ENTROPIX-MESA: A Master Entropy Selection Framework for Unification via Irreversible Quantum Information Flows

This comprehensive white paper presents the fully closed ENTROPIX-MESA unificationprogram. Grounded in three minimal axioms Information Primacy (O1), Open System Irreversibility (O2), and Monotonic Distinguishability Export (O3) the framework proves thatregulated hyperscaling violating entanglement entropy is the unique universal selector undermaster conditions M1 (stationary mutual information) and M2 (non-decreasing relative entropy export). From a pre geometric Quantum Information Network (QIN) consistent withknown results on maximal quantum chaos (SYK, MSS bound saturation), tensor networkholography (MERA/HaPPY), JT gravity duality, and higher dimensional AdS/CFT extensions via regulated hyperscaling, the theory derives D=4 spacetime as an entropic maximum(Theorem 7.2), Standard Model gauge structures, exact three fermion generations, parameter free quark mass hierarchies matching PDG 2026 estimates, proton stability, emergentEntropic Damping Force (EDF) as a theorem, and cosmological constant w ≈ −1.018, allwithout new particles or tuning.The hierarchical lineage—DME → EDF → ENTROPIA → ENTROPIX → MESA—ismathematically closed at unification grade rigor: regulator independent proofs with enhanced rigor (including non-circular variational derivation of dimensionality and EDF),variational uniqueness, and algorithmic outputs are provided