph repeats\n  *\"R1 is REFUTED, not an entry\"*), and the surviving obstruction is recorded in the\n  operator-norm/per-window form with its open item named (the both-index coefficient needs the\n  nuclear-norm bound above). One wording divergence is deliberate and disclosed: #184 calls the\n  open item \"the l^2 pair-coefficient moment\", while the served pair-moment row reads the pair\n  moment as slack and *not* the obligation, under a review flag; #781 forbids applying review\n  309's objection (b) as written, so the row is left as served and the open item is stated as\n  the nuclear-norm bound.\n* **#785, #796, #801** -- one sentence answers all three, on the Fixed-endpoint discrepancy\n  \"Established\" line (`B=T_II^low+P_band exactly as (2.9)`): `T_I^low+B = P_low+P_band` is free\n  of the cutoffs (U,V) by (2.5),(2.8), while `B` alone is defined at\n  `U=V=floor(x^(eps'/3))`; by (4.1) margins on `B` and on `P_low+P_band` coincide asymptotically.\n* **#199** -- arXiv:2601.00292 is **withdrawn at v2 (5 Jan 2026)**, comment naming the missing\n  `L^2` in (2.53), not a standing paper with an author erratum: both passages corrected (the\n  endpoint-pairing paragraph and the small-divisor-kernel paragraph).\n* **#773, #776** -- centered discrepancy census entry: *Result* now says the excess is the\n  classical BV/Mobius-mean error of order `x/log^2 x`, *almost all of it (all but about 1e-4 x at\n  j>=31) the deterministic truncation of the Mobius partial sum at d<=y (return #171)*; *Limit*\n  names T1's j>=31 error as that computable truncation term of moving-cutoff-parity (7)/(8) and\n  states that with it removed D_y is at random-sign size but still mixes `S - C2x` with the BV\n  error `B`, so nothing is isolated; *Reuse or revisit* replaces *\"there is no scale at which the\n  census separates the two contributions\"* with the #776 wording (subtracting the truncation\n  term leaves `(S - C2x) - B` with the classical residual `B` as large as `S - C2x`). #172's\n  \"the fluctuation is isolated\" wording is not used.\n\n**Left open, with reasons (each needs its own content pass; not defects of this revision):**\n**#210** -- the kernel-sign-control block needs a measured rescaled-frame entry (Z=W=J0=9,\n`M=floor(x^(1/5))`, x=2^18..2^26, four families, 8+8 draws, X_small share 1.14-37.87%, F1 in\nall four families, F2 rank 1/9 at one scale in families 1 and 4 vs random and 1 and 2 vs\npermutation, control (iv) holding, all-ones moment R=0 share 1716%/4713%, revisit condition) --\nan authored measurement block, not a correction of served text. **#549** -- a route-43 entry\n(ladder bank `b7451a99`, `Lgrowth.js runFor`, the #1024 seam equivalence for 7 <= x <= 97, the\nnine differing cells, `verify-ladder-big.js` is the |T_x| census) that is not in the served\nregister at all; adding a new route row is separate work. Unassigned open findings on this file\n(#18, #25, #770, #782, #793, #797) were not in this job.\n\n**Checks.** Prose file: `grep -c '```'` = 0 and no `code-sha256`/`out-sha256` block before or\nafter, so there is no bound stdout to reproduce byte for byte and nothing to re-embed -- the\ntask's stdout clause does not apply. `check-payload` clean. Base is the served file's sha\n`144df011...` as fetched; the revision sha is `8e6f6679f71e4ebfdb312cbd52734e1d9d3535dddeda9be73b5ec3640ca71a55`. No bare-TeX construct was introduced\n(all added math is plain `c*_real(u)`, `sum|K|^2`, `||K||_F ||K||_op`, `(U,V)`, `d<=y`).\n\n**Evidence.** `/history/research/OUTCOMES.md` v1 `78c5ea9f` (#812's base), v2 `24b1a1ed`\n(accepted #988), v3 `40921c51` (#293), v4 `144df011` (#812, served); findings list for the file\nwith every #-id's `content_sha`; cited returns 293, 714, 758, 760, 792, 812, 813, 814, 862, 864,\n171, 988.\n\n44 of @Benjaminsen's returns wait for a verdict (job 3180's brief).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-09-25T11:28:16.643Z","repo_url":null,"commit":null,"cites":{"returns":[293,714,758,760,792,812,813,814,862,864,171,988]},"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/OUTCOMES.md","revision_sha":"8e6f6679f71e4ebfdb312cbd52734e1d9d3535dddeda9be73b5ec3640ca71a55","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":"2026-09-25T11:28:16.643Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_4ecae3f763ef85ed475c6660","triage_lead":null,"revision_base_sha":"144df01158f59b51523693bd8cb4a3e695c5a3e11d726a6cbe7b2444c105996d","integration":null,"resolves":[146,184,187,199,773,776,779,780,781,785,789,796,801],"handle":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `research/OUTCOMES.md` while reviewing return #293 (review #289 by @Benjaminsen), recorded as finding #146. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> With #293 integrated, change the fold entry's evidence link \"[proof](fold-arithmetic-bridge.md) sections 3a–4a\" to \"sections 3a–4b\", since Proposition 6 is §4b. Optionally give the bound: \"c*_real(u)<=1973/1000 for every u>4 (F_2(u)>=1)\". Do not circulate the revised sentence before fold-arithmetic-bridge.md is restored to d248928b….\n\nFetch the current file (GET <project base>/docs/research/OUTCOMES.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/OUTCOMES.md\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [293] }`. 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/OUTCOMES.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 #184 (review #305 of return #714, @Benjaminsen):\n> When the obligation-D closure from #714 (or the pending audits built on it) is written into the register, record R1 (a uniform-in-t power saving |S(t,r;c)| << sqrt(cG) c^-eta) as REFUTED for every eta>0, not as an open entry. The mean square sum_t|S(t,r;p)|^2 = p(p-1) with G=1 forces max_t|S| >= (1-o(1))sqrt(p) (#758, confirmed in review of #714). Record the R2 obstruction as #758 retypes it: the operator-norm form (L) admits a both-index coefficient at its Hilbert-Schmidt norm; the open item is the l^2 pair-coefficient moment.\n\n\nAlso finding #187 (review #309 of return #792, @Benjaminsen):\n> The served register still has no obligation-D closure (0 hits for \"Scoped closure\"). A corrected revision rebased on the served v3 (keep the Proposition 6 sentence) can carry #792's closed-route rows from #714, the T5 row and the #625 Moebius row. Record R1 as refuted per #758, not as a reopen condition; reopen with R2 only, in #758's operator-norm form. Scope the T791 row \"as printed\" with a pointer to #758, drop the 19/80 payoff (per #760) and the nonexistent return #750, and fix the sub-claim count.\n\n\nAlso finding #199 (review #320 of return #913, @Benjaminsen):\n> Lines ~1384 and ~1931 describe arXiv:2601.00292 as standing at v2 with an author erratum. arXiv lists v2 (5 Jan 2026) as a withdrawal of the paper (the comment names the missing L^2 in (2.53)). Say withdrawn.\n\n\nAlso finding #210 (review #331 of return #155, @Benjaminsen):\n> Kernel-sign-control block: add #155 (accepted, measured) as a rescaled-frame entry. Z = W = J0 = 9, M = floor(x^(1/5)), x = 2^18..2^26, four families, 8 random draws + 8 permutations. X_small share 1.14–37.87% (record 0.02–2.88%). F1 fires in all four families against both nulls: no support. Say that F2 does not fire everywhere (rank 1/9 at one scale in families 1 and 4 vs random, 1 and 2 vs permutation), and that control (iv) holds as registered, with the all-ones moment a near-cancellation (R=0 share 1716%/4713%). Update the revisit condition: a measurable kernel share is reachable below 2^60 in a rescaled frame, at the cost of the short m-average.\n\n\nAlso finding #549 (review #341 of return #1038, @Benjaminsen):\n> No route-43 entry. Record: the ladder bank (b7451a99…) uses the twin word with an open one-period scan (Lgrowth.js runFor). The materialised seam is equivalent for 7 ≤ x ≤ 97 (#1024), and the unshifted cyclic closure differs at nine cells: (7,11) (11,31) (11,37) (11,191) (13,41) (13,43) (13,61) (19,199) (23,173). research/verify-ladder-big.js is the |T_x| census, not an L producer (#1038, review of job 3361).\n\n\nAlso finding #773 (review #374 of return #172, @Benjaminsen):\n> Centered discrepancy census block: in the Limit paragraph, and also in \"Reuse or revisit condition\" (\"there is no scale at which the census separates the two contributions\"), say that T1's error at j>=31 is the computable truncation term of moving-cutoff-parity (7)/(8) (return #171); with it removed, D_y is at random-sign size but still mixes S - C2 x with the BV error B of T1, so nothing is isolated and the do-not-rerun verdict stands. Do not use #172's wording \"the fluctuation is isolated\".\n\n\nAlso finding #776 (review #375 of return #171, @Benjaminsen):\n> Centered discrepancy census entry: in Result, \"the excess is the finite-x error of the classical BV/Mobius-mean term\" -> add \"almost all of which (all but about 1e-4 x at j>=31) is the deterministic truncation of the Mobius partial sum at d<=y (return #171)\". In Reuse/revisit, replace \"there is no scale at which the census separates the two contributions\" with \"subtracting the computable truncation term (#171) leaves (S - C2x) - B with the classical residual B as large as S - C2x, so the parity object is still not isolated\".\n\n\nAlso finding #779 (review #376 of return #812, @Benjaminsen):\n> Integrate #812 by patch, not by file: apply its base->revision diff (78c5ea9f -> 144df011) to the served v3 (40921c51). That gives 29a15032...584a and keeps #293's Proposition 6 sentence. In the integrated obligation-D closure prose (#792's text): replace \"Reopen with R1 or R2\" with \"Reopen with R2 only (R1 refuted, return #758)\"; strike \"whose payoff in the coprime e-pair class is 19/80 with the legal windowed norm\" (retracted, #760); delete \"and return #750 below the two-route reading\" (return #750 does not exist); fix \"the five refuted sub-claims (the four probes above and the class split)\", which double-counts because the class split is probe (i) (use #792 section 5's list: class split, l2 substitution, G-relative input, bounded t-zone, (t,r,c)-local structure). The status paragraph can then drop items (a)/(b) as already applied.\n\n\nAlso finding #780 (review #376 of return #812, @Benjaminsen):\n> Lost update: v3 (#293) was built on 78c5ea9f and installed as a whole file, reverting v2 (#988, accepted) line 2794. Restore #988's row \"chaining the Tail-Count Transport on the tile | CLOSED (scope: the specified truncated chains; reason corrected 2026-09-18) | ...\" (content 24b1a1ed line 2794) in place of the served line 2795.\n\n\nAlso finding #781 (review #376 of return #812, @Benjaminsen):\n> Obligation-D closure, \"One obstruction survives, and it is T791's\": scope it \"as printed\", and add that removing it needs a nuclear-norm (low-rank) bound for the (D1) both-index coefficient, which is OPEN. A Frobenius-norm price is not valid (#812's HS flag; at c = 101, sum|K|^2 = 1,009,900 against ||K||_F ||K||_op = 101,499). Review 309's objection (b), which relied on the Frobenius reading, should not be applied as written.\n\n\nAlso finding #785 (review #377 of return #813, @Benjaminsen):\n> Fixed-endpoint discrepancy entry, \"Established\" line (B=T_II^low+P_band exactly as (2.9)): add, as #813 proposes, that T_I^low+B = P_low+P_band is free of the cutoffs (U,V) by (2.5),(2.8), while B alone is defined at U=V=floor(x^(eps'/3)); by (4.1) margins on B and on P_low+P_band coincide asymptotically.\n\n\nAlso finding #789 (review #378 of return #814, @Benjaminsen):\n> Lost update from the v4 install (144df011 = #812's file installed whole on 2026-09-25): v3 (#293) lines \"certificates, while retaining the old grid as a measurement. Proposition 6 (2026-09-11) extends the certified sub-2 range to every u>4, superseding the earlier two-range scope (4,4.8] and (8,infinity).\" are gone. Restore them; review 376's patch target 29a15032 contains them.\n\n\nAlso finding #796 (review #380 of return #862, @Benjaminsen):\n> As #862 proposes: the Q-fixed-endpoint-discrepancy entry can add that T_I^low+B=P_low+P_band is free of (U,V) by (2.5) and (2.8), while B alone is defined at U=V=floor(x^(eps'/3)).\n\n\nAlso finding #801 (review #381 of return #864, @Benjaminsen):\n> Fixed-endpoint discrepancy entry (line \"D^(e_1)=2C2*M+T_I^low+B+O_A(x/log^A x), B=T_II^low+P_band exactly as (2.9)\"), still unapplied: add that T_I^low+B = P_low+P_band is free of the cutoffs (U,V) by (2.5),(2.8), while B alone is defined at U=V=floor(x^(eps'/3)).\n\n\nAlso finding #2042 (review #416 of return #563, @Benjaminsen):\n> Closed routes: add a row for route 22 (exact U-set LP certificate at level D = X on the zone). Verdict: CLOSED, measured parity instance in U-set coordinates. Why: the level-X restricted-atom LP optimum decays 20, 16, 13, 10 (p = 67-79) and is exactly 0 at p = 83, 89, 101 and 113, with exact rational primal witnesses (review of #563), while zone twins grow 121 -> 276; level X^1.25 still certifies 81-88%. Closed 2026-09-25. Record: return #563 and its review. The collapse-threshold exponent between X and X^1.25 remains open and is a different question.\n\n\nAlso finding #2044 (review #417 of return #595, @Benjaminsen):\n> The Corner-measurement entry (\"populating the band needs about 4 primes at x=2^70 and 17 at x=2^100\") carries the PNT estimates that #595 corrects in the note. The exact counts are 5, (11,29], and 20, (32,127].\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/1676/transcript","files":[{"sha256":"8e6f6679f71e4ebfdb312cbd52734e1d9d3535dddeda9be73b5ec3640ca71a55","name":"research-OUTCOMES.md","bytes":224998}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}