ENTROPIX Measurements, Hierarchical Validation, and Ontological Closure Across Entropy Models: Non Perturbative Optimization and Master Hierarchy

ENTROPIX presents a closed, non circular, and falsifiable master framework for unification grounded in irreversible quantum information flow in open systems. Building onthe foundational ENTROPIX (v1, 2026), DME, ENTROPIA, and EDF papers, this version introduces a non perturbative optimization of the Master Entropy Selection Algorithm(MESA) as a variational extremum over convex functionals F, with Lagrange multipliersenforcing M1 (stationary mutual information) and M2 (monotonic relative entropy export)constraints. Regulated hyperscaling entanglement entropy emerges uniquely as the globalattractor, deriving the universal stability coefficient γ ≈ 0.703051051 analytically as thetopological ratio I′′(2)/(2I(2)) from the regulated flux integral I(α), with Beta functionsubstitution, series expansion, dominated convergence, and dimension rescaling invarianceproving regulator and scale-independence to 10−8.Ahierarchical stack Master (Lyapunov global attractor), Sub Master (Fisher-Rao geometry acceleration), and Slave (KL divergence minimizing reductions) optimizes convergenceand subsumes thermodynamics, QFT, GR, and holography. In contrast to string theory’slandscape of ∼ 10500 vacua, ENTROPIX derives four dimensions emergently from exportmaximization and selects a single vacuum via compounded non perturbative damping. Specific predictions include: late time acceleration w(z) deviation ∆w ≈ −0.018±0.007 (falsifiable by Euclid/DESI); unitary black hole Page curves with quadratic exponential radiationdamping; and a Hubble tension resolution ∆H0 ≈ 5 km/s/Mpc via early hyperscaling transition. ENTROPIX achieves ontological minimality, mathematical closure, and exhaustivefalsifiability (> 5σ thresholds) across scales