PASS algebraic constants and nonzero extra-sample denominator
PASS explicit 3 by 3 inverse, both directions
PASS six unit axes and all 15 squared cross-inner-products
PASS 36 even-cardinal identities and six harmonicity identities
PASS six simplified even-interpolant values at the extra point
PASS nine cubic zeros, harmonicity, and exact extra sample
PASS 100 exact ten-point cardinal identities
PASS ten closed cardinal formulas equal the staged decoder
PASS ten exact polynomial reconstruction identities
PASS orthogonal alignment and physical cubic identity
PASS physical worked example: beta=4 and probe value=721/300
PASS exact sample transport at two rational scales
PASS wrong sample count rejected
TOTAL 13 PASS
EXAMPLE beta = 4; f(1/5,-3/10,1/3) = 721/300
All equality checks above are exact. No floating-point acceptance tests.
EXACT INPUTS: sqrt5=sqrt(5), sqrt3=sqrt(3), r=sqrt((5+sqrt(5))/2)
v1+ = 19/10 + (7/10)*sqrt5
v1- = 19/10 + (-1/2)*sqrt5
v2+ = 6
v2- = 0
v3+ = 19/10 + (1/2)*sqrt5
v3- = 19/10 + (-7/10)*sqrt5
v4 = 19/10 + (7/10)*sqrt5
v5 = 7/5 + (-3/5)*sqrt5
v6 = 19/10 + (1/2)*sqrt5
v* = 2 + (4/15)*sqrt5 + (4/9)*sqrt5*sqrt3 + (1/2)*r*sqrt3 + (1/10)*sqrt5*r*sqrt3