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

Annotations already declare read-only, idempotent, non-destructive, open-world behavior. The description adds meaningful context beyond annotations: the $0.001 USDC per successful call price, x402/Solana payment model, and an alternate HTTPS endpoint. No contradictions.

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?

Compact and front-loaded: output format and example come first, followed by range and payment details. Every sentence adds useful information with no filler.

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?

For a simple one-parameter read-only math tool with no output schema, the description covers output shape, example, valid range, cost, and alternate endpoint. Safety behavior is already covered by annotations.

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 carry parameter meaning. It defines n as the row index, states its 1-12 range, and gives a worked example for n=5, though the range itself is also present in the schema.

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?

States the returned resource precisely: the Eulerian row A(n, 0) through A(n, n-1), comma-separated, with an example and key properties. It does not name or differentiate from siblings such as eulerian, eulerian_poly, or eulerian_sum, so it falls short of a 5.

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?

Provides no when-to-use or when-not-to-use guidance, and does not name alternatives. The only constraint mentioned is n's 1-12 range, which is already in the input schema.

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