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

Abstract The internet’s backbone still relies on routing algorithms conceived over 60 years ago—designed for static road maps rather than light-speed data streams. We introduce a paradigm shift: the Spectral Geodesic Protocol (SGP). Instead of relying on iterative “search” logic such as Dijkstra or OSPF, SGP models the network as a continuous conductive field governed by fundamental physical principles. By precomputing the Laplacian pseudoinverse (L⁺), routing is transformed from a combinatorial problem (O(E · log V)) into a direct linear algebra operation (O(1)). Key Innovation Crucially, we implement an incremental update strategy based on the Sherman–Morrison formula, enabling real-time adaptation to topology changes without full recomputation. Performance Gains 240× speedup in topology reconvergence versus full matrix inversion 1,350× increase in throughput 99.9% reduction in CPU overhead Conclusion This work reframes routing from discrete digital logic into continuous physical dynamics—enabling self-healing networks where data flows with the inevitability of water moving 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. The mathematical derivations and conceptual logic described herein are released into the public domain purely to establish Prior Art. This publication renders the specific application of Laplacian Spectral Logic for Packet Routing unpatentable by third parties under 35 U.S.C. § 102 and international equivalents. 2. SOFTWARE LICENSE (Implementation Rights) While the mathematical concepts are disclosed defensively, the source code, specific algorithmic implementations, binary executables, and hardware description languages (Verilog/VHDL) associated with SGP are NOT in the public domain. They are licensed strictly under the PolyForm Noncommercial License 1.0.0. 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