Cascade Framework: Deriving Standard Model Observables from x³ = x² + 1 (v2).

The cascade framework derives all Standard Model parameters and the cosmological constant from the single cubic polynomial x³ = x² + 1 with zero free parameters. From the real root ψₛ = 1. 4655712319, the framework generates 27 physical observables spanning the electroweak sector, fermion mass ratios, CKM quark mixing matrix, CP-violating phase, Jarlskog invariant, neutrino mass ratio, and dark energy density — 20 of 27 sub-0. 1%, all 27 sub-3%, with 26 exact algebraic theorems proven from the polynomial alone. This upload contains five papers covering the framework overview, fermion mass derivations, electroweak and CKM predictions, dark energy and the cosmological hierarchy, and the arithmetic geometry foundations establishing the Langlands-dual modular form as 31. 1. b. a on Γ₀ (31) and the fusion algebra as Fib ⊗ Silver. Version 2 incorporates 10 days of intensive theoretical development following the initial upload, including the direct derivation of the Jarlskog invariant to 0. 055%, exact derivation of lepton exponents (Theorems 15–17), the CKM-Electroweak Correspondence Theorem, Exact Theorem 26 (Galois-Geometric Faithfulness), and a new fifth paper on arithmetic geometry.