Internet Spectral Geodesic Routing for High-Throughput Traffic Engineering via Laplacian Potentials

Abstract The internet's backbone is built on a 60-year-old algorithm designed for road maps, not light-speed data streams. We present a paradigm shift: the Spectral Geodesic Protocol (SGP). By abandoning the iterative "search" logic of Dijkstra and OSPF, we model the network as a continuous conductive field governed by fundamental physical laws. Through the pre-computation of the Laplacian Pseudoinverse (L^+), we transform routing from a combinatorial problem (O(E \log V)) into a linear algebra operation (O(1)). Crucially, we introduce an Incremental Update strategy based on the Sherman-Morrison formula, achieving: 240x speedup in topology reconvergence compared to full matrix inversion. 1,350x increase in throughput. 99.9% reduction in CPU overhead. This work transitions routing from digital logic to physical dynamics, enabling self-healing networks that route data with the inevitability of water flowing downhill. 🛡️ INVENTION DISCLOSURE, DEFENSIVE PUBLICATION & SOFTWARE LICENSE Title: Spectral Geodesic Routing Protocol (SGP) Inventor: Andrés Sebastián Pirolo Date of First Publication: January 9, 2026 Canonical DOI: 10.5281/zenodo.18193686 1. STATEMENT OF PRIOR ART (Defensive Publication) This document and its associated datasets/code constitute a formal public disclosure of the "Spectral Geodesic Routing" methodology. Spectral Geodesic Routing is formulated as a matrix-driven flow optimization process in which routing potentials are obtained from the solution of a constrained linear operator system and dynamically stabilized using rank-one inverse correction operators to preserve numerical conditioning and computational efficiency. 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