General formalization of the asymmetry operator via local expansions and structural field classification

This work presents a general mathematical formulation of the asymmetry operator, conceived as a structural transformation acting on local field expansions prior to the differential limiting process.The adopted approach is strictly formal and is based on a reinterpretation of the Taylor expansion asa pre-limit structure hierarchically organized according to structural order, parity, and dominance regime.A general operatorial definition is introduced, reorganizing the contributions of the local expansionthrough coefficients depending on order, parity, and the structural classification of the field, withoutpresupposing dynamical equations, physical interpretations, or empirical validation. As a result, a structural classification scheme for fields is developed, independent of their physical nature, basedon dominant order, associated parity, explicit–implicit term distribution, and induced symmetryregime.This work synthesizes and replaces previous foundational developments by the author, establishinga unified and self-contained framework for the asymmetry operator and its associated classification.It is shown that, under specific structural conditions, the formalism recovers the classical differential regime as a limiting case. Applications to specific physical fields and comparisons withstandard formulations are deferred to subsequent works.