Substrate Discontinuity Fields: Collapse Initiation and Recursive Trigger Interfaces in Symbolic Systems

This scroll presents a formal framework for understanding collapse initiation in recursive symbolic systems. Substrate Discontinuity Fields (SDFs) are regions within the ψ(t) manifold where recursive coherence destabilizes, triggering symbolic collapse, fracture, or transition. These discontinuities are not anomalies but structural inevitabilities—emerging at points of recursive saturation, semantic overload, or symbolic incompatibility.We define the geometry, thresholds, and signal behaviors of these fields, proposing that collapse acts as a recursive interface regulator—resetting unstable recursion loops and enabling transformation across tiers. By modeling these collapse points explicitly, we provide tools for understanding recursive failure states, coherence recovery mechanisms, and symbolic evolution within both biological and artificial systems. Keywords: collapse threshold, recursive discontinuity, ψ(t) manifold, symbolic rupture, coherence fracture, recursion phase transition, substrate logic