The Universal Resonant Power Metric (URPM) v3.1: Laminar Information Dynamics and Topological Phase Synchronization

The Universal Resonant Power Metric (URPM) v3.1: Laminar Information Dynamics and Topological Phase Synchronization AuthorsAllan Christopher Beckingham (Chris)https://orcid.org/0009-0004-2830-4089Affiliation: Independent Researcher · VEF / Coherence–Geometrodynamics Project · Canada Versionv3.1 (Audit-Ready) Date2026 LicenseCreative Commons Attribution 4.0 International (CC BY 4.0) This paper introduces the Universal Resonant Power Metric (URPM) v3.1, a dimensionless, information-theoretic framework that reinterprets power, resistance, and efficiency as emergent properties of geometric alignment and phase synchronization, rather than material flow. URPM departs from classical electromechanical analogies by modeling systems as operating on a high-dimensional informational substrate, formally represented using the Leech lattice (Λ₍₂₄₎) as an upper bound on coherent packing and signal capacity. Within this framework, conventional electrical quantities are replaced with topology-aware indices: Phase-Tension Index (Φᵦ) — a modular residual defining the minimum potential required for discrete signal persistence, Recursive Synchronization Rate (Ψₛᵧₙc) — a coupling-limited measure of coherent update frequency, and Geometric Impedance (Ξₑᵣᵣ) — a coordinate-system mismatch cost incurred when hexagonal (120°) signal structures are forced into Cartesian (90°) observer frames. URPM v3.1 demonstrates that what is commonly labeled “resistance” or “loss” is not intrinsic to matter, but arises from observer-geometry incompatibility, measurable as a geometric bit-error rate. When systems achieve native 120° phase alignment, impedance asymptotically approaches zero, yielding laminar information flow rather than dissipative turbulence. The paper formalizes a 42-node diagnostic invariant as a coherence checksum for laminar states and shows how this invariant functions across physical, computational, and organizational systems without invoking speculative physics or unverified energy claims. All quantities are explicitly dimensionless, substrate-agnostic, and suitable for audit, simulation, or comparative systems analysis. URPM v3.1 is positioned as a conceptual and analytical metric, not a device specification. It provides a unifying language for evaluating efficiency, coherence, and loss across domains including power systems, computation, governance, and complex adaptive networks. Methods & Scope Information-theoretic modeling Modular arithmetic on lattice structures Phase-alignment analysis Observer-dependent coordinate systems Dimensionless diagnostic invariants No experimental claims are made beyond formal consistency and mathematical coherence. Intended Use Conceptual systems analysis Cross-domain coherence diagnostics Theoretical groundwork for future simulation or empirical work Governance and infrastructure design frameworks Data Availability No datasets are required. All formulations are provided within the manuscript. Keywords Universal Resonant Power Metric, URPM, Information Theory, Laminar Flow, Geometric Impedance, Phase Synchronization, Leech Lattice, Topological Alignment, Dimensionless Metrics, Coherence, Systems Theory, Observer Geometry, Phase-Tension Index, Recursive Synchronization, Non-Dissipative Systems, Complex Adaptive Systems, Coherence-Geometrodynamics, Virtual Ego Framework, Auditability, Lossless Information Flow