Proposal of Mathematical Modeling of Schizophrenia

This technical report presents a proposal of a formal mathematical model of schizophrenia that synthesizes two prior frameworks: (i) the philosophical conceptualization of schizophrenia as a state of mind in which the mind contradicts itself, and the Knot Theory of Mind, in which recurrent psychological dynamics are modeled as knots, links, and braids embedded in a reconstructed psychological state space, and psychological abuse acts as a family of topological operators. Self-contradiction may be formalized as a topological property of the self-knot: a mind whose lived trajectory and its introspective mirror image are maximally distant in the Gordian metric. Positive symptoms (delusions, hallucinations, word salad) are modeled using virtual knot theory, in which delusional content appears as virtual crossings—apparent self-intersections that have no counterpart in objective reality. Negative symptoms (affective flattening, alogia, avolition) are modeled as a dimensional collapse of the emotion manifold together with trivial holonomy of the motivation loop. Thought disorder is formalized as braid entropy divergence and the failure of word reduction in the braid group. The two-hit hypothesis is recast as a two-parameter topological bifurcation problem. Subtype-specific constructions are given for psychopathic schizophrenia (a composite knot with zero inter-personal linking) and for anorexia nervosa as monosymptomatic schizophrenia (a body-image satellite trefoil with broken-mirror symmetry breaking). A battery of computable invariants—the Contradiction Index, Virtuality Index, Flattening Dimension, Braid Entropy, and the standard Structural Complexity and Therapeutic Resistance Indices—is proposed, together with algorithms for estimation from experience-sampling and neuroimaging time series. Therapeutic interventions are mapped to Reidemeister moves, crossing changes, and virtual-to-classical crossing resolution.