Dynamic Topological Friction: A Non-Equilibrium Information-Geometric Framework for Conscious Phase Transitions

Integrated Information Theory (IIT), the Free Energy Principle (FEP), and the Integrated World Modeling Theory (IWMT) each formalize a distinct aspect of consciousness—causal integration, active inference, and precision-modulated temporal dynamics—yet they operate on incompatible mathematical substrates. We introduce Dynamic Topological Friction (DTF), an information-geometric framework that resolves this manifold inconsistency by constructing a causal statistical manifold on which all three theories can be expressed simultaneously. The causal Fisher metric—the unique invariant Riemannian metric on this manifold (Chentsov's theorem)—absorbs IIT's geometric integrated information as a quadratic form in the minimum-information-partition direction. A dissipation cost functional, anchored in Landauer's principle and calibrated against empirical neural energy budgets, provides thermodynamic grounding. These ingredients combine in a Grand Equation for consciousness intensity, Ω(t) = κ · π(t) · Eg v², whose multiplicative structure requires both integrated causal architecture and active inferential dynamics. Analysis of the precision–prediction-error interplay yields four scaling regimes—pathological divergence (I), self-consistent steady state (II), near-critical enhancement (II*), and quasi-static equilibrium (III)—mapping onto clinical states from psychosis through normal waking and flow to deep sleep. Post-hoc validation against the COGITATE multi-site study (n=256, 7 labs) yields 9 of 13 evaluable predictions confirmed with zero contradictions. A proof-of-concept κ-invariance test using Chennu propofol–EEG data (N=20) yields CV(κ̂) = 0.146, with 16/20 subjects meeting the stability threshold and a permutation null model confirming non-triviality (p = 0.047). We specify four falsifiable predictions with pre-registered effect-size thresholds and outline an empirical programme combining MEG, pharmacological manipulation, and TMS-EEG.