Recovery of Double-Pendulum Chaos from a Screened Enchan Field--Matter Model

Abstract

Recovery of Double-Pendulum Chaos from a Screened Enchan Field–Matter Model Without System-Specific Equations of Motion This work investigates whether the previously proposed Enchan Field can recover ordinary Newtonian constrained dynamics in its strongly screened terrestrial limit without supplying the known system-specific equations of motion of a double pendulum. Starting from the previously proposed weak-field effective metric, a pendulum-independent point-particle matter sector is derived. Its nonrelativistic limit gives the matter response ẍ = c²∇S, where S(x,t) is the dimensionless Enchan field variable. Generic holonomic distance constraints are then introduced only through Lagrange multipliers. The model under test evolves Cartesian particle coordinates and does not execute the standard double-pendulum angular acceleration equations. Under the pre-existing Solar-System screening prescription, the Enchan correction at Earth-surface acceleration is negligible, providing a controlled Newtonian-limit benchmark. The generic Cartesian constrained model reproduces the standard double-pendulum trajectory to numerical precision and independently reproduces the expected sensitive dependence on initial conditions. A topology-driven implementation also recovers single- and two-link systems without changing the solver equation. The result is deliberately scoped. It does not constitute a detection of a non-Newtonian force, a derivation of particles or rigid rods from the pure Enchan Field, or a proof of the full Enchan Field theory. Rather, it establishes that a matter response derived from the existing Enchan effective metric, combined with generic geometric constraints, recovers known Newtonian constrained mechanics and double-pendulum chaos in the strongly screened regime. The accompanying reproducibility_code.zip contains the canonical model, independent analytic evaluator, Solar-System screening calculation and provenance snapshots, generic constraint tests, numerical audit tools, exact Python dependencies, machine-readable CSV/JSON outputs, and scripts used to regenerate the reported trajectory and chaos results. Licensed under the Enchan Research & Verification License v1.0. The full license text is included in reproducibility_code.zip. Version: v1.0Date: August 11, 2026Author: Mitsuhiro Kobayashi