Nonlinear Vacuum Medium Model: Technical Supplement 2.0 — Mathematical Structure, Numerical Validation Architecture, Correspondence Obligations, and Reproducibility Specification

This Technical Supplement 2.0 provides the detailed mathematical, computational, and methodological architecture accompanying the September 2026 formulation of the Nonlinear Vacuum Medium (NVM) Model. The supplement develops the canonical candidate action, field equations and constraints, Hamiltonian and Legendre structure, nonlinear-background hyperbolicity criteria, homogeneous-vacuum linearization, topology and localization diagnostics, Derrick scaling and virial conditions, organizational persistence and stability criteria, dynamical accessibility, and dimensionless reduction. It further specifies a preregisterable numerical validation architecture organized into Tests A–F, separating nonlinear solution existence, dynamical persistence, accessibility, spectral and scaling behavior, infrared propagation, and common characteristic geometry. Subsequent sections define independent correspondence requirements for electromagnetism, gravitation, quantum-state reconstruction, the Born rule, Bell correlations, spinorial structure, fermionic statistics, and effective quantum field theory. Calibration, parameter identifiability, observable mapping, differential prediction, falsification, reproducibility, provenance, and three-valued PASS/FAIL/INCONCLUSIVE decision rules are treated as distinct methodological stages. The technical appendices provide normative equation sets, computational schemas, diagnostic requirements, provenance rules, and bidirectional specification-to-implementation traceability requirements. The supplement does not report numerical or experimental confirmation of NVM. The canonical realization remains a specified and mathematically developed candidate model awaiting nonlinear numerical validation. In particular, the immediate validation target is to determine whether the canonical NVM action admits a converged, finite-energy, localized nonlinear solution that remains within the required Legendre-regular and strongly hyperbolic domain. Technical Supplement 2.0 incorporates the final integrated cross-section consistency audit of the 35-section technical architecture and constitutes the controlling September 2026 technical specification accompanying the NVM framework.