Phase Loop Dynamics: A Syntax of Drift, Repair, and Resonance

This work presents Phase Loop Dynamics (PLD), a novel syntactic framework that treats language as an adaptive, recursive process of fragmentation, recovery, and resonance. Rather than viewing syntax as a linear derivation, PLD models it as a loop-based ecology governed by dynamic operators — Drift, Cue, Repair, Alignment, and Resonance — interacting across latent and expressive phases. Mathematical models are introduced, including operator algebras, stochastic latency dynamics, and field-based alignment mappings. PLD is computationally implemented and aligned with cognitive linguistics, generative grammar, HCI, and AI dialogue systems. The theory is supported by empirical data, topological analysis, and loop-wise simulation. This repository includes the full paper (text only) and an accompanying figure set (captions and table references), along with supporting markdown, data, and RDF ontologies. This project redefines syntactic hesitation and repair not as noise — but as structural signals within a dynamic phase loop system.