A Deterministic Spectral Framework at the Planck Scale with Parameter-Free Cosmological Predictions

We develop a deterministic spectral framework for Planck-scale physics based on a self-adjoint operator with compact resolvent and Weyl-type eigenvalue growth. All physical quantities are derived exclusively from spectral invariants and fundamental constants (c, , G), without adjustable parameters or empirical fitting. Closed-form trace and heat-kernel formulas yield explicit predictions, including: exponential ultraviolet spectral suppression consistent with the observed smallness of the cosmological constant, parameter-free heat-kernel coefficients inducing cosmological corrections, null bounds on low-energy drift effects constrained by precision metrology. All observables are algebraic functions of spectral data, mathematically well-posed, and directly falsifiable. The framework provides a reproducible bridge between spectral geometry and cosmological-scale phenomena.