C10: n=10 |E|=15 degrees [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
PASS C10 3-regular
PASS C10 energy strictly decreases (min drop 1)
solved 1024 states in 0.0 s
C10 union of per-state monomial supports (k, j): [(0, 0), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (4, 0), (4, 1), (4, 2), (5, 0), (5, 1), (6, 0), (6, 1), (7, 0), (8, 0), (8, 1), (8, 2), (9, 0), (9, 1), (10, 0)]
C10 monomial pairs with nonzero aggregated coefficient: [(0, 0), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (4, 0), (4, 1), (4, 2), (5, 0), (5, 1), (6, 0), (6, 1), (7, 0), (8, 0), (8, 1), (9, 0), (9, 1), (10, 0)] count 19
PASS Table 1 has 19 entries
PASS C10: set of nonzero pairs (E basis) = the 19 pairs of Table 1
PASS C10: c_(0, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(1, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(1, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(2, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(2, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(3, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(4, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(4, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(4, 3)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(5, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(5, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(6, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(6, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(7, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(8, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(8, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(9, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(9, 2)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: c_(10, 1)(p) = Table 1 (direct polynomial in p, no interpolation)
PASS C10: max k = 10, max i = 3
PASS C10: no t^2 e^{-t} term in f (aggregated c_{1,3} = 0)
C10: per-state monomials with k = 1: [(1, 0), (1, 1)]
PASS C10: no state has a t^2 e^{-t} term
degrees in p of the Table 1 entries: [7, 9]
PASS C10: every Table 1 entry has degree <= 9 in p
PASS C10: (4.1) quadratic-in-r form = quartic-in-p form
PASS C10: 80905(p^4-2p^3)-5274599p^2+5355504p = 80905r^2+5355504r
PASS C10: p^4-2p^3 = r^2 - p^2
PASS C10: c_{1,2}(7/10) = 1485516389/20000000000
roots in r of the quadratic: [-65.140627, -1.0543428]
PASS C10: quadratic in r has only negative roots
PASS C10: f_p(0) = p
PASS C10: symmetry (odd under p -> 1-p for k >= 1)
PASS C10: f_inf(1-p) = 1 - f_inf(p)
PASS C10: aggregated coefficients have degree <= 10
PASS C10: Table 1 entries agree with the exact coefficients at the 11 nodes j/12
C10 f_inf(7/10) = 90794489017687/115200000000000 = 0.7881466060563108
PASS C10: f_inf(7/10) = 90794489017687/115200000000000
PASS C10: constant term = absorption value
Method I: f(3)-f_inf in [3.4740871121831e-03, 3.4740871121831e-03], width 1.61e-115
PASS Method I: f(3) - f_inf >= 3.474e-3
Method II (uniformization, Lambda=10, K=160): f(3)-f_inf in [3.4740871121831e-03, 3.4740871121831e-03], width 1.78e-62 (0.1 s)
PASS Method II: f(3) - f_inf >= 3.474e-3
PASS Methods I and II overlap
FLOAT C10 p=0.52: max_t (f - f_inf) = 6.2085e-04 at t = 2.805
FLOAT C10 p=0.55: max_t (f - f_inf) = 1.5098e-03 at t = 2.815
FLOAT C10 p=0.70: max_t (f - f_inf) = 3.4748e-03 at t = 3.020
FLOAT C10 p=0.80: max_t (f - f_inf) = 1.9309e-03 at t = 3.445
A: degrees [2, 4, 4, 3, 3, 4] pools [[1, 2, 0], [0, 3, 4, 5, 1], [0, 3, 4, 5, 2], [1, 2, 5], [1, 2, 5], [1, 2, 3, 4, 5]]
PASS A: degrees (2,4,4,3,3,4)
PASS A: energy strictly decreases with the ABB pools (min drop 1)
A: nonzero monomial pairs [(0, 0), (1, 0), (1, 1), (1, 2), (4, 0), (5, 0), (5, 1)]
PASS A: f_inf = p + r w (1 + 83 r/50)
PASS A: closed form of Prop. 5.1 identical (p, t symbolic)
PASS A: E-basis pairs = (0,1),(1,1),(1,2),(1,3),(4,1),(5,1),(5,2)
PASS A: f_inf(7/10) = 1016603/1250000
A: f(27/5)-f_inf in [4.776913650723e-04, 4.776913650723e-04] (closed form), [4.776913650723e-04, 4.776913650723e-04] (uniformization)
PASS A: f(t0) - f_inf >= 4.776e-4 (both methods)
A: (state, vertex) pairs with k = d/2 at even degree (coin rule would flip with H unchanged): 104
PASS K5: f_p(t) = ABB (3.7) with alpha = p
time 0.4 s
TOTAL FAIL: 0 []
