k5 verifier (RQ-AUD), data RQ-AUD/audit/rqa/k5_data: 4 cell files, 101 box files; 861 cells, 9166 boxes, kinds {(-1, 'lpv'): 1059, (1, 'lpv'): 3804, (1, 'ms'): 4303}
M  md5 of the 106 files vs k5_MD5SUMS.txt: 0 mismatches []
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  861 one-coordinate cells tile [U_LO,U_HI] x [0,A_S]: OK; inside True; area True
B  each of the 101 box files tiles its own region: failures 0
B  s=+1: 68 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  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}: []
C  one-coordinate cells (ten-moment bound with certified kappa enclosures, Theta_1 for T5): failures 0/861; degrees {10: 861}; 12s
D  52292 vertex-certificate sets (784616 vertices; by number of patch parameters {2: 9168, 3: 14735, 4: 17399, 5: 10990}); record-side cap/phi/type problems: 0 []
D  vertex certificates: failures 0/52292; sets by role {'L0 SG': 2, 'L0 TC+': 5445, 'L0 TC-': 4301, 'L0 cut': 4303, 'L1 TC+': 5768, 'L1 TC-': 4873, 'L1 TCS SG': 58, 'L1 TCS cut': 58, 'L1 cut': 4873, 'L2 TC+': 6240, 'L2 TC-': 3958, 'L2 TCS SG': 1400, 'L2 TCS cut': 1400, 'L2 cut': 3958, 'L3 TCS SG': 396, 'L3 TCS cut': 396, 'lpv': 4863}; cone sub-boxes max 1, sets needing a split 0; 1470s
F  split trees: failures 0/4303; nodes, pieces and near-sphere tests {'L0 minus SG': 2, 'L0 minus TC': 4301, 'L0 plus TC': 5445, 'L0 plus TCN': 4873, 'L0 plus TCS': 58, 'L1 TCS plus A4': 58, 'L1 minus TC': 4873, 'L1 plus A4': 127, 'L1 plus TC': 5768, 'L1 plus TCN': 3958, 'L1 plus TCS': 1400, 'L2 TCS plus A5': 1769, 'L2 minus TC': 3958, 'L2 plus A5': 1431, 'L2 plus TC': 6240, 'L2 plus TCS': 396, 'L3 TCS plus A6': 644, 'node L0': 4303, 'node L1': 4873, 'node L2': 3958}; root cuts ['3/10', '7/20', '2/5', '9/20', '1/2', '3/4']; 1478s
RESULT: ALL CHECKS PASSED (parts MABCDF, 1478s)

real	24m39.304s
user	193m40.283s
sys	0m7.075s
DONE-K5FULL
