A1 cumulants of chi from its moments: kappa_j = d^[j odd] G_j(w) for j = 3..10 (w = u^2 + u^-2, d = u - 1/u): OK
A2 moments from cumulants (recursion): Gaussian moments (n-1)!! and E chi^n at u = 5/2 reproduced for n <= 10: OK
D vertex certificates: 2763 sets (44584 vertices; by number of patch parameters {2: 388, 3: 755, 4: 928, 5: 692}) from 388 boxes re-verified exactly (cone enclosure, domination on R, strict objective), 1765s: OK
E near-circle boxes: 0 re-verified (mpmath intervals, prec 120, strict), 0s: OK
F m-split boxes: 217 boxes; at every split node the pieces cover [m_c, cap] (top: [m_c, min(1, mbar)]) on both sides; caps, p3-conditions, nested TCS covers and all near-sphere pieces checked (mpmath, strict); pieces by type/level {'A5/2': 55, 'TC/0': 275, 'TC/1': 338, 'TC/2': 371, 'TCN/0': 263, 'TCN/1': 235, 'TCS-sub/A5': 57, 'TCS-sub/A6': 67, 'TCS/1': 46, 'TCS/2': 43, 'minus-TC/0': 217, 'minus-TC/1': 263, 'minus-TC/2': 235}, 1s: OK
G1 three-bit lemma (k=5): all 256 f satisfy sum_i Delta_i^2 < 20(1-q)^8 on [q6, q5] (exact Sturm, 39 distinct polynomials; no equality): OK
G2 four-bit lemma (k=5): all 65536 f satisfy sum_i Delta_i^2 <= 20(1-q)^8 on [q6, q5] (exact Sturm, 1630 distinct polynomials, 9s); equality only at q5 and only for +-OR_4 (2 f): OK
ALL REQUESTED PARTS PASS (A D E F G), 1778s
