Conjecture 41: A Geometric Extension of the Syntony Principle with Continuous L²/L¹ Firmware Interpolation

The Syntony law remains structurally unchanged; the adaptation occurs at the level of the statistical geometry used to estimate the scale quantities entering the law. Document version 1.1 (archived in Zenodo record version 2). The Syntony Principle states that the optimal temporal integration constant satisfies τ* = κ·γσ/γλ, where γσ and γλ denote scale estimators of dispersion and innovation. This note asks whether, under non-Gaussian noise, the norm used to estimate these scales can itself be selected from the same observables. For the symmetric Generalized Gaussian family, we show that the tail-ratio observable ρ = σ/MAD is a scale-free, strictly monotone function of the shape parameter β, with exact…