Geometric Latency Constraints on High-Energy Particle Propagation in a Discrete Spatial Topology V2

Abstract

In the search for quantum gravity phenomenology, testing the limits of Lorentz invariance typically requires introducing arbitrary free parameters. This paper investigates an alternative: propagation latency inherent to a strictly discrete, holographically bounded spatial topology. By enforcing Landauer's principle and Bekenstein holographic bounds on localized state transitions, we derive a zero-parameter geometric impedance constant ξ_theory = √2 ≈ 1.414, representing the root-mean-square propagation drag in a Planck-scale L1 lattice. We cross-validate this purely theoretical asymptote against recent Fermi/LHAASO Gamma-Ray Burst (GRB) high-energy photon logs. The empirical data strictly aligns with a zero-intercept regression slope of ξ_fit = 1.4128, matching the geometric prediction with a minimal variance of Δξ = 0.0014. All data-extraction algorithms are open-sourced for independent replication, and we propose further blind testing utilizing broader ultra-high-energy datasets from facilities such as the IceCube Neutrino Observatory. Data Availability: Python data-extraction scripts and Fermi/LHAASO log processing protocols are open-sourced at: https://github.com/eaden0438-coder/GRB-Latency-Miner [VERSION 2 MAJOR UPDATE: TOPOLOGICAL FORMALIZATION & LORENTZ RECOVERY] This V2 release represents a rigorous formalization of the underlying mathematical framework, elevating the propagation latency model from a lattice-specific heuristic to a generalized topological theorem suitable for standard quantum gravity phenomenology. Key Upgrades in V2: 1. Generalization to Finite Information Topology: We have completely removed the reliance on specific Cartesian or cubic lattice geometries. The microscopic vacuum is now strictly formalized as a Finite Information Topology graph G=(V,E). The geometric impedance factor (1.414) is now rigorously derived not as a grid artifact, but as the expected statistical asymptote of the Isotropic Graph Limit Theorem. 2. The Dynamical Bridge (Landauer & Margolus-Levitin Limits): The gap between geometric path length and physical propagation delay (Delta t) has been decisively closed. By unifying Landauer's principle of information erasure with the Margolus-Levitin dynamical limit, the model now mathematically binds the maximum rate of orthogonal state transitions to local energy saturation. 3. Explicit Low-Energy Lorentz Recovery: To ensure absolute compatibility with existing Standard Model constraints, we have reformulated the propagation modifier as an "Excess Latency Coefficient." We formally demonstrate that in standard low-energy environments (E << E_P), the latency modifier vanishes, flawlessly recovering continuous Lorentz invariance as an immaculate low-energy effective theory. 4. Rigorous Statistical Audit & Marginalization: The empirical cross-validation against Fermi/LHAASO GRB datasets has been substantially upgraded. The analysis now actively parametrizes and marginalizes intrinsic source emission lags and redshift-dependent systematics, yielding a highly robust regression slope of 1.412 +/- 0.045 (1-sigma) with a reduced chi-square of 1.08, perfectly encompassing the theoretical zero-parameter prediction of 1.414.