A Bounded Residual Certificate for a Two-Component Nonlinear Oscillator

Abstract

Original English methodological note deriving a conditional continuous-trajectory error certificate for an unforced, damped two-component cubic oscillator. It works step by step through an energy envelope, a local Lipschitz tube, a cubic Bernstein residual bound and a finite-step error recurrence. The archived 31 unit and 2,600 stress checks passed locally with Python 3.14.6; symbolic and SciPy checks remain source-reported. These bounded results do not establish a general nonlinear solver theorem, physical oscillator validation, fluid/PDE validation, cosmological claims, or independent review. Only this newly original explanatory PDF is deposited; source code, earlier archives and third-party material are not included or relicensed. CC BY 4.0 applies solely to this PDF. Riccardo Giudici is responsible for the presentation as an independent SIGMA systems orchestrator; computational and AI assistance is disclosed. No institutional endorsement is claimed.