Geometric-Cybernetic Unification: TUM Cl(8.0) Invariant and Science 4.0

We present the numerical closure of the joint TUM / Science 4.0 framework. This collaboration provides the computational validation of the geometric invariant in Cl(8,0) and its coupling to multi-scale autonomous feedback. Results with zero free parameters: 1. Exceptional Point of order 2 (EP2) at theta = pi/4 where sin²(theta) = cos²(theta) = 0.5. The self-interaction operator J_self(theta) = [[lambda0, 1], [-cos(2theta), lambda0]] becomes an exact Jordan block with discriminant Delta = 4*delta = 0. Algebraic multiplicity 2, geometric multiplicity 1. 2. True self-organization: from generic Psi(0) = 0.5 + 0.1i, the effective potential V_eff(Psi) = ||Psi - F(Psi)||² drives the flow to a stable attractor Gamma_eq = 0.8470 +/- 0.0012, with critical spectral slowing tau_gap ~ 1/(2*gamma0*sqrt(|delta|)) and algebraic dynamics exp(J_EP*t) at the EP. 3. Emergent metric: gmu nu = etamu nu + alpha(Gamma_eq) , alpha = (1 - Gamma_eq)/Gamma_eq ~ 0.1806. 4. Empirical protocol: bioelectric tau1 (ms-s) SNR_bio, metabolic tau2 (min-h) projection P_perp, epigenetic tau3 (days-weeks) and D_KL divergence bound d/dt D_KL = -sigma_S <= -2/tau_gap * D_KL.