Absolute Maxwellian Closure: Operator-Theoretic Limits of Impulse Electrodynamics

This manuscript formalizes the absolute theoretical closure of impulse-driven electrodynamic systems (such as high-voltage capacitor discharges, Tesla-style resonances, and Lindemann-type pulse networks) strictly within the framework of Maxwellian electrodynamics. The paper demonstrates that all purportedly anomalous observables in these systems are completely exhausted by Maxwell evolution, constitutive response, and switching/boundary data. By enforcing rigorous functional domain precision and extending the Poynting closure to spatial infinity, the framework eliminates mathematical gaps that could harbor "hidden" or non-Maxwellian energy channels. The unitarity of the scattering operator and Weyl's essential spectrum invariance are used to prove that no localized or compact physical modification to an electromagnetic system can introduce new essential dynamical modes. Furthermore, the manuscript elevates impulse electrodynamics into the realm of spectral geometry. Physical anomalies and transient behaviors are mapped to finite-rank deformations of the Maxwell resolvent. Using the heat kernel asymptotic expansion, zeta-regularized determinants, and the Spectral Action principle, the paper proves that the same operator structures governing these transient pulses natively generate the Einstein-Hilbert action and higher curvature invariants. Finally, the text establishes a rigorous link to number theory by demonstrating that odd-sector spectral projections of these networks force the emergence of Riemann zeta invariants (such as zeta(3) and zeta(5)) as measurable physical response coefficients. Ultimately, the manuscript concludes that electrodynamics, spacetime geometry, and arithmetic invariants are unified through the spectral action of the Maxwell operator, and that all high-voltage transient anomalies are purely spectral redistributions rather than new physics.