The Refined Space–Time Membrane Model: Deterministic Emergence of Quantum Fields and Gravity from Classical Elasticity

We show that through an eight-parameter, Planck-anchored elasticity equation, the Space–Time Membrane model (STM) derives all nine CKM moduli, the three PMNS angles and the Jarlskog invariant from first principles, while simultaneously reproducing gauge symmetries, solitonic black-hole cores and a dark-energy offset — all without stochastic postulates or extra dimensions. The single high-order PDE ρ∂t2u+T∇2u−[ESTM(μ)+ΔE]∇4u+η∇6u−γ∂tu−λu3−guΨΨˉ=0dummy is fixed by the dimensionless set {ρ,T,ESTM(μ),ΔE,η,λ,g,γdummy} anchored once to c, G, αdummy and Λdummy. A bimodal split of udummy furnishes spinors; enforcing local phase invariance generates the U(1)×SU(2)×SU(3)dummy gauge structure as zero-energy wave/anti-wave cycles. With no flavour tuning, a flat-prior Monte Carlo scan of 50 000 draws reproduces all nine CKM moduli to sub-per-mille precision (best L²-error 3.13×10−4dummy, acceptance 0.012 %), the PMNS angles to within a few per cent (best L²-error 5.603×10−3dummy, acceptance 0.038 %), and captures the Jarlskog invariant to |ΔJ|<1.1×10−10dummy. Fewer than one in 22 000 joint draws meets both criteria, making STM the first deterministic model to capture the full flavour sector without parameter fitting. Functional-renormalisation-group flow, stabilised by the sextic regulator η∇6udummy, produces three infrared minima—qualitatively mirroring the generation hierarchy, though exact masses await refinement—and removes curvature singularities by forming finite-energy solitonic cores that still satisfy SBH=A/4Gℏdummy. Coarse-grained sub-Planck waves leave a residual stiffness ⟨ΔE⟩dummy acting as dark energy; a percent-level late-time drift can ease the Hubble-rate tension. Because the quartic coefficient A4=ESTM/(TL∗2)dummy is locked, a 25 µm-Mylar flexural interferometer should display a 0.24 rad phase shift and a 3 % envelope contraction, while controlled damping must convert algebraic decay into the STM-predicted exponential law governed by γdummy making the model immediately testable. Future work targets three pillars: (i) gauge-compatible Lindblad quantisation that remains ghost-free and BRST-consistent on curved backgrounds, (ii) rigorous proofs of self-adjointness, spin–statistics and anomaly cancellation, and (iii) three-loop renormalisation together with a UV-complete elastic embedding.