Mathematical Zero-Operations as Distributional Reconfiguration Operators

This exploratory preprint proposes a minimal mathematical framework in which zero-like entities are treated as operations on probability-distribution structure rather than only as values. Building on the noise-induced reconfiguration classification introduced in Paper 1, the paper defines additive, reference, transition, open, connective, and undefined zero-operations. The framework shows how zero-like interventions produce distinct structural outcomes only when paired with redistribution rules, observation maps, or connection structures.