k5 verifier (RQ-AUD), data RQ-AUD/audit/rqa/k5_data: 0 cell files, 56 box files; 0 cells, 3867 boxes, kinds {(-1, 'lpv'): 1059, (1, 'lpv'): 1268, (1, 'ms'): 1540}
A  u5 = sqrt(4+2sqrt5), u6 = sqrt(5+sqrt30) give q5 = 1-2/sqrt5, q6 = 1-sqrt(5/6): True; 2 <= U_LO <= u5 and U_HI >= u6: True (u5 - U_LO = 9.338e-05, U_HI - u6 = 7.285e-07); tan(pi/8) <= T8 < 1: True; 5 w-^8 > 1, 5 w-^6 > 2: True; sqrt5- <= sqrt5: True
A  T5(u) = 2sqrt5 (1-q)^4 tau = 2sqrt5 u^9/(1+u^2)^5: True; d/du u^9/(1+u^2)^5 = u^8(9-u^2)/(1+u^2)^6 (unimodal, max at u = 3): True
A  critical points of kappa_3..kappa_10 on [U_LO, U_HI]: kappa_9: 1 root(s) of kappa_j' in [U_LO,U_HI] (sympy), enclosure(s) [3.077853471070, 3.077853471070] width 6.9e-70; enclosures agree with exact root counts: True
A  kappa enclosures contain 99056 exact sample values on 302 intervals: True; kappa_9 upper end exceeds the 4001-point sample maximum by at most 1.82e-09 (relative)
A  kappa_9 on [U_LO, U_HI]: enclosure [15692.115570, 16419.260355], end values max 15761.329581 (the endpoint enclosure would be wrong by 657.9308); objective bound uses this enclosure: True
kappa_1..12(chi): Bernoulli derivative recursion == moment-cumulant recursion: True (kappa_2 = 1, kappa_3 = u - 1/u)
E M^0..12: power-series exponential == set partitions without singletons: True; monomial counts [1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21]
exact enumeration check (u in 12/5, 5/2, 21/10; n in 3, 5, 7; random rational beta): 351 moment identities, all exact: True
B  no one-coordinate cells in this data set (not yet delivered)
B  each of the 56 box files tiles its own region: failures 0
B  s=+1: 23 file regions inside True, overlapping pairs 0, volume fraction of [U_LO,U_HI]x[0,T8]x[1/4,1] covered 0.371657 => partial
B  s=-1: 33 file regions inside True, overlapping pairs 0, volume fraction of [U_LO,U_HI]x[0,T8]x[1/4,1] covered 1.000000 => FULL TILING
B  box kinds outside {lpv, ms}: []
D  20976 vertex-certificate sets (319004 vertices; by number of patch parameters {2: 3869, 3: 5575, 4: 6881, 5: 4651}); record-side cap/phi/type problems: 0 []
D  vertex certificates: failures 0/20976; sets by role {'L0 SG': 2, 'L0 TC+': 1966, 'L0 TC-': 1538, 'L0 cut': 1540, 'L1 TC+': 2420, 'L1 TC-': 1959, 'L1 TCS SG': 56, 'L1 TCS cut': 56, 'L1 cut': 1959, 'L2 TC+': 2641, 'L2 TC-': 1568, 'L2 TCS SG': 467, 'L2 TCS cut': 467, 'L2 cut': 1568, 'L3 TCS SG': 221, 'L3 TCS cut': 221, 'lpv': 2327}; cone sub-boxes max 1, sets needing a split 0; 602s
F  split trees: failures 0/1540; nodes, pieces and near-sphere tests {'L0 minus SG': 2, 'L0 minus TC': 1538, 'L0 plus TC': 1966, 'L0 plus TCN': 1959, 'L0 plus TCS': 56, 'L1 TCS plus A4': 56, 'L1 minus TC': 1959, 'L1 plus A4': 112, 'L1 plus TC': 2420, 'L1 plus TCN': 1568, 'L1 plus TCS': 467, 'L2 TCS plus A5': 646, 'L2 minus TC': 1568, 'L2 plus A5': 658, 'L2 plus TC': 2641, 'L2 plus TCS': 221, 'L3 TCS plus A6': 330, 'node L0': 1540, 'node L1': 1959, 'node L2': 1568}; root cuts ['3/10', '7/20', '2/5', '9/20', '1/2', '3/4']; 604s
RESULT: ALL CHECKS PASSED (parts ABDF, 604s)
EXIT=0
