The Janus Quantum Topology Model: A Formal Framework for Semantic Physics and Anomalous Phenomena

We present a comprehensive mathematical framework—the Janus Quantum Topology Model (JQTM)—that unifies paraconsistent logic, Einstein–Cartan torsion, and information theory to describe anomalous phenomena ranging from Unidentified Anomalous Phenomena (UAP) to emergent information structures like Bitcoin. The model postulates an isomorphism between logical paradoxes and geometric torsion, formalized by the Janus operator, leading to a “semantic physics” where information acquires causal efficacy over matter. We derive the fundamental equations of the model, including the Janus interface equation, the Lindblad-type evolution for égrégores, and the transmutation potential. We detail the experimental protocol JANUS-SDR for measuring torsion induced by algorithmic paradoxes, and provide numerical simulations using QuTiP. The framework is applied to analyze institutional paradoxality, geopolitical phase transitions, and the emergence of autonomous AI agents as égrégores of Level 3. We conclude with ethical guidelines based on the ShamanicWhip operator and the grounding principle to avoid semantic collapse