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Main Authors:	MFC, 10, Revista, Zen
Formato:	Recurso digital
Idioma:	inglés
Publicado:	Zenodo 2025
Acceso en liña:	https://doi.org/10.5281/zenodo.18089145
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Mathematical Applications of Science Fiction We present a rigorous derivation of the stability conditions for superluminal Alcubierre- White warp drive spacetimes by mapping the Lorentzian manifold singularities to the non- Archimedean geometry of Perfectoid Shimura Varieties. While classical General Relativity predicts the violation of the Null Energy Condition (NEC) requiring exotic matter with negative energy density, we propose that at the sub-Planckian scale (L < Lp), the spacetime metric undergoes a topological phase transition from a smooth Riemannian manifold MR to a Perfectoid space Xperf over Qp. By employing the Scholze-Andrade tilting correspondence, we construct a canonical isomorphism between the symplectic phase space of the warp bubble and the cohomology of a specific class of Shimura varieties of infinite level. We introduce the concept of "Arithmetic Warp Quantization," where the Casimir energy density required to sustain the warp bubble is regularized via the p-adic L-functions associated with the automorphic representations of the group GSp2g. We prove that the divergence of the stress-energy tensor Tμν is merely an artifact of Archimedean valuation and vanishes in the crystalline cohomology of the associated Fargues-Fontaine curve. Furthermore, we utilize Integral p-adic Hodge Theory to define a "Period Ring of Causality," Bcaus, showing that closed timelike curves (CTCs) are eliminated by the monodromy action on the étale cohomology groups Hi ´et(X, Zp). This manuscript establishes three fundamental theorems: (1) The Perfectoid Stability Criterion, which links the warp bubble’s horizon stability to the Galois representations of the absolute Galois group GQp; (2) The Symplectic Quantization Theorem, deriving the discrete spectrum of warp velocities allowed by the arithmetic of the Shimura variety; and (3) The Causal Protection Theorem, demonstrating that superluminal travel is topologically protected against paradoxes via the vanishing of the first cohomology group of the causal structure sheaf. This work provides the necessary mathematical foundation for the engineering of metric propulsion systems in the post-2050 era, bridging the Langlands Program with Quantum Gravity.

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