TERM: The Spectral Invariant — Stability-Induced Emergence of Scale, Time, and Dynamics

This work develops the spectral layer of the TERM framework, showing that variational stability necessarily induces a fourth‑order operator with a scale‑invariant quantity. The resulting spectral invariant generates an intrinsic scale without free parameters. Smoothing deformations monotonically increase spectral entropy, establishing an intrinsic arrow of time. The operator admits a universal decomposition into minimal and excited modes, and its long‑wavelength limit reduces to effective second‑order dynamics. The results provide a structural foundation in which scale, time, and dynamical laws emerge from spectral stability.