Phase-Woven Manifolds and Degenerate Emergent Metrics:A Geometric Mechanism for Near-Zero Geometric Length Channels

We propose a geometric framework in which spacetime structure emerges from complex phase fields. An induced positive-semidefinite metric is generated by phase gradients and becomes degenerate when correlations develop, producing kernel directions that support finite coordinate displacement with vanishing induced length. In connected near-degenerate sectors, these kernel modes define an effective geometric adjacency between distant points through phase-coherence constraints. Beyond this constructive mechanism, we show that a realizability-based displacement cost admits a leading-order indefinite quadratic form whose null directions define local causal cones; when realized via internal phase increments, this form naturally takes a pullback representation generated by phase gradients. We emphasize that we do not posit any superluminal signalling or dynamical influence: “adjacency” is purely metric/representational and is defined by coherence constraints rather than by physical propagation. Together, the construction provides a minimal closed mechanism linking realizability, emergent geometry, metric collapse, kernel-mode pathways, and emergent causal structure.