B: n=6, |E|=8, degrees [3, 1, 3, 3, 3, 3]
PASS B all degrees odd
PASS B energy strictly decreases at every flip (min drop 1)
B monomial pairs (k, j) occurring in the per-state solutions: [(0, 0), (1, 0), (1, 1), (3, 0), (4, 0), (5, 0), (5, 1), (6, 0)]
B union of per-state supports: [(0, 0), (1, 0), (1, 1), (3, 0), (4, 0), (5, 0), (5, 1), (6, 0)]
  coef of t^0 e^{-0t}: p**2*(28*p**3 - 70*p**2 - 94*p + 211)/75
  coef of t^0 e^{-1t}: -p*(p - 1)*(2*p - 1)*(p**2 - p - 4)/4
  coef of t^1 e^{-1t}: 9*p**2*(p - 1)**2*(2*p - 1)/16
  coef of t^0 e^{-3t}: -7*p**2*(p - 1)**2*(2*p - 1)/24
  coef of t^0 e^{-4t}: 0
  coef of t^0 e^{-5t}: 71*p**2*(p - 1)**2*(2*p - 1)/200
  coef of t^1 e^{-5t}: 7*p**2*(p - 1)**2*(2*p - 1)/80
  coef of t^0 e^{-6t}: 0
PASS B: nonzero aggregated pairs (E basis) = the six pairs of Theorem 3.1
FINDING (fix 1 of run 2): the per-state functions g_s also contain the pairs [(4, 1), (6, 1)] (E basis); their sums over |s| = j vanish for every j: True
PASS B: extra per-state pairs are exactly (4,1) and (6,1) and cancel for every popcount
PASS B: c_(0, 1)(p) identical to the note (p symbolic)
PASS B: c_(1, 1)(p) identical to the note (p symbolic)
PASS B: c_(1, 2)(p) identical to the note (p symbolic)
PASS B: c_(3, 1)(p) identical to the note (p symbolic)
PASS B: c_(5, 1)(p) identical to the note (p symbolic)
PASS B: c_(5, 2)(p) identical to the note (p symbolic)
PASS B: f_inf = p^2(28p^3-70p^2-94p+211)/75
PASS B: f_inf = p + r(2p-1)(1+14r/75)
PASS B: f_p(0) = p
PASS B: f - f_inf = r w e^{-t} [bracket] identically
PASS B: bracket(0) = -1 - 14r/75
PASS B: f'(0) = r(2p-1)
PASS B: f'(t) = r w e^{-t}[derivative bracket of the note]
PASS B: symmetry f_{1-p}(t) = 1 - f_p(t) coefficientwise
PASS Cor 3.2: 1/4 + 7/24 = 13/24
PASS Cor 3.2: threshold = 16/(9r) + 26/27
threshold at p=61/100: 60206/7137 = 8.43575732100
PASS threshold(61/100) = 60206/7137 < 223/25
PASS threshold(61/100) = 8.43575... (8.43575 < threshold < 8.43576)
FINDING (fix 2 of run 2): version 1 of the note printed 60206/7137 = 8.4358..., but the expansion is 8.43575...
PASS r <= 1/4 gives threshold >= 64/9 + 26/27 > 8.07
B: f_inf(61/100) by absorption = 41541389119/62500000000 = 0.664662225904
PASS B: f_inf(61/100) = 41541389119/62500000000
PASS B: constant term of the exact closed form = absorption value
Method I (own closed form, rational bounds of e^{-t0}): f(t0)-f_inf in [9.3891186962315e-07, 9.3891186962315e-07], width 2.77e-95
PASS Method I: lower bound of f(t0) - f_inf > 0
PASS Method I: lower bound > 9.389e-7
Method II (own uniformization, Lambda=6, K=230, integer arithmetic): f(t0)-f_inf in [9.3891186962315e-07, 9.3891186962315e-07], width 1.34e-71 (0.0 s)
PASS Method II: L - f_inf > 0
PASS Method II: L - f_inf > 9.389e-7
PASS Methods I and II overlap
  digits of L - f_inf: 93891186962314
mutation B-45: degrees [3, 1, 3, 3, 2, 2]
PASS mutation: absorption = constant term
mutation: f(t0)-f_inf in [-3.021371e-05, -3.021371e-05] (closed form), [-3.021371e-05, -3.021371e-05] (uniformization)
PASS mutation: no overshoot at (61/100, 223/25) (upper bound < f_inf)
mutation: coefficient of t e^{-t} = -23*p**2*(p - 1)**2*(2*p - 1)/16
PASS mutation: c_{1,2}(61/100) < 0
time 0.1 s
TOTAL FAIL: 0 []
