The Digital Fabric of Spacetime: Eradicating Black Hole Singularities via Dynamic Covariant Sampling and Decentralized Logs in the Relativistic Klein-Gordon Information Membrane (SDM-V Theory)

Overview This paper introduces the Sampled Digital Membrane with Variable Information Loop (SDM-V) Theory, a novel, Lorentz-covariant quantum field theory framework designed to eradicate the mathematical breakdown of gravitational singularities at the center of black holes. Synthesizing core insights from the Holographic Principle, Loop Quantum Gravity (LQG), and the Generalized Uncertainty Principle (GUP), we redefine smooth spacetime as a multi-layered digital information membrane sampled at the Planck scale. Key Contributions Dynamic Covariant Sampling Specification: Proves that pixelated spacetime sampling can fully co-exist with Lorentz invariance by defining intervals relative to the observer's four-velocity vector. Energy-Momentum Phase Reversal: Demonstrates that when a physical matter wave reaches the Nyquist threshold (fN = 1/ (2P) ), an information-theoretic anti-aliasing phase inversion mathematically flips the sign of the energy-momentum tensor, converting gravitational attraction into a repulsive force that drives a cosmological bounce. Unified Holographic-LQG Architecture: Formulates a type-safe bidirectional communication protocol across dimensions, where the continuous bulk spacetime dynamically emerges from decoded discrete boundary data using sinc-interpolation kernels. Document Information Author: Hitoshi Ibuki (Lead Architect / Independent Researcher) Version: 1. 0. 0 (Foundational Paper) Keywords: Quantum Gravity, Loop Quantum Gravity, Holographic Principle, Shannon-Somerya Sampling Theorem, Sinc Interpolation, Black Hole Singularity Debugging, Cosmological Bounce For inquiries or collaborative research regarding the SDM-V framework, please refer to the corresponding contact details or open an issue via the associated research repository.