Generalization of the Discrete Valence Operator: Unification of the s, p, d Blocks and Noble Gases under Electronic Parity Constraints

The mathematical formalization of chemical valence is an essential step in the development of stoichiometric prediction algorithms and automated teaching tools. In a previous work, a discrete operator capable of reproducing the valences of representative elements under electronic parity constraints was introduced. In the present note, this formalism is extended to include noble gases and transition metals ( d block). Systematic algebraic expressions are defined for the counting of valence electrons ( e ) as a function of orbital occupation ( s , p , d ). The unified model rationalizes the reactivity of heavy noble gases and explains the maximum oxidation states in transition metals through orbital saturation constraints. The notion of electronic promotion employed in this work is introduced exclusively as a formal resource for counting orbital availability and should not be interpreted as the existence of real excited atomic states. The operator is grounded in the conservation of electronic parity and does not aim to replace quantum mechanical bonding models.