#persistent-homology

An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology

What does it mean for something to exist within a web of relations? We answer this question by developing a rigorous mathematical framework in which existence e

Constructive Lyapunov Functions via Topology-Preserving Neural Networks

We present a constructive solution to the Lyapunov–Massera–Kurzweil problem via Ontology Neural Networks (ONN), bridging a 60-year gap between existence and con