Dynamic Continuum Regularization (DCR): Complete Monograph Series

This monograph series presents the unified mathematical architecture of Dynamic Continuum Regularization (DCR) across classical, fluid, solid, and quantum gauge fields. The collection establishes non-singular dynamic viscosity and field closures that eliminate finite-time blowups, resolve complex phase-gradient channel orthogonalities, enforce 4th-order adaptive shock layer filtering, and establish exact thermodynamic dissipation matching empirical NIST water data. Further extensions derive analytic single-field scalar reductions via Lambert W_0 functions, field enthalpy boundary mappings, and a non-perturbative proof of the 4D Yang-Mills mass gap under BRST invariance and OS2 reflection positivity.