Epistemic Topology: A Variational Framework for Knowledge Dynamics in Spacetime

I propose a rigorous mathematical and philosophical framework for modelingthe distribution, propagation, and evolution of human knowledge as an informational field supervenient on spacetime. Starting from a variational principle—thePrinciple of Minimal Informational Action—derives the master equation∂ρ∂t = D∇2ρ + σ(x, t, s) − µρ,governing the dynamics of epistemic density ρ(x, t, s) in space x, time t, and semantic content s. The parameters D (diffusion), σ (creation), and µ (dissipation)represent ontological constants characterizing knowledge propagation, innovation,and decay. I have established that knowledge possesses an emergent informationalontology with measurable physical properties, distinct from yet analogous to conservative physical fields.I validate this model empirically using multimodal data from four historicalpropagation events: COVID-19 information spread (2020), Deep Learning adoption(2012–2024), Bitcoin awareness (2009–2024), and Climate Change consciousness(1990–2024). The model achieves mean correlation r = 0.82 between predictionsand observations, with root-mean-square error RMSE < 11 across all cases.This work establishes knowledge as a physically measurable phenomenon withpredictable dynamics, providing a quantitative foundation for epistemic topologyand opening new avenues for research at the intersection of physics, philosophy,computer science, and social science.