The Shattered Crystal Architecture: Theory V19.5 — β Sharpened

The Shattered Crystal Architecture (SCA) proposes that the quantum vacuum is an A15 Frank-Kasper crystal of Faddeev-Skyrme Hopfion topological solitons (space group Pm3̄n), from which the Standard Model, gravity, and cosmology emerge. The theory operates with zero adjustable parameters beyond the Skyrme couplings (c₂, c₄) ; Axiom M (mono-metricity) has been dissolved to derived status (S165). V19. 5 (April 17, 2026) — "β Sharpened" This version integrates results from Sessions 171–181 (53 Prism insertions since V19. 2, 0 errors; 191/191 cumulative lifetime). The headline result is the structural decomposition of the PPN parameter β into geometric and constitutive contributions (new §15. 21), reducing the β = 1 question to a single measurable exponent difference δ₄ − δ₂ on the relaxed A15 crystal. In parallel, the Strong CP solution is completed in-print and the gravity landscape is fully mapped (eight routes killed, one blocked, one surviving). What's new since V19. 2 Item V19. 2 V19. 5 β (PPN parameter) Deeply characterized: 11 NRs, 1 conditional thread ★★★★ STRONGLY CONDITIONAL — structural decomposition in-print (§15. 21) ; Cbare = Cgeom · Cconst = 1/72 + 4/72; ψ-slaving identified as sole surviving mechanism; β = 1 locus χ_ψ = (1 ± √3) /3 derived; decisive GPU test specified Strong CP Partial (S158 baryogenesis bridge) ★★★★★ COMPLETE — 5/5 pieces closed, zero free parameters; Ag × Aᵤ decoupling + all-orders Tₕ protection of CKM real-determinant documented (S172–S174) Gravity landscape Partially explored Fully mapped: 8 killed, 1 blocked, 1 mechanism surviving (defect-gauge/PGT via internal-mode integration) ; A100 target sharpened to Euclidean vacancy correlator Cᵥ (τ) Density-biased nucleation D_ρ Open ★★★★ DERIVED (three-channel, S172): D_ρ −1 everywhere with non-CPL shape (6% H (z) residual at z ≈ 0. 35). P (k) Gaussian cutoff at kc ~ 0. 9–1. 3 h/Mpc (distinguishable from WDM plateau and νDM oscillatory pattern; testable by Rubin DP2, July–September 2026). New falsifiable prediction in V19. 5 β = 1 iff δ₄ − δ₂ ∈ 1. 84, 2. 61 on the relaxed A15 crystal. Self-similar FS→Brazovskii scaling gives χ_ψ = −3, analytically disfavoring β = 1 absent O (1) non-self-similar constitutive corrections. One-shot measurement on A100; decisive. Derived constants (selected, zero free parameters) RH = (5√5 + 4√2) /24 ≈ 0. 70155 (Hopfion radius) g₂ = 0. 5574 (SU (2) coupling from Wilson loop holonomy) S₈ = 0. 786 (phason model) Elastic tensor: C₁₁=158. 8, C₁₂=−41. 5, C₄₄=29. 2; Poisson ratio ν=−0. 090 σwall = 3. 59 EH/a₀² (grain boundary tension) ξKZ = 0. 035 pc comoving at zf=6 (Kibble-Zurek correlation length) Companion paper: "Three falsifiable predictions from a crystalline vacuum" (DOI: 10. 5281/zenodo. 19520378). Status: SM coverage ~90%, ToE ~76%, dark sector ~90%, baryogenesis ~84%, gravity ~87%. 190 documented negative results. Zero active axioms (Axiom M dissolved S165; structural postulate only). Manuscript: 598 pages, 191 verified Prism insertions.