This analytical edition presents the Sc-Rubs model — a field-based framework describing how stable structures emerge and persist within continuous media.The work develops the Laplace Continuation formalism, uniting rectifier and snubber dynamics into a single PFτ-driven field law. Through dimensional analysis, numerical validation, and geometric synthesis, it reproduces quantised morphological transitions (octahedral → spherical → cubic) and defines persistence as a measurable state of equilibrium between inflow and outflow. The document integrates the principles of the dipole electron and the first law of persistence, outlining how reactive fronts such as ozone photolysis and UVA-driven emergence fit within a single, energy-balanced continuum.All sections are presented in final analytical form with verified derivations, suitable for citation, reproduction, and peer verification. Prepared by Paul V. R. Stanford MSc FRSA, Lead Researcher, Sc-Rubs Modelling UK Ltd, with ISBN-linked archival record (978-1-919204-09-3).This edition constitutes the definitive analytical reference for the Sc-Rubs Laplace Continuation model.