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 (over 3.5 Billion routing decisions per second). *(Tested on a simulated 28-node Spine-Leaf data center fabric using L1-resident Zero-Float/Fixed-Point arithmetic).* * 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.# ================================================== STATEMENT OF PRIOR ART AND ADDITIONAL LICENSE TERMS Aligned with PolyForm Noncommercial License 1.0.0Author: Andrés Sebastián PiroloORCID: 0009-0004-3899-1222Email: letrnc1@gmail.com / apirolo@abc.gob.arDate: January 2026DOI: https://doi.org/10.5281/zenodo.196675031. PERMITTED USE Academic research, independent study, education, benchmarking, validation, reproducibility studies, and experimental evaluation is permitted under the terms of the PolyForm Noncommercial License 1.0.0, provided proper attribution is given.==================================================2. STATEMENT OF PRIOR ART This document constitutes a formal public disclosure establishing prior art for the following work:**Title:** Spectral Geodesic Routing Protocol (SGP)**Format:** Pseudocode, Algorithmic Logic, and Mathematical Models**Language:** Agnostic (Applicable to C/C++, Rust, Python, P4, Verilog/VHDL, etc.)**Target architecture:** Any (CPU, GPU, FPGA, ASIC, SmartNIC, or Programmable Switch).Specific contributions disclosed herein:(a) The Spectral Geodesic Routing methodology: a paradigm shift transforming packet routing from a combinatorial graph search (O(E \log V)) into a continuous matrix-driven linear algebra operation (O(1)) using Laplacian pseudoinverses.(b) Incremental update strategy via the Sherman-Morrison formula, achieving microsecond topology reconvergence without requiring full matrix inversion upon link failure.(c) Zero-Float Arithmetic execution (128-bit fixed-point) enabling over 3.5 Billion routing lookups per second and 953+ Mpps throughput, establishing a new limit for software-based L1-resident forwarding engines.(d) Network Slicing via Laplacian Superposition, mathematically isolating virtual networks (L^{(k)}=L+\alpha_{k}P^{(k)}) at the data plane level without relying on traditional VLAN encapsulation.==================================================3. SCOPE OF THE LICENSE While the mathematical concepts and pseudocode are disclosed defensively, all subsequent software or hardware implementations of the algorithms described herein are governed exclusively by the PolyForm Noncommercial License 1.0.0.This includes translations of the pseudocode into any programming language and deployment on any programmable or dedicated hardware platform. License applicability is determined by functional equivalence rather than textual code similarity. The license applies to any system reproducing the Laplacian Spectral Logic, Sherman-Morrison update strategy, or Zero-Float Arithmetic routing mechanisms disclosed in this algorithmic framework.There is no de minimis exception. The extraction, translation, translation to hardware description languages (HDL), or reimplementation of the described algorithms constitutes derivative use.==================================================4. NONCOMMERCIAL RESTRICTION Any use of this work that falls outside the definition of noncommercial use, as defined by the PolyForm Noncommercial License 1.0.0, is not permitted under this license.==================================================5. COMMERCIAL AND OPERATIONAL USE Any commercial, corporate, governmental, financial, military, or revenue-generating use—in whole or in part—requires explicit written authorization from the author.This strictly prohibits unauthorized integration into: * Proprietary hardware (Routers, Switches, FPGAs, ASICs, SmartNICs). * Commercial networks (ISPs, Hyperscale Data Centers, Cloud Providers). * AI / GPU clustering fabrics and telecom architectures (5G/6G Core).Commercial licensing contact: letrnc1@gmail.com / apirolo@abc.gob.ar==================================================6. DERIVATIVE WORKS AND FUNCTIONAL EQUIVALENCE Reimplementation, translation from pseudocode to compiled code, architectural modification, optimization, or claims of functional equivalence do not remove a work from the scope of the PolyForm Noncommercial International License 1.0.0.6.a. CODE SIZE IRRELEVANCE (NO MINIMUM THRESHOLD) Because this publication discloses algorithmic logic, the applicability of the license is independent of code size, number of lines, or percentage of implementation in the final product. Implementing even a single mathematical stage (e.g., the Sherman-Morrison update block) in a commercial environment triggers the license restrictions.================================================== 7. KNOWLEDGE CONTAMINATION AND ATTRIBUTION Exposure to this work constitutes prior knowledge of the disclosed methods. Subsequent implementations making material use of the disclosed concepts remain subject to attribution and license requirements.==================================================8. INTELLECTUAL PROPERTY OWNERSHIP All intellectual property rights remain with the author, subject only to the permissions explicitly granted under the PolyForm Noncommercial License 1.0.0.==================================================9. NO ADDITIONAL RIGHTS GRANTED This document does not grant any rights beyond those expressly provided by the PolyForm Noncommercial License 1.0.0.==================================================10. ENFORCEMENT AND REMEDIES Any use in violation of the PolyForm International Noncommercial License 1.0.0 shall be addressed through the remedies provided by that license and by applicable International law.==================================================11. VERSIONING Updates to presentation, terminology, benchmarks, or documentation do not alter the core methodological contributions, the scope of protection, or the license terms. The most recent license statement is authoritative.==================================================12. KNOWLEDGE CONTAMINATION (NON-CLEAN-ROOM USE) Any individual or entity that has reviewed, studied, tested, or otherwise been exposed to the algorithms, pseudocode, mathematics, or technical descriptions in this record shall be considered knowledge-contaminated.Subsequent implementations are not considered clean-room unless supported by contemporaneous, auditable evidence of prior independent development. Claims of independent development are invalid where development occurred after exposure to this algorithmic disclosure.==================================================Copyright © 2026 Andrés Sebastián Pirolo. All Rights Reserved.This algorithmic framework is protected by international intellectual property laws and the PolyForm Noncommercial License 1.0.0.