PASS ubar^4 - 2 ubar^2 - 1 > 0
PASS u0 = sqrt(1+sqrt2) ~ 1.5537740 (7 dp): [1.55377397403004 +/- 2.70e-15]
PASS ubar > u0
PASS r1a: region ('1', '776887/500000', '0', '4/25') and 94 cells, none failed: 94 cells
PASS r1b: region ('1', '776887/500000', '4/25', '8/25') and 59 cells, none failed: 59 cells
PASS r1c: region ('1', '776887/500000', '8/25', '12/25') and 32 cells, none failed: 32 cells
PASS r1d: region ('1', '776887/500000', '12/25', '16/25') and 71 cells, none failed: 71 cells
PASS r2a: region ('1', '13/10', '77/100', '9/10') and 16 cells, none failed: 16 cells
PASS r2b: region ('13/10', '776887/500000', '77/100', '9/10') and 47 cells, none failed: 47 cells
PASS r3a: region ('1', '13/10', '16/25', '77/100') and 16 cells, none failed: 16 cells
PASS r3b: region ('13/10', '611/400', '16/25', '77/100') and 44 cells, none failed: 44 cells
PASS total cells 379: 379
     cell u-width min = 126887/16000000 = 0.0079304 at u [24733497/16000000, 776887/500000], a [2529/3200, 1271/1600]
     cell u-width max = 276887/2000000 = 0.1384435 at u [1276887/1000000, 2830661/2000000], a [7/50, 4/25]
     cell a-width min = 13/3200 = 0.0040625 at u [24733497/16000000, 776887/500000], a [2529/3200, 1271/1600]
     cell a-width max = 13/400 = 0.0325000 at u [49/40, 13/10], a [347/400, 9/10]
PASS Table 1 caption: cell u-widths 0.0079 to 0.139: true 0.0079304..0.1384435; nearest rounding: False; stated range encloses true: True
PASS Table 1 caption: cell a-widths 0.0040 to 0.0325: true 0.0040625..0.0325000; nearest rounding: False; stated range encloses true: True
PASS sample cell found once in r1d
PASS sample cell has 7 coefficients
PASS c1 = 114188429368/981419917709: 114188429368/981419917709
PASS c5 = -22338039/10529058835: -22338039/10529058835
PASS c0 ~ 0.0281054: 0.0281053840
PASS c1 ~ 0.1163502: 0.1163502261
PASS c2 ~ 0.1316753: 0.1316752718
PASS c3 ~ 0.0212156: 0.0212156085
PASS c4 ~ -0.0041259: -0.0041258873
PASS c5 ~ -0.0021216: -0.0021215608
PASS c6 ~ 0.0003276: 0.0003276066
PASS Q region [611/400, ubar] x [9/25, 471/1000]
PASS 641 boxes, none failed, every c4 > 0: 641
PASS 7.2: box u-widths 0.0008 to 0.0033: true 0.0008211..0.0032842; nearest rounding: True; stated range encloses true: True
PASS 7.2: box t-widths 0.0017 to 0.0069: true 0.0017344..0.0069375; nearest rounding: True; stated range encloses true: False
PASS a(9/25) = 225/353 < 16/25
PASS a(471/1000) = 942000/1221841 > 77/100
PASS exactly one box contains (u0, sqrt2-1) in its interior: 1
     box: u [2483411/1600000, 776887/500000], t [2637/6400, 831/2000], c4 = 13162/5452309
PASS box u1 ~ 1.5521319, u2 = ubar
PASS box t1 ~ 0.4120313, t2 ~ 0.4155: t2 = 0.4155000000
PASS box c4 ~ 0.0024140: 0.0024140231
     appendix box, 4 c4 s - B0^2: exact corner values u1,t1: 6.0761068e-04, u1,t2: 5.7266702e-04, u2,t1: 6.1620304e-04, u2,t2: 5.8149093e-04
PASS appendix box: 4 c4 s - B0^2 >= 5.7e-4 (Arb, 64x64 split; exact corner minimum at ('u1', 't2')): certified lower 5.724501e-04, grid min 5.726670e-04, exact value at corner ('u1', 't2') = 5.7266702e-04 (>= 5.7e-04)
     appendix box, kappa3 B0 - 4 c4: exact corner values u1,t1: 6.2919843e-03, u1,t2: 6.8490680e-03, u2,t1: 6.1635125e-03, u2,t2: 6.7218784e-03
FAIL appendix box: kappa3 B0 - 4 c4 >= 6.2e-3 (Arb, 64x64 split; exact corner minimum at ('u2', 't1')): certified lower 6.159735e-03, grid min 6.163513e-03, exact value at corner ('u2', 't1') = 6.1635125e-03 (< 6.2e-03)
     kappa3 B0 - 4 c4: min certified lower (8x8 per box) 1.755248e-03; min grid value 1.777103e-03 at box 640 (u [611/400, 12233137/8000000], t [9/25, 11631/32000], c4 = 18373/9659018); exact value at its corner (12233137/8000000, 9/25) = 1.7771026e-03
PASS all 641 boxes: kappa3 B0 - 4 c4 > 0 certified (8x8 split)
PASS 7.2: stated minimum certified lower bound 1.77e-3 is <= the exact value at the minimising corner: 1.7771026e-03
PASS 7.2: and is within 1e-5 of it: gap 7.103e-06
PASS G = E|X| (4-point Gauss-Hermite) rounds to 0.8880738 and to 0.8881: [0.8880738339771153 +/- 3.79e-17]
PASS q* with 2 tau(q*) = G rounds to 0.2701496 and to 0.27015: [0.2701495783095085 +/- 3.05e-17]
A6E_CLAIMS_NOT_CONFIRMED ["appendix box: kappa3 B0 - 4 c4 >= 6.2e-3 (Arb, 64x64 split; exact corner minimum at ('u2', 't1'))"]
