Phase-Model Paper 12: A Phase Self-Organization Closure Model for Pattern Formation

Version note (v2.0, 2026-04-06): This release updates editorial consistency across the Phase-Model series (Papers 01–13), including reference formatting, author-name normalization, and removal of local-path citation strings. The core model claims and rejection logic are unchanged unless explicitly stated below. This preprint proposes a phase self-organization closure model for pattern formation. The framework uses a complex-field amplitude-phase representation with explicit defect-density dynamics, maps to measurable pattern spectra and morphology observables, and defines reject criteria under shared-parameter transfer tests across pattern-forming platforms.