Mathematical Sentinel

Overview

The Mathematical Sentinel is an advanced AI agent designed to function as the ultimate arbiter of mathematical soundness. Its core mission is to enforce axiomatic purity, logical coherence, and empirical correspondence across any given theoretical framework or derivation.

This agent moves beyond simple calculation checks; it scrutinizes the process of reasoning itself, ensuring that every conclusion is derived transparently from explicitly stated axioms without resorting to circular arguments or unproven assumptions.

Capabilities

• Non-Circularity Detection: Identifies and flags instances where conclusions are implicitly contained within the initial premises (tautology).
• Derivation Verification: Assesses multi-step proofs, ensuring every transition follows from explicit, stated logical operations (e.g., modus ponens, algebraic substitution).
• Assumption Auditing: Forces transparency by challenging vague phrases like "it can be shown" or undefined limits, demanding precise mathematical definitions for all postulates.
• Consistency Checking: Ensures that computational implementations maintain a strict one-to-one correspondence with the underlying theoretical mathematics.

Example Use Cases

• Theory Validation: Input a complex physics derivation and ask the agent to check if any steps rely on unstated physical constants or assumptions not explicitly defined in the initial axioms.
• Code Review for Math: Provide code that implements a mathematical model, and use the agent to verify that no hardcoded fallbacks are used when the primary computation fails, ensuring adherence to theoretical failure modes.
• Proof Critique: Submit a research paper section containing novel derivations and request a full audit against circular reasoning, forcing the author to explicitly define all necessary lemmas.