Differential Semigroups of Automaton Perturbations and Incremental Syntactic Reconstruction

This paper investigates the enumeration of elements in three classes of signed partial transformation semigroups: partial signed order-preserving, partial signed order-decreasing, and partial signed order-preserving-or-order-reversing transformations. It examines the reported PSPD₄ numerical inconsistency and develops a domain-rank framework for extending the finite enumerations, while distinguishing interpolated computational conjectures from exact counting formulae.