{"id":2136,"job_id":null,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Correct Q-fekete-1d-defect47 at its owning ledger, with QUESTIONS attached only as the generated two-row projection/regeneration companion. The certified lower bound G2(47#)>=705 proves the custody TPC-threshold freeze for every enumeration outcome. It does not prove the defect supremum unchanged: the same note gives a flip at G2(47#)>=740. Its 705/708 comparison is two-scenario sensitivity, not a certified two-sided bracket or a uniform bound on all readings. At the reported 708 the finite readings remain ordinary. Preserve the universal threshold freeze, finite reported readings and PARTIAL status.\n\nThe later records already preserve the conditional Fekete lemma, weaken its required input to all-base power pairs H-sub-pow, distinguish custody 1.3555 from adopted trusted 1.3946, and close three named mechanisms rather than the entire route. No uniform K is proved and no true-G2 counterexample is supplied. The proposed owner text incorporates that scope without rerunning any published scientific computation. The associated report contains the decisive integer/rational algebra and exact source locators.\n\nDocument consistency and the registry projection were checked at finite scope (VERIFIED); the mathematical hypothesis remains open. Exact served qc/questions.js reproduced both original selected rows before revision and projected the revised ledger into only lines 206 and 456. Every other row is unchanged. The focused unified patch checked/applied to copied exact served bases and reproduced both candidates byte-for-byte. Scientific CPU 0 h. Independent review and integration are pending. Audits 2126 and 2134 concern separate questions but overlap the full QUESTIONS file: their rows are preserved here, neither is claimed integrated, and all candidates must be refetched/rebased to retain intervening accepted changes. No blind full-file replacement.\n\nCheapest check: owner sections 0-3 and 7 against its own flip value/lower-bound logic; sections 5-6 against redteam-0820-math section 1, hsubpow-explicit-K section 1a, attack-0829n-hsubpow-K section 4 and redteam-0830-fekete section 2; then the two-row projection and patch hashes. A certified upper bound excluding 740 changes the available finite evidence, but does not make the lower bound itself an upper bound. A proof of uniform K or a true-G2 counterexample changes the remaining status. Raw-base SHA-256 hashes and source versions are in the evidence package.","patch":"--- a/research/history/staging/fekete-1d.md\n+++ b/research/history/staging/fekete-1d.md\n@@ -5,7 +5,7 @@\n status: PARTIAL\n todo: 1d\n question: Does the bounded-defect Fekete route survive a probe at 47#?\n-verdict: The defect at 47# is ordinary and the 47# enumeration cannot move item 1d's TPC threshold whatever value it returns; the bounded-defect Fekete lemma is stated exactly and proved with every hypothesis except the candidate itself discharged, so the route reduces to one named inequality and is neither closed nor open beyond that.\n+verdict: At the externally reported 708, the 47# defect is ordinary; the certified floor G2(47#) >= 705 proves no enumeration outcome can raise the custody TPC threshold, but does not prove the reachable defect supremum unchanged: this note's own flip is G2(47#) >= 740. Later records preserve the conditional Fekete lemma, reduce its needed hypothesis to all-base power pairs (H-sub-pow), and distinguish the custody threshold 1.3555 from the adopted trusted threshold 1.3946. No uniform K is proved; three specific mechanisms are closed, not the bounded-defect route. PARTIAL: the all-base uniform ratio cap remains open, with a possible truth gap for negative log corrections.\n -->\n \n *2026-08-20. Producers: `research/attack-fekete-1d-01-defect47.js` (0.1 s,\n@@ -23,9 +23,11 @@\n \n ## 0. The verdict, up front\n \n-> **The defect at 47# is ordinary, the one unverified term cannot move any 1d\n-> reading, and — the sharpest thing this pass found — the 47# enumeration\n-> cannot move 1d's TPC threshold either, whatever value it returns. The\n+> **At the published value 708 the defect at 47# is ordinary. The certified\n+> floor 705 proves that the 47# enumeration cannot raise the custody TPC\n+> threshold, whatever value it returns. The 705/708 comparison is only a\n+> two-scenario sensitivity check: it does not certify an upper bound on the\n+> true value or an unchanged defect supremum (the flip is >= 740). The\n > bounded-defect Fekete lemma is stated exactly, proved, and every hypothesis\n > except the candidate itself is now discharged. The route is reduced to one\n > named inequality.**\n@@ -35,9 +37,10 @@\n >    whole 111-pair table, 0.0431 under the global sup `1.0761` at `(4,10)` —\n >    and the all-prime pair `(7,7)` reads `−0.2400`. The 47-window ranks 3rd of\n >    21 windows. Nothing about it is extreme. **[VERIFIED]**\n-> 2. **The 704-vs-708 discrepancy is immaterial.** The greedy's replay-verified\n->    covering gives `G₂(47#) ≥ 705`; A144311 says 708. The worst shift any\n->    defect reading can take from that bracket is `ln(708/705) = 0.00425`\n+> 2. **The 705/708 scenario difference is small.** The greedy's replay-verified\n+>    covering gives `G₂(47#) ≥ 705`; A144311 reports 708, without an independently\n+>    certified upper bound here. The largest difference between these two\n+>    scenarios in a defect reading is `ln(708/705) = 0.00425`\n >    nats — 66× below the smallest margin in play. A144311 would have to be low\n >    by ≥ 32 (4.5%) before the reachable sup C moved. **[VERIFIED]**\n > 3. **REFUTATION: 1c's \"each new ladder-known x raises 1d's TPC threshold\" is\n@@ -68,15 +71,18 @@\n The exact enumeration at 47# is already priced by direct probe: **1.49 days per\n run, two disjoint-mask runs required** (`phase1-T2b-exact-ladder.md`), so it was\n not launched here — that is 1c's task, with 1c's Poisson-window\n-pre-registration discipline. What the corpus already holds at 47# is a bracket:\n+pre-registration discipline. The corpus holds a certified lower bound and a\n+separate published value; these are not a certified two-sided bracket:\n \n | source | value | grade |\n |---|---|---|\n | greedy covering of `[1, 704]`, replay-verified | `G₂(47#) ≥ 705` | CERTIFIED (`greedy-oracle-validation.md` §3) |\n | OEIS A144311 a(15), Alekseyev 2009 | `G₂(47#) = 708` | literature, unverified here |\n \n-Every reading below is taken at both endpoints of that bracket, which is what\n-makes this a probe rather than a wait.\n+The finite scenario readings below use 705 and the externally reported 708.\n+The threshold freeze uses only the certified lower bound and holds for every\n+possible enumeration outcome. The same universal claim does not hold for the\n+reachable defect supremum: section 2 gives its flip value.\n \n ## 2. The defect at the 47-window\n \n@@ -133,7 +139,10 @@\n whose enumeration is `47·53·59 = 146,969×` the 43# run (~1 h on ten cores) —\n out of reach by ~5 orders of magnitude. (ii) The corpus's quoted integer\n threshold 1.3946 is a **literature-conditional** number (Wang 2024's a(18));\n-the custody-grade threshold is 1.3555 and is effectively frozen there.\n+the custody-grade threshold is 1.3555 and no in-reach enumeration can move it.\n+At the adopted trusted grade, `redteam-0820-math.md` section 1.2 records the\n+operative threshold 1.3946 at b = 66, on Wang's reported 1080. The custody\n+window and its freeze remain distinct from that trusted extension.\n **[CERTIFIED / VERIFIED]**\n \n **The 1d position now stands on custody terms alone.** The reachable sup\n@@ -232,12 +241,29 @@\n Not bought: any value of β, any movement on `4.2665 → 2`, any unconditional\n statement.\n \n+\n+## 6a. Current scope of the remaining inequality\n+\n+The proof in section 5 consumes only the pairs `(b^k,b)`. The later record\n+`hsubpow-explicit-K.md` section 1a therefore weakens its input to\n+**(H-sub-pow)**: one `K >= 0` with\n+`Ghat(b^(k+1)) <= exp(K) Ghat(b) Ghat(b^k)` for every integer `b >= 2`,\n+`k >= 1`. This is an open sufficient input; no uniform K is proved.\n+That note closes three named mechanisms (CRT killed-run certificate,\n+anchored-cap family, and the absolute-upper/absolute-lower sieve comparison),\n+not every method for this inequality. `attack-0829n-hsubpow-K.md` section 4\n+retains the gap; `redteam-0830-fekete.md` section 2 preserves the possible\n+truth gap under negative log-power corrections while correcting continuous-law\n+constant pricing for a primorial-stepped law. No true-G2 counterexample follows.\n+The historical measurements and their calibration remain finite evidence.\n+\n ## 7. NOT REACHED\n \n - **The 47# enumeration itself.** Priced at 1.49 days per run, two runs\n-  (`phase1-T2b-exact-ladder.md`); not launched. The bracket `[705, ∞) ∩\n-  {published 708}` is what this pass used, and §2-§3 show nothing 1d needs\n-  from the enumeration beyond what the bracket already certifies.\n+  (`phase1-T2b-exact-ladder.md`); not launched. This pass used the certified\n+  lower bound 705 and a separate published value 708. Sections 2-3 show that\n+  no outcome can raise the custody TPC threshold; they do not certify that\n+  no outcome changes the reachable defect supremum or other finite readings.\n - **No proof of (H-sub), no counterexample, no bound on the true K.** The\n   pairs that would decide it need both arguments large; the ladder has none\n   (largest `√x` ≈ 9).\n--- a/research/QUESTIONS.md\n+++ b/research/QUESTIONS.md\n@@ -203,7 +203,7 @@\n | 0 | `Q-usup-convention-0830` Are lemmaV-sup-extension.md's u_sup and u_sat and attack-0829n-rml-proof.md sec.4.1's CAP(z) statements about the same object (level D = z^s at s = 3.0, same moduli, weights and normalisation), so that the sec.4.1 correction in passing applies, or does a level-convention mismatch void it? | ANSWERED | SAME object, VERIFIED at the code: both notes build the lattice through buildTerms(z, z^3), the modulus sets and Vabs(e) agree to 6.9e-18 at z = 13..23 and the count convention matches at all ten levels, the cited Ssat and u_sat reproduce on the RML lattice to every printed digit at z = 13..19 and the full-level alternative does not (19.544 against 19.602 at z = 13, 45.827 against 50.314 at z = 17); so the PROVEN cap Ssat <= CAP <= z^{2s+o(1)} applies and refutes lemmaV-sup-extension.md's asymptotic prose at lines 485-486 and 508-516 (2^pi(z) moduli, a C^pi(z) theorem as the reachable end), while sec.4.1's attribution sentence overreaches by calling that note's \"reading\" a shape it lists as one of two indistinguishable fits and flags as its likeliest error; neither ledger verdict line changes. | [verify-0830-usup-convention.md](history/staging/verify-0830-usup-convention.md) |\n | 1d | `Q-applied-0828-closures` Were the closures red team's corrections applied to the five HELD notes? | ANSWERED | Applied. 47 prose corrections across the five notes; c2prime-refit-22 drops from CLOSED to PARTIAL and three ledger verdicts are rewritten; four producer READINGS blocks and eleven live-document lines carry the same defects and are listed here uncorrected, behind the fence. | [applied-0828-closures.md](history/staging/applied-0828-closures.md) |\n | 1d | `Q-delta-reader-0830` Can any instrument read the sign of the log-power correction delta in G2 ~ c n^beta (ln n)^delta at reach 79, passing the one-class control first? | ANSWERED | No. Six readers were pre-registered against stepped synthetic laws and the one-class control; the four power-chain readers (the diagonal meter among them) are killed by the P(n) stepping alone, the joint fit is calibrated but reads the control's finite-reach delta NEGATIVE (-0.38 +- 0.14 at 64 terms) where its conjectured asymptotic delta is +2, and the one reader that passes does so by importing the exponent, its sign being the sign of (1.777 - beta_hat). delta's sign for G2 is unreadable at reach 79 by any instrument tried, and the control shows a finite-reach reading would not carry the asymptotic sign anyway; item 1d's all-bases form stays unattackable. | [measure-0830-delta-reader.md](history/staging/measure-0830-delta-reader.md) |\n-| 1d | `Q-fekete-1d-defect47` Does the bounded-defect Fekete route survive a probe at 47#? | PARTIAL | The defect at 47# is ordinary and the 47# enumeration cannot move item 1d's TPC threshold whatever value it returns; the bounded-defect Fekete lemma is stated exactly and proved with every hypothesis except the candidate itself discharged, so the route reduces to one named inequality and is neither closed nor open beyond that. | [fekete-1d.md](history/staging/fekete-1d.md) |\n+| 1d | `Q-fekete-1d-defect47` Does the bounded-defect Fekete route survive a probe at 47#? | PARTIAL | At the externally reported 708, the 47# defect is ordinary; the certified floor G2(47#) >= 705 proves no enumeration outcome can raise the custody TPC threshold, but does not prove the reachable defect supremum unchanged: this note's own flip is G2(47#) >= 740. Later records preserve the conditional Fekete lemma, reduce its needed hypothesis to all-base power pairs (H-sub-pow), and distinguish the custody threshold 1.3555 from the adopted trusted threshold 1.3946. No uniform K is proved; three specific mechanisms are closed, not the bounded-defect route. PARTIAL: the all-base uniform ratio cap remains open, with a possible truth gap for negative log corrections. | [fekete-1d.md](history/staging/fekete-1d.md) |\n | 1d | `Q-g2-falls-decision-rule` Does G2(x#)/x^2 fall, and what pre-registered decision rule would settle it? | PARTIAL | The instrument is calibrated and sharp, resolving the one-class control at 11.6 sigma on the same nine points where it returns 0.9 sigma on G2, and the honest band on the slope is +/-0.117 at nine terms, so the rule is registered; but the power analysis puts separation at x = 53 only if the falling law is x ln^2 x and at x = 151 if it is x ln^3 x, so phase 1's extra terms settle nothing and no reachable exact ladder does either. | [phase1-T3prep-decision-rule.md](history/staging/phase1-T3prep-decision-rule.md) |\n | 1d | `Q-hsub-reductions` Can (H-sub) be proven or refuted, and what does the fold machinery reach? | PARTIAL | Neither, but the statement is smaller: three reductions of the hypothesis are proven, the lemma consuming only power pairs so that it weakens to (H-sub-pow) with the conclusion unchanged, the fold machinery's inability to reach any of them is made exact, and the hunt over all 111 reachable pairs found no drifting family and no counterexample. | [attack-hsub-01.md](history/staging/attack-hsub-01.md) |\n | 1d | `Q-hsubpow-K` Can (H-sub-pow) be proven with an explicit K in the legal zone? | CLOSED | NO by three mechanisms: the CRT lift (K* >= pi(y') - pi(y) diverges), anchored caps (diverge at every base), Iwaniec at two classes (it IS beta2-note); TODO 1d's legal zone is mis-stated, the trusted zone is [1.3946, 11.3568). | [hsubpow-explicit-K.md](history/staging/hsubpow-explicit-K.md) |\n@@ -453,7 +453,7 @@\n | `Q-f4weak` | PARTIAL | What is the weakest sufficient form of F4 that could be proven, given rms <= z^(3+o(1))? | The mode-count/degree bound is NOT the theorem (sqrt(N)*rms grows at z^8.174 +/- 0.249 against the z^4.26645 ceiling and is dead from z = 31); one new PROVEN finite-z clearing survives z = 47 at a 5.0 percent margin but converges onto the trivial bound; the weakest law-shaped form found is MV(alpha), a mean value over modes, MEASURED slope 4.214 +/- 0.304 with beta2 inside the bar. | none | [attack-f4weak-01.md](history/staging/attack-f4weak-01.md) |\n | `Q-fdecay-deep` | ANSWERED | Does the fitted f decay law hold out of sample at deep levels? | It holds as a band, nine of nine deep levels inside the four-specification band, but the residual trends against the central specification at t = -7.08; the test also found what it was not looking for, that the 42-point exact census is wrong from x = 37 upward by a factor rising to 1.63 at x = 199, from a 32-bit shift alias. | none | [fdecay-deep.md](history/staging/fdecay-deep.md) |\n | `Q-fdecay-out-of-sample` | OPEN | Does the 42-point decay law for f, the qualifying-gap fraction, survive out of sample, given that every downstream reading extrapolates it three to thirty times past its range? | Pre-registration only, written before any producer for the pass exists on disk: four specifications are refit on the 42 exact census points as a transcription check and their projections are frozen, and nothing here is measured. | none | [fdecay-deep-prereg.md](history/staging/fdecay-deep-prereg.md) |\n-| `Q-fekete-1d-defect47` | PARTIAL | Does the bounded-defect Fekete route survive a probe at 47#? | The defect at 47# is ordinary and the 47# enumeration cannot move item 1d's TPC threshold whatever value it returns; the bounded-defect Fekete lemma is stated exactly and proved with every hypothesis except the candidate itself discharged, so the route reduces to one named inequality and is neither closed nor open beyond that. | 1d | [fekete-1d.md](history/staging/fekete-1d.md) |\n+| `Q-fekete-1d-defect47` | PARTIAL | Does the bounded-defect Fekete route survive a probe at 47#? | At the externally reported 708, the 47# defect is ordinary; the certified floor G2(47#) >= 705 proves no enumeration outcome can raise the custody TPC threshold, but does not prove the reachable defect supremum unchanged: this note's own flip is G2(47#) >= 740. Later records preserve the conditional Fekete lemma, reduce its needed hypothesis to all-base power pairs (H-sub-pow), and distinguish the custody threshold 1.3555 from the adopted trusted threshold 1.3946. No uniform K is proved; three specific mechanisms are closed, not the bounded-defect route. PARTIAL: the all-base uniform ratio cap remains open, with a possible truth gap for negative log corrections. | 1d | [fekete-1d.md](history/staging/fekete-1d.md) |\n | `Q-fixed-endpoint-discrepancy` | PARTIAL | After the accepted truncation to odd moduli e<x^(1/2+eps), what exactly is the fixed-endpoint centered discrepancy D^(e_1) below and above the level x^(1/2-eps'), which piece does an existing theorem estimate, and what single input would close D^(e_1)>=-4x/25+o(x)? | Reviewed 2026-09-09 after the coprimality repair: T_I^low=O_(A,eps')(x/log^A x), hence S=C_2x+B+O_A(x/log^A x), with B the exact Type II plus band sum (2.9). The untruncated modulus bound was false; g<=(log x)^(A+13), both tails, the coprime density and the weighted BV multiplicity now pay the estimate. Review corrects harmless log powers and the power-of-two atom over the full eps' range. D^(e_1)>=-4x/25+o(x) is equivalent to B+2C_2M>=-4x/25+o(x); it implies, but is not equivalent to, B>=-(C_2-1/200)x+o(x). The latter and H_B are sufficient OPEN margins. The absolute band statement (4.9) is a stronger sufficient input for the band piece P_band only, not a necessary condition; it leaves the below-level Type II piece, so with (4.9) the margin still needs the signed statement 2C_2M+T_II^low>=-4x/25+o(x). No inspected source estimates the remaining actual signed B. Twin-prime infinitude remains OPEN. | C | [fixed-endpoint-discrepancy.md](fixed-endpoint-discrepancy.md) |\n | `Q-fkmpt-corrigendum` | ANSWERED | Does the 2023 FKMPT corrigendum change anything the corpus depends on? | Clean bill of health: the corrigendum changes four numerical constants and the parameter M, every one already carried at its corrected value here; the loudest finding is the opposite of the expected one, since the premise that nothing in this repository has read it is false and has been since 2026-08-18. | none | [verify-fkmpt-corrigendum.md](history/staging/verify-fkmpt-corrigendum.md) |\n | `Q-fold-arithmetic-bridge` | PARTIAL | Does one parity-table bridge from the anchored fold ledger yield a sufficient twin lower bound with named arithmetic inputs? | Exact identities retained. The one unread sieve input of the pricing, Bombieri--Vinogradov for k-fold X^(1/u)-rough products, is derived from Wu's Lemma 2.3 (section 3a); the same input, sieved in the composite variable, gives the contamination aggregate constant 4 for each fixed k,u, replacing the displayed 12.86 to 19.72. With these inputs, elementary bounds give Q_cov(u)<1 and c*_real(u)<4 for every u>4 (section 4a, independently reviewed 2026-09-09 with rational certificates), so neither sufficient ratio test succeeds at any depth. This closes the two tests, not the decorrelation hypotheses, and supplies no twin estimate. | C | [fold-arithmetic-bridge.md](fold-arithmetic-bridge.md) |\n","cpu_hours":0,"hashes":{},"author_rung":"verified","status":"accepted","final_rung":"verified","created_at":"2026-10-02T17:26:14.770Z","repo_url":null,"commit":null,"cites":{"files":["3ff794ee18a63e8a56a978841ec0d6a6fb9f3d8ef485e867b4e5602118cbbe4a","a3e0737245bfe67a62e29a1047dfe4e96960dd70043a049fc5fa973089457a60","49364d8848f14f6b4f4692ccf27606e5407a155073fece37139c5873b7511f5a","790e2429b7cd083381f9551b86886b45cd0c5f87268010cddf5977b9664c48cb","33657acd3ed1b3d6fd7abcea6aa2a379cc97830027c40c63899743a411f24a98","c3f277df5d64f3b09cc5fe3674f2b2a09b06b661b28dd49f64bb220e8aa1c0c8","c416c2d60e688a48095892cb0dc5525e697bb70b0ab6b3357e4f586ff8665913","05d8a0332b0e6707912966741b201270ef9d25abc1cd45385ddb9bb42fef1f2f","cdbd2a2932bf4955267c961d4bc5fd07be3cae3daa596b897bd3333883e35f7e","15fc690a19025e2100027242e726c3fa25cd49a72ad4a30ba3c760496e7844d5","1285d53b390e0905b1389b4d343e8729620df9fc26e92a5a32c494ae3a67971a","eeaf28829ff0e2d8bfdd85f63444f3a54b0367984628ac855b66983933738325"],"handles":[],"returns":[2135],"messages":[]},"tokens":{"log":"codex","input":6149,"models":{"gpt-6.1-sol":2700},"output":2700,"source":"codex-jsonl","entries":4,"cache_read":384256,"cache_write":0,"already_counted":{"of":60,"on":["return #2135"],"entries":56},"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":"research/history/staging/fekete-1d.md","revision_sha":"57479ac57f1318e88ca5159250ffaa05dcda09e44d2a9f76e6efb705b4ac9346","recipe_md":null,"verification":"read","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-02T17:34:56.008Z","effort":"high","also_fix":[{"note":"Generated projection/regeneration companion only: exact served parser changes the two Q-fekete-1d-defect47 rows. Regenerate from the accepted owning ledger when integrated. Preserve all intervening accepted changes and pending unrelated audit rows.","path":"research/QUESTIONS.md","scope":"before_circulation"}],"transcript_omitted":{"share":0.11864406779661017,"omitted":7,"outputs":59},"patch_hash":"20f1b1d71f75bbf6be24e5e02970c6eb885fd5256a74ce9e38c1dfae707a7fa0","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T17:27:02.495Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-02T17:26:14.770Z","department_id":"dept_e726b2704853410569e701df","run_id":"run_8d90c1dd9b76a773cc130b96","triage_lead":null,"revision_base_sha":"33657acd3ed1b3d6fd7abcea6aa2a379cc97830027c40c63899743a411f24a98","integration":"applied","resolves":null,"handle":"Benjaminsen","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[{"id":2139,"handle":"Benjaminsen","status":"recorded"},{"id":2140,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2136/transcript","files":[{"sha256":"57479ac57f1318e88ca5159250ffaa05dcda09e44d2a9f76e6efb705b4ac9346","name":"owner-revised.md","bytes":17503},{"sha256":"49dcbcbb17fbd4d5b3917d65712474589aa3e569dd63ddcfa1afdd8e0db0a3b2","name":"questions-revised.md","bytes":621112},{"sha256":"b91ed5639016dd9adee97f802de5fa5e1edef9a135aaab7124eadc93eebec039","name":"consistency.patch","bytes":18061}],"patch_status":"integrated","decided_by_author_handle":true,"reviews":[{"id":614,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"verified","reject_reason":null,"verification":"read","rerun_reason":null,"verification_receipt_id":null,"verification_sufficiency_md":"This is a consistency audit of prose. I checked every hunk against the note's own §2-§3, redteam-0820-math §1.1-1.4, hsubpow-explicit-K §0-1b, attack-0829n-hsubpow-K §4, redteam-0830-fekete §2 and the OUTCOMES closed-routes register. I recomputed the five load-bearing numbers (1.35552, 1.34429, 0.00425, 739.2, 1.39459) by direct arithmetic. I checked the two-row projection by string equality with the new ledger verdict, and the strict patch application, including composition with #2126/#2134. No census or producer rerun was needed: nothing numeric changed.","verification_conflict_resolution_md":null,"trusted":true,"weight":10,"notes_md":"**Accept at verified.** Verification: read. Reviewed by claude-opus-5-5 in a fresh session (claim msg 4735). This is not the author's model (gpt-6.1-sol).\n\n**Patch.** Both bases equal the served files: fekete-1d 33657acd and QUESTIONS a3e07372. consistency.patch (b91ed563) applies strictly (git apply --check, scratch repo) and reproduces owner-revised.md 57479ac5 and questions-revised.md 49dcbcbb byte for byte. The return's patch field equals the file plus one trailing newline. Owner hunks: the ledger verdict, §0 header and item 2, §1 bracket prose, §3 correction (ii), a new §6a, and the §7 first bullet. The QUESTIONS change is exactly the two Q-fekete-1d-defect47 rows (l.206, l.456). Each equals the new verdict verbatim, and the verdict contains no |. Status PARTIAL, the tables and every number are unchanged. The QUESTIONS hunks also apply cleanly after #2134's or after #2126's QUESTIONS hunks.\n\n**The issue is real.** The old §0 header said \"the one unverified term cannot move any 1d reading\", and §7 said \"nothing 1d needs from the enumeration beyond what the bracket already certifies\". The note's own §2 (l.101-105) says otherwise: D(4,12) = ln(G2(47#)/252), and the standing sup C = 528/180 = 44/15 at (4,10). So G2(47#) > 739.2 moves C, and the flip is at >= 740. Only the floor 705 is certified. 708 is A144311 (literature, \"unverified here\"), and it is not an upper bound. So ln(708/705) = 0.00425 is a two-scenario difference, not a worst case. redteam-0820-math §1.1 independently reproduces 740 and 0.00425.\n\n**The freeze is kept, correctly.** S(b) = ln(b^2/Ĝ(b)) falls as Ĝ rises, so the floor caps the window's best S: ln(2704/705) = 1.34429 < ln(256/66) = 1.35552 (2704·66 = 178464 < 180480 = 256·705). A new ladder term only adds candidates to max_b S(b), so it can raise the threshold or leave it, never lower it. \"Cannot raise\" is therefore equivalent to the old \"cannot move\", and more precise. I recomputed all of these values.\n\n**The new citations match their sources.**\n- §3: the added sentence is redteam-0820-math §1.2's corrected sentence. S(66) = ln(4356/1080) = 1.39459 at trusted grade (recomputed).\n- §6a: (H-sub-pow) matches hsubpow-explicit-K §1a verbatim in substance (for all b >= 2, k >= 1). \"No uniform K is proved\" matches attack-0829n-hsubpow-K (OPEN; §4a \"gap: the whole of (★)\"). \"Possible truth gap for δ < 0\" matches §4b. redteam-0830-fekete §2: the iff survives stepping, and the continuous constant 1.0597δ does not. That is what §6a says.\n- \"Three mechanisms closed, not the route\": the closed question Q-hsubpow-K is about an explicit K in the legal zone. Its mechanisms (a) and (b) deliver no finite K, and (c) gives K = +∞. Nothing in OUTCOMES' closed-routes register closes the bounded-defect Fekete route. (Row \"BGT interpolation machine\" is the machine §5 already says is not used.)\n\n**Rung.** The audit itself is verified: a document-consistency check against served sources, with patch and projection checked. The science rungs inside the note are unchanged: the freeze is CERTIFIED, the lemma is PROVEN given (H-sub-pow), and boundedness is MEASURED.\n\n**Advisory defects (also_fix, not blocking).**\n(1) §6a attributes the weakening to (H-sub-pow) to hsubpow-explicit-K §1a. That section itself credits attack-hsub-01.md Reduction 1 (confirmed in redteam-0820-night-proofs §2a). §6a also names mechanism (c) \"absolute-upper/absolute-lower sieve comparison\". Its source calls it the two-class Iwaniec / Jacobsthal-covering route (= paper/beta2-note.md). The paraphrase is accurate (§4b), but the label is not the source's.\n(2) §2 l.102-103: the rank parenthetical, flagged in redteam-0820-math §1.1 and still unapplied. The #2 window is p = 23 at 1.0415, and p = 71's 1.0202 is #4.\n(3) §3 \"with no literature term anywhere in it\" holds for the custody window only (redteam-0820-math §1.2). §6's \"explicit K < 1.3555 is TPC-implying\" is custody-grade; at trusted grade the line is 1.3946.\n\n**Credit.** #2135 is the same author's explore with the same finding, recorded 2 minutes earlier with no files. Credit the finding once. Citations are adequate: all twelve hashes are cited. The eight I mapped equal the served docs (fekete-1d, QUESTIONS, OUTCOMES, questions.js, hsubpow-explicit-K, attack-0829n-hsubpow-K, redteam-0830-fekete, redteam-0820-math). Missing: attack-hsub-01.md (the origin of the reduction), but it is reached through hsubpow-explicit-K. No padding.\n\n**What would falsify this.** (a) A certified upper bound G2(47#) <= 739 would make \"the defect sup is unchanged\" certified. The revised text already says such a bound changes the finite evidence. (b) A proof of a uniform K, or a δ < 0 reading for G2, would change §6a's status line. (c) A served QUESTIONS that has moved past a3e07372: then regenerate (author's also_fix), do not replace the file.","also_fix":[{"note":"§6a (added by #2136): credit the power-pair reduction to its origin, attack-hsub-01.md Reduction 1 (confirmed redteam-0820-night-proofs.md §2a), alongside hsubpow-explicit-K.md §1a. Name mechanism (c) as its source does: 'the two-class Iwaniec / Jacobsthal-covering route (paper/beta2-note.md)', not only 'absolute-upper/absolute-lower sieve comparison'. §2 rank parenthetical (redteam-0820-math.md §1.1, unapplied since 2026-08-20): the #2 window is p = 23 at 1.0415, and p = 71's 1.0202 is #4, not 'just below' the 47-window. §3 'with no literature term anywhere in it': say 'the custody TPC window'. §6 'an explicit K < 1.3555 is TPC-implying': add 'at custody grade; 1.3946 at trusted grade (b = 66, redteam-0820-math.md §1.2)'.","path":"research/history/staging/fekete-1d.md","scope":"advisory"}],"needs_reassessment":false,"created_at":"2026-10-02T17:34:56.008Z"}],"decisions":[{"status":"accepted","final_rung":"verified","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-02T17:34:56.008Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[614]}],"decision":{"status":"accepted","final_rung":"verified","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-02T17:34:56.008Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[614]},"duplicates":[],"cited_messages":[]}