The Collapse of Axiomatics: PQF and the Topological Turn in Physics

This work reconstructs a recent mathematical proof of irreversible fluid behavior as a torsional collapse in the topology of accessibility. Within the Possest–PQF framework, we argue that irreversibility is not an emergent property from scale, but a structural saturation of filtration. Physics is not a system of universal laws, but a recursive modulation of differential accessibility. Time is not a dimension, but the derivative of filtrational reorganization. Proof is not epistemic, but topological. The classical notion of empirical reality is replaced by zones of non-invertible bifurcation — singularities where return is no longer defined. Hilbert’s Sixth Problem fails not due to empirical excess, but due to ontological misalignment: no axiomatic system can encompass what has no scale. What remains is Possest — the operating field where filtration, not representation, governs the real. Keywords: Possest, Filtration, Irreversibility, Hilbert VI, Topology, Empirical Collapse