OMEGA geometry/operator bridge: independent Python reference v1.0
Python 3.13.5 NumPy 2.3.5 SymPy 1.14.0
Optimization mode: 0
Julia execution: NOT RUN. This is a separate implementation.
PASS 01 exact golden and fourth-power identities
PASS 02 exact 36-entry Gram factorization and signed sum
PASS 03 exact moment and focal polynomials
PASS 04 exact Bloch projection and operator polynomial
PASS 05 exact inverse-family and monotonicity identities
PASS 06 published unit-node transcription
PASS 07 seed radii, retained-arc endpoints, feet and gaps
PASS 08 all fifteen center angles and exact-form bearing identities
PASS 09 circle-centered rank two versus centroid-centered rank one
PASS 10 isometric placement of marks, arc and foot samples
PASS 11 ellipse singular values and constructive ball preimages
PASS 12 full-kernel affine ellipse chart and angle-recovery metric
PASS 13 scale covariance of geometry, ellipse and operator
PASS 14 shape/scale recovery within the declared golden-step family
PASS 15 1548 sampled point-to-unit-vector witnesses
PASS 16 2163 support/boundary comparisons including translations
PASS 17 operator square, norm and explicit diagonalization
PASS 18 translated-ellipse zero-tail regression and correction
PASS 19 finite block supports and exact-form tail-error checks
PASS 20 matrix-polynomial similarity bound without a Crouzeix oracle
PASS 21 twelve independent directions in a finite product section
REFERENCE_80_DIGIT R 1.618035795544614180078576964005621879833735508870611819311079366125294
REFERENCE_80_DIGIT r 0.9999999999970619461826142029743643671516492482925342295009977060335934
PASS 22 80-digit canonical-value cross-check
PASS 23 invalid-input rejection and zero Python assert nodes
GROUPS 23 PASS; explicit require calls 7539
CANONICAL phi 1.6180339887498949
CANONICAL s 2.4240684055453061e-06
CANONICAL R 1.6180357955446143 r 0.99999999999706191
CANONICAL d 1.2720219477939714
CANONICAL norm(T) 2.618035795541676
CANONICAL kappa 2.058168728992495
MAX_ERROR source_node_max_abs 0
MAX_ERROR inverse_s_max_abs 2.549958806391181e-16
MAX_ERROR witness_max_abs 1.1322097734007351e-15
MAX_ERROR boundary_max_abs 8.0059320849734421e-15
MAX_ERROR support_max_abs 5.3290705182007514e-15
No Julia runtime, Lean build, infinite simulation or physical experiment is claimed.