Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden. It discloses that the tool audits numerical stability, condition number, and cancellation risks, which gives insight into its behavior and potential output. However, it does not mention side effects, read-only nature, prerequisites, or error behavior. It provides some transparency but not full disclosure.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise, one sentence, and front-loads the primary purpose ('Formally verify') before listing secondary audit features. It is well-structured and every phrase contributes meaning. A slight longer list could be streamlined, but it is efficient.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool has 5 parameters, some optional, and an output schema, the description covers the core purpose but leaves gaps: it does not explain when to enable audit_stability, how matrix and tolerance interact, or how it compares with solve_and_compare. It is not fully complete for an agent to select and invoke without additional inference.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It gives semantic hints: 'condition number' implies the matrix parameter, 'numerical stability' implies tolerance and audit_stability, and 'arithmetic equality claim' implies claim_lhs and claim_rhs. However, it does not explicitly describe any parameter, leaving some interpretation to the agent. It partially compensates for the coverage gap.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states a specific action ('Formally verify an arithmetic equality claim') and distinguishes this tool from siblings like cognitive.solve_arithmetic and cognitive.solve_and_compare by emphasizing verification and numerical auditing (stability, condition number, cancellation risks) rather than solving or comparing. The verb and resource are precise and unambiguous.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage: use this when you need to verify an equality claim or audit numerical stability. However, it does not explicitly state when to prefer this over alternatives (e.g., solve_and_compare) or provide exclusion criteria. The guidance is implicit rather than explicit.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.