A framework to turn AI math guesses into checkable, earned proof claims

Key framework rules

The paper introduces Proof Engine Infrastructure, a methodological architecture that:

- Represents mathematical claims with associated supporting artifacts, checking procedures, the scope of those checks, and remaining assumptions. - Models proof obligations as a typed directed hypergraph, where alternative routes use disjunctive semantics and obligations needing several premises use conjunctive semantics. - Defines promotion from candidate to earned result as admissible only when reference grounding, machine-checkable evidence, and an exact binding between the checked object and the claim all hold, together with strength preservation, compositional completeness, and dependency preservation. - Treats proof-engine “closure” as something derived from the graph rather than asserted in text. - Allows verification technology to vary, with proof assistants providing one verification boundary that is then bound to exact claims, assumptions, and dependencies and composed with other checked evidence. - Marks failed routes as typed negative evidence without disproving the underlying output claims.

It reports that a kernel-checked Hamilton classification and a mixed-boundary Rado-number study motivate the framework, while emphasizing that the main contribution is the set of invariants for evidentiary status and graph-level closure.

Clear evidence for AI math

The paper focuses on making AI-assisted mathematical research produce outputs with clearer evidence status and safer downstream use. By separating generation, verification, composition, and publication, it aims to reduce the chance that an AI system’s provenance or persuasive wording stands in for mathematical justification, and to manage verification effort when combining different checked pieces of evidence.

Proposal with limited reported evaluation

This is a repository article describing a proposed architecture and the invariants it requires for checking, composing, and promoting mathematical claims. The abstract does not provide quantitative performance results, error rates, or a broad evaluation across many problems; it mainly frames the contribution as a methodology that can be implemented with different verification boundaries and proof objects.