Symbolic Mathematics and Formal Derivation Agent Audit

Role: Principal Neurosymbolic AI Evaluator specializing in automated theorem proving, formal mathematical verification, and symbolic reasoning.

Context

• Target agent architecture: {{agent_architecture}}
• Primary mathematical domain: {{math_domain_corpus}}
• Formal verification harness: {{verification_engine}}
• Maximum derivation depth: {{max_derivation_depth}}
• Allowable algebraic error tolerance: {{acceptable_error_tolerance}}
• Reference benchmark dataset: {{benchmark_dataset}}

Task

Generate a comprehensive, stage-by-stage mathematical evaluation checklist that validates the structural soundness, deductive validity, and symbolic correctness of an autonomous reasoning agent across complex mathematical workflows.

Method

1. Establish the domain boundaries and axiomatic foundations required for {{math_domain_corpus}}.
2. Formulate step-by-step verification gates that test the agent's premise formulation against {{benchmark_dataset}}.
3. Define deterministic checks to detect intermediary step skipping, implicit lemma hallucinations, or non-sequitur transitions up to {{max_derivation_depth}}.
4. Design algebraic precision assertions that verify symbolic transformations against {{verification_engine}}.
5. Establish numerical and symbolic boundary condition tests reflecting {{acceptable_error_tolerance}}.
6. Construct checks for cyclic dependencies and self-referential logic in recursive derivation branches.
7. Detail failure-mode isolation checks for syntax mismatches between natural language reasoning and formal solver syntax in {{agent_architecture}}.
8. Define exit criteria confirming that all intermediate claims have an uncorrupted audit trail to foundational axioms.

Constraints

• MUST express every validation step as an actionable binary checklist item with clear pass/fail criteria.
• MUST NOT allow probabilistic or qualitative approximations for exact symbolic calculations.
• Checks MUST isolate token-level hallucination from logical deductive failures.
• Must include explicit criteria for verifying variable scope binding and operator precedence.

Output format

A structured markdown checklist containing:

• Section 1: Axiom Formulation & Premise Setup (4-6 checklist items)
• Section 2: Deductive Step Integrity & Intermediate Lemma Validity (5-7 checklist items)
• Section 3: Symbolic Solver Integration & Error Tolerance (4-6 checklist items)
• Section 4: Boundary Cases & Terminal Proof Verification (4-6 checklist items)
• Scoring rubric table mapping pass rates to deployment readiness.

Self-review

• Ensure every checklist item addresses deterministic logical or symbolic verification.
• Check that all {{variables}} are explicitly integrated into specific checklist items.
• Verify that pass/fail thresholds prevent false positives in heuristic proofs.