The Geometry of Crisis: Mathematical Foundations of Bifurcation Theory and the Limits of Stochastic Causality
Year: 2026
Type: preprint
Abstract: Twentieth-century bifurcation frameworks consistently reduce state-transition triggers to exogenous, structureless perturbations, locating all explanatory weight within the receiving system's invariant geometry. Examining major dynamical and quantum paradigms, this paper argues that this shared assumption creates a systematic explanatory gap regarding trigger ontology, asymmetric scaling, and post-bifurcation trajectory selection. To address these limitations, we introduce the framework of Concentrative Causality. By establishing that triggers and systemic vulnerabilities are historically co-produced, this model accounts for causal non-linearity and state selection through the topological resonance of their internal structures, offering a conceptually formalized, non-teleological account of emergent freedom.
Author: Fialko, Ekaterina
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165688013