[{"type":"thinking","thinking":"Committed as ab47b78. Now summarize for the user. Key points:\n\n1. Item A (margin): done — Step 4 now 13 160 / 88 911, footnote trail with the certified ≥ 4 001 (I used the four-value trail 16 020 → 15 764 → 14 682 → 13 160, adding the intermediate 14 682 from the honest-B(n) corrections — explain why).\n\n2. Item B (Trudgian pinpoints): became a bigger finding — the constants are ROSSER 1941's, not Trudgian's, AND the bib entry trudgian2014 was miscited (vol 83/2014 → vol 81/2012). Both fixed. The three Props are now documented as derived specializations with the derivation note. Mention that the archive (D-036/D-037/NGUYEN.md/Lean docstrings/E-scripts) carries the same misattribution — propose the archive sweep as follow-up.\n\n3. Item C (γ₁): Platt–Trudgian [9] prints no zero ordinates (checked the full text); the value is now sourced to Platt 2017 (rigorous isolation) + Gram 1903 (classical primary).\n\n4. Item D: bib note fixed.\n\nAlso flag: the archive propagation question from before (NGUYEN.md/R-004/STATE.md \"2+5\" classification) now merges with the Rosser misattribution in the archive — both are session-end archive items. Suggest handling at end-protocol or as a dedicated sweep. Keep it brief.","signature":""},{"type":"text","text":"Committed as `ab47b78` — 13 pp, zero overfull, zero undefined refs/citations.\n\n**Item A (margin):** Step 4 now reads margin(8×10⁴) = 13 160, margin(10⁵) = 88 911 — consistent with §3.1. The footnote carries the trail with one extra intermediate value you didn't list but which has a distinct cause: 16 020 (E-028, F+S_b) → 15 764 (FAlt enlargement) → **14 682 (the F-A/F-B honest-B(n) corrections)** → 13 160 (dog-leg, E-034), ending with the exact certified facts the Lean consumes: B(8·10⁴) ≤ 332 000, S_∞(8·10⁴) ≥ 336 000 ⟹ margin ≥ 4 001, plus the direct comparison lemma `marginTilde_FAlt_80000_lt_100000`.\n\n**Item B (pinpoints) — became a real finding.** The constants 0.137/0.443/1.588 are **Rosser 1941** (valid T ≥ 1467), not Trudgian's — verified against Trudgian-II's own Table 1 (arXiv:1208.5846), which attributes them to \"Rosser [10] 1941\"; your own resources atlas (Von Koch–Schoenfeld note) also says Rosser 1941. Additionally the `trudgian2014` bib entry was itself miscited: Math. Comp. **83** (2014) doesn't exist at those pages — the paper is Math. Comp. **81** (2012) 1053–1061 (its S(T) bound is 0.17 log T + 1.998; the II paper improves to 0.111/0.275/2.450). Fixes: the three ZeroCount Props are now presented exactly as you prescribed — *derived* specializations of N(T) = F(T) + S(T) + Rosser's bound (window forms by differencing at endpoints, global via N ≤ F+|S|), with the T < 1467 ranges covered by the |S| ≤ 1 / |S| ≤ 2 verifications cited to Trudgian-II Eq. (1.2); a derivation note sits under the table. The bib entry `trudgian2014` is corrected to vol 81/2012 and kept for the frozen draft.tex.\n\n**Item C (γ₁):** I read all 8 pages of Platt–Trudgian — it prints **no** zero ordinates (and deliberately avoided precise isolation). The value is now sourced to Platt 2017 (*Isolating some non-trivial zeros of zeta*, Math. Comp. 86:2449–2467 — rigorous isolation of zeros to 3.06×10¹⁰ at ±2⁻¹⁰²) plus Gram 1903 as the classical primary source; [9] is cited for what it actually provides (Turing-method completeness to 3×10¹²).\n\n**Item D:** bib note now says \"the Keiper coefficients $\\Lambda_n$\".\n\n**Archive follow-up flag (now bigger):** the same \"Trudgian 2014\" misattribution lives in D-036, D-037, NGUYEN.md (§5B perimeter block, multiple spots), the Lean docstrings (LiSkeleton/LiContour comments — comment-only, proofs unaffected), and the E-scripts' comments. That sweep + the pending \"2+5 → 4+3\" reclassification note are both archive-side; say the word and I'll do them (naturally folds into the session-043 end protocol)."}]