Apocalypsis and Apocalyptic Events: The Morphogenetic Ontology of Synchronized Catastrophes

TL;DR

This paper introduces a formal topological and mathematical framework for understanding apocalyptic events as synchronized systemic collapses, using catastrophe theory, dynamical systems, and probabilistic models to demonstrate their inevitability.

Contribution

It develops a novel formalization of apocalyptic events as synchronized morphogenetic manifolds, integrating topology, dynamical systems, and probabilistic dependence to model systemic collapses.

Findings

Defines Apocalypsis as a topological meta-singularity.

Proves the existence and genericity of Apocalypsis.

Shows almost-sure occurrence under stochastic coupling.

Abstract

I formalize the ontology of apocalyptic events as synchronized morphogenetic manifolds within the framework of Thom's catastrophe theory. Local catastrophes (folds, cusps, umbilici) are extended to higher-order systemic collapses through the synchronization of multiple morphogenetic manifolds. The resulting construct is the Apocalypsis: a topological meta-singularity generated by the alignment of local singularities into a global structure of collapse. The mathematical formalization of Apocalyptic events and Apocalypsis integrates dynamical systems theory, topological stability, and probabilistic dependence structures using Archimedean copulas that capture nonlinear interrelations among coupled subsystems. The Inevitability Theorem demonstrates the existence, genericity, and almost-sure occurrence of Apocalypsis under stochastic coupling.