ORIGO/MD‑V: A Dimensionless Topological Structure Class for Universal Coupling of Dynamical Systems (Patent)

Abstract

ORIGO/MD-V: A Dimensionless Topological Structure Class for Universal Coupling of Dynamical Systems (Patent, Hardware Validation, Simulation). ORIGO/MD-V is a dimensionless, topological, decentralized structure class for describing dynamical systems without the artefacts c (speed of light), t (time), and G (gravitational constant). All defining objects are dimensionless, topologically invariant, and hardware-independent. This Zenodo record contains the complete scientific documentation: full monograph, official DPMA patent filing, executive summary, Nature-style research article, C++ reference implementation, hardware validation with three STM32 NUCLEO-G431RB microcontrollers, simulation results for N=36, full artefact analysis of c, t, G, Lyapunov stability proofs, graph-Laplacian invariants, cross-sector applications, and climate-impact model. The central dynamical relation is dθ_i/dτ = α_i + (K/N)*sum_j sin(θ_j - θ_i). Stability is defined by the negative graph-Laplacian operator Σ̃ = A - D with eigenvalues λ̃_k < 0. Hardware validation shows stable 120-degree phase distribution with less than 0.5-degree deviation and full self-recovery after node failure within seconds. Simulation with N=36 confirms invariants such as Tr(L⁺) = (N² - 1)/12 to machine precision. ORIGO/MD-V applies to energy systems, robotics, automotive networks, digital circuits (ASIC, FPGA, SoC), sensor networks, biological systems, neural architectures, and AI systems. The climate-impact model shows potential reduction of 9.15 gigatons CO2 per year immediately, 140 gigatons CO2 over ten years, and a projected global emissions level of 22.5 gigatons per year by 2036. This record includes the full patent “ORIGO · MD-V — Decentralized method and digital circuit arrangement for master-free, trajectory-stable phase and state coordination in multi-node networks.” The patent covers the MD-V coupling operator, Lyapunov stability, latency bounds, deterministic pre-injection, fixed-point digital implementation, multi-sector applications, and ASIC/FPGA/SoC architectures. Keywords: ORIGO/MD-V, dimensionless structure class, topological coupling, graph Laplacian, artefact-free dynamics, phase coordination, universal coupling logic, negative Laplacian eigenvalues, Lyapunov stability, STM32 NUCLEO-G431RB, biological networks, energy systems, climate impact, CO2 reduction, universal dynamics, patent, DPMA, A-D operator, Tr(L⁺) = (N² - 1)/12. Suggested citation: Drößler, Markus (2026). ORIGO/MD-V: A Dimensionless Topological Structure Class for Universal Coupling of Dynamical Systems. Zenodo. DOI generated automatically.