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

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