Emergent Modular Structure in Coherence-Driven Oscillator Fields: Spontaneous Phase Alignment and Internal Refinement in Conservative Lattices

This research paper studies the spontaneous emergence of modular attractor basins in conservative oscillator lattices governed by coherence-driven phase dynamics. Starting from random initialization, the field relaxes into stable, segmented, memory-like coherence structures without supervision, training, stochastic sampling, symbolic encoding, or central control. The primary result is basin formation: local alignment under constraint produces robust modular regions that serve as geometric representations of self-organized coherence. These basins arise from deterministic field relaxation and provide an early model of how structured memory and coherent segmentation can emerge from local phase interaction alone. The paper also documents a secondary effect: ripple-like coherence waves that arise from trapped phase tension after attractor structure begins to form. These compact, radially propagating realignment fronts refine basin boundaries, redistribute alignment gradients, and improve convergence. They are not required for structure formation, but appear naturally as internal correction events during field optimization. Together, basin formation and ripple correction show how conservative phase fields can generate organized structure and refinement dynamics from local coherence constraints. The results are relevant to coherence-driven inference, analog memory stabilization, modular structure formation, and later CG applications such as protein folding and CDI basin dynamics. This paper was written in April 2025, before the later CG canon records and Foundations texts were publicly organized. It is released as an early framework paper on modular attractor formation, internal refinement, and coherence-driven structure emergence. The record includes two Jupyter notebooks used to generate visual materials associated with the paper. Soliton_HD_Video_Creator.ipynb generates phase-field evolution frames showing attractor-basin formation from random initialization. Soliton_Cuda_Video_Frame_Creator-InteractiveRadius.ipynb generates close-up ripple morphology and before/after refinement frames. The notebooks are provided as research artifacts for inspection and experimentation, not as maintained software. Internal reference: CGI-RSR-000025.