Verifier Theory and Unverifiability
It addresses a foundational gap in mathematics and computer science for researchers in theorem proving and verification, though it appears incremental as it builds on existing proof theory.
The paper tackles the lack of formal study on proof verifiers by proposing a classification system and introducing the concept of unverifiability, aiming to serve as a general citation in theorem proving and verification domains.
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers (people, programs, oracles, communities, superintelligences) as mathematical objects. Such an effort could reveal their properties, their powers and limitations (particularly in human mathematicians), minimum and maximum complexity, as well as self-verification and self-reference issues. We propose an initial classification system for verifiers and provide some rudimentary analysis of solved and open problems in this important domain. Our main contribution is a formal introduction of the notion of unverifiability, for which the paper could serve as a general citation in domains of theorem proving, as well as software and AI verification.