Mathematical Prediction of the Dysmetric Dimension: A3. Differential Dysmetry

This work extends the theory of dismetric spaces by developing a generalized framework to describe the intrinsic variations of physical quantities in spacetime. Building upon the homogeneous division properties of the Dyadic Algebra of Magnitudes, we construct a formulation that extends dysmetric concepts beyond length to general physical quantities, allowing their variations to be treated within a unified structure. We show that this generalized dysmetry arises naturally from the underlying algebraic framework and leads to modified relations for physical fields in non-vanishing dysmetric regimes. In this view, dysmetry becomes an inherent property of physical magnitudes themselves, affecting their dynamical behavior. Conventional invariant descriptions are recovered in the limit of vanishing dysmetry, while nontrivial dysmetric regimes provide a consistent extension of standard physical theory.