PASS eight basis embeddings have nonzero sign determinant
PASS basis has eight ordered square-free monomials
PASS F sits inside K because sqrt(5) is a basis element
PASS phi = (1+sqrt(5))/2 uses only the rational and sqrt(5) slots
PASS 1 and phi squared are distinct and share the golden norm 1
PASS 1 and phi share the larger norm and not the golden norm
PASS larger norm is the fourth power of the golden norm at (0, 1)
PASS larger norm is the fourth power of the golden norm at (1, 0)
PASS larger norm is the fourth power of the golden norm at (1, 1)
PASS larger norm is the fourth power of the golden norm at (2, -3)
PASS larger norm is the fourth power of the golden norm at (3/2, -4/5)
PASS 13 is not one of the seven square-free radicands of the quadratic subfields
PASS n=(2,3,0) has squared length 13
PASS displayed reflection equals I-2nn^T/(n^T n)
PASS R squared is the identity
PASS R is orthogonal
PASS Rn = -n
PASS integer first disagreement is attained
PASS a continuous infimum need not be a disagreement point
PASS positive floor identity recovers the input
PASS normalized integral of J squared is 1/21
PASS x^2 y^2 z^2 has normalized spherical mean 1/105
PASS coefficient order is the displayed basis order recorded in basis_order and BITS
PASS coefficient schema enforces the omega-exact-coefficient/1 record format
PASS a reduced eight-coefficient record is accepted
PASS schema rejects missing coefficients and records that are not eight coefficient objects
PASS schema rejects malformed integer strings
PASS schema rejects a zero denominator
PASS reduced-form validator rejects unreduced fractions and any zero other than 0/1
TOTAL 29 PASS
Checked: basis sign determinant, golden-to-larger norm, reflection, disagreement, floor identity, J^2 moment, coefficient schema.
Not checked here: transcendence of pi, a general Galois-correspondence proof, or a new cubature rule.