RQ-AUD A.21 verifier; file k4_data/s13_2620_2640.json; md5 acd0e21e322a16d59a7a5a481d626dde; parts MTCNK
region u in [131/50, 66/25] = [2.62, 2.64]; q in [625/4981, 2500/19661]
== M: cumulants, partition counts, monotonicity of kappa_j
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
  text formulas kappa_3..kappa_10 in (w, d) == own Laurent polynomials: True
  G_k = N(k, ()) = (k-1)!! [k even], k <= 10: True  [Fraction(1, 1), Fraction(0, 1), Fraction(1, 1), Fraction(0, 1), Fraction(3, 1), Fraction(0, 1), Fraction(15, 1), Fraction(0, 1), Fraction(105, 1), Fraction(0, 1), Fraction(945, 1)]
  spot values N(k, mu) (including those printed by RQ-C's verifier): True  N(10,())=945, N(10,(3, 3))=6300, N(10,(3, 3, 4))=2100, N(10,(3, 5))=2520, N(10,(4, 4))=1575, N(10,(5, 5))=126, N(6,(3, 3))=10, N(5,(3,))=10, N(10,(10,))=1
  kappa_j monotone on u in [127/50, 71/25] (Sturm on u^m kappa_j'): k3 increasing, k4 increasing, k5 increasing, k6 decreasing, k7 decreasing, k8 decreasing, k9 increasing, k10 increasing
  M: PASS
== T: tilings
  phase 1, s2 = +1: 600 boxes, inside region True, volume sum == region True, overlapping interior pairs 0: OK
  phase 1, s2 = -1: 400 boxes, inside region True, volume sum == region True, overlapping interior pairs 0: OK
  skipped boxes: all satisfy a2- >= a1+ or (a1-)^2 + (a2-)^2 >= 1: True (465)
  split boxes: all s2 = +1: True; all with (a1+)^2 + (a2+)^2 < 1 and a2- > 0 (so D3 restricted to B x [0, a2+] is the closure of its interior): True
  phase 2: 2557 boxes, each inside exactly one split box: True
  phase 2 tilings of B x [0, a2+] for all 132 split boxes and both s3: OK
  empty boxes: all satisfy a3- >= a2+ or sum (a-)^2 >= 1: True (0)
  record kinds as described in the text (comparison kinds with matching degree), failed lists empty: True
  T: PASS
== N: near-sphere boxes
  [ns: 19 records, 0.0 s]
  near-sphere: 19/19 pass; max K (b+)^2 / (S3/2) = 0.9810
  N: PASS
== K: four-point comparison boxes
  [comp: 320 records, 18.0 s]
  comparison: 320/320 pass; (kind, degree D): count {('comp3', 6): 320}; u-bisection depth (boxes by depth) {0: 320}; multi-block cases ['(3, 3):l']
  K: PASS
== C: ten-moment cells, (W1) and folded (W2)
  [cells: 2621 records, 155.2 s]
  cells: 2621/2621 pass (by kind, pass/total: {'cell10d': '103/103', 'cell10d_3': '461/461', 'cell10f': '300/300', 'cell10f_3': '1757/1757'}); Arb root isolations 2916416; u-bisection depth needed in W1 (cells by max depth) {0: 2621}
  W2 margin T^- - (sum c_k G_k + F): min 9.650e-07, median 3.294e-02
  C: PASS
summary: {'M': True, 'T': True, 'N': True, 'K': True, 'C': True}; total 176 s
ALL PARTS PASS

real	2m57.352s
user	22m57.541s
sys	0m0.502s
