The Same and Not the Same: A Machine-Checked Genealogy of Photochemical Theory

Abstract

Chemistry's phenomenological theories multiply with its observables: the same physical reality is repeatedly named in different measurement contexts, and the relations among theories have never had an auditable carrier. Here we present PhotoLean, a machine-checked genealogy of seventeen photochemical and photophysical theories formalized in Lean 4 over a shared kernel. Every pair of theories carries either a verified relation (equivalence, implication, composition with registered premises, definitional certificate) or a registered reason for its absence, covering all 136 pairs. Three adjudications resolve inherited conflations with if-and-only-if boundaries and witnesses: the symmetry factor $β$ equals one-half exactly when reactant and product force constants coincide; Kasha's rule and the Kasha-Vavilov rule agree only under closed quantification with a loss channel; and intensity-only Stern-Volmer data cannot distinguish static from dynamic quenching, whereas the lifetime channel discriminates exactly. As proposition generation shifts to machines, such machine-checked relational ledgers offer a replicable audit layer for theory itself.