Responsible AI Mathematics Verification Standard

Math Proof Audit Workbench

Assess, verify, and responsibly communicate AI-assisted mathematical proofs. Decompose theorems into dependency DAGs, detect circular inferences, score formalization readiness, and generate peer-review audit dossiers.

Audit Configuration

Select Theorem or Conjecture Loaded from standardized peer verification fixtures.

Step Mathematical Statement

Validation Status & Rigor Level

Parent Step Dependencies (Comma-separated) Direct premises required to establish this claim.

Peer Advisory Observation

Rigor Score 92% Formal Deductive

Proof DAG State Acyclic 0 Circular Loops

Lean 4 Readiness Ready 6 / 7 Formalizable

Review Status Conditional 1 Heuristic Warning

Step S4: Density Regularity Lemma Rigorous Deduction

Premises: S2, S3

∀ ε > 0, ∃ M(ε) such that G can be partitioned into k equitable clusters with discrepancy ≤ ε·|V|²

Advisory Group Review: Bounds match Szemerédi regularity specifications. Translation to Lean Mathlib algebra hierarchy verified.

Audit Ready: All steps parsed. DAG contains 7 vertices and 8 directed premises.

Rigorous Step Decomposition

AI-generated proofs frequently combine genuine symbolic insights with subtle hallucinated lemmas. Structuring arguments as Directed Acyclic Graphs ensures each premise can be checked independently.

Circularity Detection

Language models often introduce indirect circular dependencies where Lemma A implicitly assumes Theorem B via notation shift. The cycle checker spots topological deadlocks instantly.

Formal Verification Pipeline

Bridge informal mathematical prose and interactive theorem provers like Lean 4, Coq, and Isabelle. Steps flagged as sound are formatted for automatic translation into formal tactics.

Mathematical Standards & Advisory FAQ

Why must AI mathematical advancements be vetted by independent advisory bodies?

AI reasoning systems can produce persuasive prose that mimics rigorous proof while glossing over subtle topological, analytic, or edge-case singularities. Independent oversight guarantees mathematical truthfulness, establishes credit attribution, and prevents academic pollution from unverified preprints.

How is the Rigor Score computed in this workbench?

The Rigor Score evaluates the ratio of rigorously proven and axiomatically grounded nodes against heuristic leaps and unverified premises, penalized by missing lemma citations or circular dependencies.

Can this workbench export directly to Lean 4 formal syntax?

Yes, the JSON and Markdown dossier exports structure declarations into `theorem`, `lemma`, and `have` tactic blocks with explicit premise hierarchies, streamlining formalization in Lean 4 and Mathlib.