No Exempt Node: A Typed Theory of Recursive Auditability

An assurance system whose own operation is not auditable is indistinguishable from absent assurance — the falsifiability thesis turned upon the assurance system itself. We propose a typed theory of assurance systems organised around one idea: every observation has a typed birth, a complete genealogy, and an audit mode determined by that birth. The axiom is structural (no exempt node); the type system concerns knowledge transformations by admissible input domain (connection, derivation, assurance), with no fourth. Three theorems follow (closure of transformations; complete genealogy; completeness of influence representation), a taxonomy of assurance failures as type violations (of which automated assurance is canonical), and a change of status for contradiction (an observable, not a judgement). Independence from the audited party is a corollary, not the subject; we separate the structural independence of the graph from the source independence of each observation.