No-Go Theorems and Boundary Analysis for the J₃(𝕠ₛ) Flavor Sector: Constraints on CKM Polynomial Routes and Pentagonal Escape Mechanisms

A proof-of-impossibility framework for candidate J₃(𝕠ₛ)-based flavor models. Two derived no-go theorems systematically eliminate four polynomial routes to CKM prediction: (1) the CKM polynomial no-go demonstrates that degree-3 Jordan-algebra polynomials cannot simultaneously satisfy the Kobayashi–Maskawa unitarity triangle and hermiticity constraints, and (2) the non-associator lemma shows that non-associative correction terms cannot rescue failed polynomial ansatze without introducing spurious eigenvalues outside the physical spectrum.

Both theorems are independently verified by direct symbolic computation using the Grok kernel. The λ = φ−³ tension, where the CKM mixing-angle eigenvalue conflicts with the vacuum torsion coefficient at 27σ, is confirmed as a physical constraint (not a computational artifact). Conjectural “pentagonal escape” mechanisms, involving exotic E₆(₆) outer-automorphism cycles, are explored as potential beyond-Standard-Model pathways.