This manuscript constructs a closed operator-theoretic model of mass psychosis by unifying the psychological frameworks of Carl Jung (archetypes and projection), Joost A. M. Meerloo (menticide), Viktor Frankl (meaning and purpose), and Wilhelm Reich (character rigidity) into a rigorous mathematical physics architecture. The central thesis is formalized without metaphor: collective capture occurs when a stabilized cognitive-social operator loses its mathematical invertibility. In this model, mass psychosis is not merely a social phenomenon or a diagnostic label, but a literal spectral rupture triggered by four coupled mechanisms: archetypal amplification, projection perturbations, menticidal external forcing, and rigidity-weighted susceptibility. By mapping a population's cognitive-social state onto a Hilbert space and analyzing a rigidity-weighted graph Laplacian, the manuscript derives a closed mathematical condition for collective psychological collapse. It proves that the onset of mass psychosis corresponds exactly to a Birman-Schwinger spectral threshold, where the system's regularized Fredholm determinant vanishes. Conversely, the framework mathematically operationalizes "individuation" and psychological resistance as the restoration of spectral distance. Frankl's meaning curvature and independent ego-structures act as mathematical anchors that preserve systemic stability and prevent the determinant from reaching zero. The manuscript includes appendices providing full spectral decomposition, Fredholm index closure, trace-class determinant rigor, and a finite-dimensional JAX numerical protocol for computationally modeling empirical proxies of social capture.
A. Kim (Fri,) studied this question.