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); C_bare = C_geom · C_const = 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; A_g × A_u decoupling + all-orders T_h 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 C_v(τ) Density-biased nucleation D_ρ Open ★★★★ DERIVED (three-channel, S172): D_ρ < 0 at EFT/scaling level P16 topological term Classical overlap only (S161) Spin-structure WZW / Arf construction identified; third independent proof of vacancy fermion statistics (S175) Acoustic strong equivalence Not formalized Reformulated as composition law C(e+δe) = C(e)·C(δe) (§15.21) Gravity coverage ~85% ~87% (sharpened, not resolved) Baryogenesis coverage ~83% ~84% Dark sector coverage ~89% ~90% Negative results 173 190 (+17) Prism insertions (cumulative) 138/138 191/191 (zero errors) Three falsifiable predictions (unchanged) S₈ = 0.786 from phason-mediated νDM scattering (DES Y6: 0.789 ± 0.012 — within 0.3σ). w(z) > −1 everywhere with non-CPL shape (6% H(z) residual at z ≈ 0.35). P(k) Gaussian cutoff at k_c ~ 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) R_H = (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 σ_wall = 3.59 E_H/a₀² (grain boundary tension) ξ_KZ = 0.035 pc comoving at z_f=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.