Apocalypsis and Apocalyptic Events: The Morphogenetic Ontology of Synchronized Catastrophes

TL;DR

This work develops a Thom catastrophe theory–driven ontology for apocalyptic phenomena, distinguishing local catastrophes from synchronized higher-order collapses. By integrating gradient dynamics $dx/dt = -\nabla_x V(x;\alpha)$, Thom–Mather morphogenetic topology, network coupling via $V_\varepsilon$ and cross-system discriminants, and Archimedean copulas for interdependence, it defines Apocalypsis as a morphogenetic manifold of synchronized singularities. The central contribution is the Inevitability Theorem, which proves that under weak coupling and elliptic control trajectories the coalescence of local catastrophes occurs almost surely, producing multi-subsystem cascades and global rupture across connected components. This framework reframes apocalypse as an intrinsic, statistically emergent phase transition within complex morphogenetic systems, with operational criteria for detecting transitions and guarantees of structural stability under perturbations.

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.