Energy Equilibrium Manifold for Qubit Coherence Stabilization in Gaussian-Coupled Field Models

This package presents a complete formulation of the Energy Equilibrium Manifold applied to qubit coherence stabilization in Gaussian-coupled scalar field models.The work introduces an analytical balance condition ETt=E∇ϕ, which defines a self-consistent manifold where the system remains dynamically stable. Deviations from this balance are quantified through the energetic ratio Δlog⁡=log⁡10(ETtE∇ϕ), yielding a robust geometric dephasing law of the form T2(Δlog)/T2(0)=1/1+κ(Δlog/Δ0)^2. This mechanism produces a sharp coherence peak on the manifold and a controlled suppression off-manifold, suggesting a new strategy for qubit protection based on energetic self-consistency rather than dynamical error correction. The deposit includes: Technical report: full derivation of the energy-equilibrium law and its application to qubit coherence. Figures (SVG): block diagram of the physical model and coherence law. Python code: scripts for reproducing the diagrams and numerical coherence curves. Checksums file: integrity verification (SHA-256). The model is directly testable in experimental platforms such as superconducting qubits, cavity QED, trapped ions, and bosonic modes, offering a falsifiable prediction for geometric dephasing suppression at equilibrium.