Geometric Quantification of Chronon Decay Singularities in p-adic Berkovich Spaces via Ultrametric Spectral Deformation

Mathematical Applications of Science Fiction We present a rigorous framework for the quantization of temporal singularities through the lens of non-Archimedean analytic geometry. By modeling the chronon—the fundamental quantum of time—as a coherent sheaf over a p-adic Berkovich curve ( X_{\mathrm{an}} ), we derive the decay rates of temporal singularities using ultrametric spectral deformation theory. We introduce the Chronon Laplacian ( \Delta^{\varepsilon}p ), a deformation of the standard Laplacian on the reduction graph of ( X{\mathrm{an}} ), and prove that the decay of a chronon singularity is governed by the spectral gap of this operator in the limit as the deformation parameter ( \varepsilon \to 0 ). Our Main Theorem establishes a direct isomorphism between the cohomology of the chronon decay complex and the tropical homology of the skeleton of the Berkovich space. This provides a geometric quantification of Hawking radiation analogues in non-Archimedean spacetimes, suggesting that spacetime discreteness at the Planck scale is naturally encoded in the branching structure of the Berkovich tree.