== U: unimodality of a_j and the OR-region condition for E_k (exact)
  at q = q_i (i = 2..60): a_1 < ... < a_(i-1) = a_i > a_(i+1) > ... > a_80; q_i < 1/(i+1) < 1/i: True
  U: PASS
== B: every Boolean f on m <= 4 bits, every k (exact)
  m = 1: 4 functions, 3 distinct P_f, 6 interval checks; +-OR_S tables 2; zero sets (interval, where): count {('tail', 'ident'): 2, (1, 'ident'): 2}: OK (0.0 s)
  m = 2: 16 functions, 11 distinct P_f, 33 interval checks; +-OR_S tables 6; zero sets (interval, where): count {('tail', 'ident'): 2, ('tail', 'left'): 2, (1, 'ident'): 4, (1, 'left'): 2, (2, 'ident'): 2, (2, 'right'): 4}: OK (0.0 s)
  m = 3: 256 functions, 79 distinct P_f, 316 interval checks; +-OR_S tables 14; zero sets (interval, where): count {('tail', 'ident'): 2, ('tail', 'left'): 30, (1, 'ident'): 6, (1, 'left'): 6, (2, 'ident'): 6, (2, 'left'): 2, (2, 'right'): 6, (3, 'ident'): 2, (3, 'right'): 6}: OK (0.0 s)
  m = 4: 65536 functions, 3679 distinct P_f, 18395 interval checks; +-OR_S tables 30; zero sets (interval, where): count {('tail', 'ident'): 2, ('tail', 'left'): 4094, (1, 'ident'): 8, (1, 'left'): 12, (2, 'ident'): 12, (2, 'left'): 8, (2, 'right'): 8, (3, 'ident'): 8, (3, 'left'): 2, (3, 'right'): 12, (4, 'ident'): 2, (4, 'right'): 8}: OK (5.4 s)
  B: PASS
== L: every LTF on <= 6 bits (outputs/a5_classes_W9.txt), every k (exact)
  r = 1: 2 classes, 2 distinct P_f, 4 interval checks; zero sets {('tail', 'ident'): 2, (1, 'ident'): 2}: OK
  r = 2: 6 classes, 6 distinct P_f, 18 interval checks; zero sets {('tail', 'ident'): 2, (1, 'left'): 2, (2, 'ident'): 2}: OK
  r = 3: 24 classes, 24 distinct P_f, 96 interval checks; zero sets {('tail', 'ident'): 2, (2, 'left'): 2, (3, 'ident'): 2}: OK
  r = 4: 144 classes, 144 distinct P_f, 720 interval checks; zero sets {('tail', 'ident'): 2, (3, 'left'): 2, (4, 'ident'): 2}: OK
  r = 5: 1542 classes, 1542 distinct P_f, 9252 interval checks; zero sets {('tail', 'ident'): 2, (4, 'left'): 2, (5, 'ident'): 2}: OK
  r = 6: 36736 classes, 36736 distinct P_f, 257152 interval checks; zero sets {('tail', 'ident'): 2, (5, 'left'): 2, (6, 'ident'): 2}: OK
  38456 classes read; 267242 interval checks (189.5 s)
  L: PASS
== E: OR-region identity (exact enumeration)
  322 random positive c in the OR region (m <= 10, rational q): identity exact in all: True
  without c_i > 0: c = -(1,1,1,1), q = 2/5 satisfies c_i > q sum c: True; E|.| = 2592/3125 != 2q(1-q)^4 sum c = -1296/3125: True  (for m q < 1 the condition forces sum c > 0, hence c_i > 0)
  E: PASS
summary: {'U': True, 'B': True, 'L': True, 'E': True}; total 197 s
ALL PARTS PASS

real	3m16.733s
user	3m16.602s
sys	0m0.024s
A24 DONE Thu Oct 22 03:31:08 PM UTC 2026
