Nonlinear Vacuum Medium (NVM) Model: Mathematical Foundations

NVM Mathematical Foundations Version 1.0 provides the formal mathematical specification underlying the Nonlinear Vacuum Medium (NVM) Model. It develops the framework from its proposed physical ontology toward an explicit system of equations, constraints, solution criteria, parameter definitions, correspondence requirements, calibration procedures, and falsifiable differential predictions. The document specifies the mathematical architecture required to evaluate NVM as a physical hypothesis, including field content, action and Euler–Lagrange structure, constraint and topological sectors, fixed-amplitude and full-amplitude certification gates, dimensional and coupling parameter dictionaries, correspondence targets, calibration/test separation, uncertainty propagation, and a hierarchy of differential experimental predictions. The purpose of this document is not to claim that the required numerical, correspondence, or experimental tests have already been satisfied. Rather, it establishes a formal pathway from the proposed NVM ontology to mathematical solutions and ultimately to empirical testing: Ontology → Model → Equations → Certified Solutions → Correspondence → Calibration → Differential Predictions → Experiment → Retain, Revise, or Reject NVM proposes that particles, fields, quantum behavior, gravitation, and spacetime may emerge as organized dynamical regimes of a deeper continuous, nonlinear, non-equilibrium physical medium. The framework is presented as a developing and falsifiable theoretical model rather than an experimentally established replacement for existing physical theories. This document forms part of the broader NVM research program and should be read alongside the primary NVM Model manuscript, Technical Supplement, and Computational Specification.