== L: lem:lines
  400 random (u, s, a, b, y), exact: phi == max over monotone sigma: True
== P: lem:patch
  300 random points of patch cells: lower and upper hull values bracket g(a): True
== C: cells (single-polynomial and vertex-decoupled), lemma chain on random configurations
  212 configurations {'cell10f_3': 99, 'cell10d_3': 76, 'cell10d': 23, 'cell10f': 14}: E|L| <= sum_v w_v E P_v(M), E P_v(M) <= sum c G + F_v < T on all: True; max E|L|/T = 0.982089
== N: near-sphere boxes on random configurations
  267 configurations: E|L| <= S3: True; max E|L|/S3 = 0.994380
== K: comparison boxes on random configurations
  200 configurations: P >= R on the grid, P(-v) = 0, P(u) = l_R(u), E|L| = E|X| + E R(M) <= E|X| + E P(M) <= E|X + b chi_4| <= T: True; max E|L|/T = 0.999594
  by kind (tested, chain holds, max E|L|/T): {'comp3': (100, 100, 0.999594), 'comp8': (100, 100, 0.988239)}
== A: adversarial search (hill climbing on E|L| / |alpha|)
  u = 2.6400: max found E|L|/T = 0.999999998; top |alpha_i| [0.5 0.5 0.5 0.5]
  u = 2.6450: max found E|L|/T = 0.999999998; top |alpha_i| [0.5 0.5 0.5 0.5 0. ]
  u = 2.6500: max found E|L|/T = 0.999999998; top |alpha_i| [0.5001 0.5    0.5    0.5   ]
  u = 2.6550: max found E|L|/T = 1.000000000; top |alpha_i| [0.5 0.5 0.5 0.5]
  u = 2.6600: max found E|L|/T = 0.999999997; top |alpha_i| [0.5001 0.5    0.5    0.5   ]
  no configuration above T: True
== U: (K4) exactly at degree 6 and 8 (identity, L/U table, H bound)
  2000 exact tests (1000 with P from comparison records {'comp8': 64, 'comp3': 936}, 1000 with random P of degree 8); passed: {'identity': 2000, 'table': 2000, 'H (records)': 1000, 'H (random P, deg 8)': 1000}; multi-block mu seen [(3, 3), (3, 4), (3, 5), (4, 4)]
  smallest slacks over beta with >= 2 nonzero coordinates (one nonzero coordinate gives equality): {'H (random P, deg 8)': 0.9271582059623876, 'H (records)': 2.9231965467631957e-09, "('L', (3, 3))": 2.5767165828120973e-07, "('L', (3, 4))": 0.0015889482035925059, "('L', (3, 5))": 0.0009156307544149977, "('L', (4, 4))": 1.750485750678559e-05, "('U', (3, 3))": 1.0965129405463624e-06, "('U', (3, 4))": 8.069523822454007e-06, "('U', (3, 5))": 1.0090838432820479e-05, "('U', (4, 4))": 3.167523530160104e-06}
  U: PASS
summary {'L': True, 'P': True, 'C': True, 'N': True, 'K': True, 'A': np.True_, 'U': True}; 13 s
ALL SEMANTIC TESTS PASS

real	0m14.609s
user	0m15.304s
sys	0m0.088s
