Energy Equilibrium Manifold in a Gaussian-Coupled Field Model

This work presents the identification and characterization of an energy equilibrium manifold in a radial scalar field model with Gaussian profiles.The equilibrium condition is defined by the balance between the field gradient energy (E∇Φ) and the exponential source energy (Eₜₜₜ).A parametric scan, local optimization, and robustness analysis reveal a stable log-linear equilibrium law between the shape parameter a₀ and the coupling parameter K₀: log₁₀ K₀ ≈ (0.37 ± 0.01) a₀ + (2.48 ± 0.02) This law is analytically motivated, numerically verified, and reproducible.The study explores theoretical implications for 5D→4D projection (post-collapse interpretation) and potential impacts on quantum coherence stabilization (qubit systems). Included files: Technical_Report_Eros_Profumo_Manifold_Balance_eng.pdf EP_Equilibrium_Manifold_Package.zip Checksum (SHA-256):a179521aa3d23d0c4aa76fafe8521367562e0bbfb42007a658e566d9970d5171 © 2025 Eros Profumo — All Rights Reserved