The Formal Logic of Modulign

This document does not explain Modulign. It proves it. Every claim the Standard makes about its own properties — validity, uniqueness, intersubjectivity, non-accidentality, chain-of-custody integrity, and scale-sensitivity — is here rendered in formal notation, derived from stated axioms, and subjected to structural verification. There are no hidden assumptions. There are no informal bridges. There are no claims that rest on good intentions rather than structural necessity.