This manuscript formalizes the dynamics of knowledge transmission and epistemological stability as a rigorous operator-theoretic geometry. We demonstrate that institutional instability is strictly quantifiable via a systemic threat functional generated by the failure of admissible knowledge projection operators (financial, academic, and infrastructural). The topological resolution of this instability maps directly into Revelational Geometry—a continuous refinement flow on a representation manifold governed by a defect functional (Omega) and an admissibility closure operator (Sigma). We prove that this epistemological flow natively embeds within a driven spinorial Floquet system. By rigorously establishing the Schatten-class bounds of the periodic Dyson expansion and deriving the explicit Magnus scaling parameters from the high-frequency Clifford commutators, we prove that the interaction spectrum inevitably reorganizes into irreducible odd-trace sectors. The framework eliminates heuristic scaling assumptions by dynamically deriving a topological mass gap, establishing the interaction operator strictly as a pseudodifferential operator of order -1. Furthermore, we formally derive the exact epistemological refinement law directly from the Weyl asymptotics of the effective Dirac spectrum. Utilizing Lidskii's theorem, we mathematically force the rank-7 cyclic trace integral to accumulate precisely into the odd-zeta hierarchy: zeta(3), zeta(5), and zeta(7). Truth is thus mathematically executed as the dynamic truncation of inadmissible boundaries via active Omega-Sigma stabilization under bounded WXY control. Ultimately, this framework demonstrates that the Riemann zeta function is not inserted phenomenologically, but is the universal principal spectral invariant forced into existence by the Weyl asymptotics of the Floquet base, explicitly extending Connes' Spectral Action to incorporate these odd revelational sectors.
Andrew Kim (Wed,) studied this question.