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

Annotations already declare readOnlyHint, idempotentHint, non-destructive, and openWorld behavior. The description adds valuable context beyond the annotations: results become decimal strings past 15 digits, each successful call costs $0.001 USDC via x402 on Solana, and an alternate HTTPS endpoint is provided. This is solid, though no rate-limit or failure-mode details are included.

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 dense but front-loaded with the formula, example, and parameter ranges before output format, pricing, and endpoint details. Almost every sentence adds distinct information, though the pricing and alternate endpoint feel slightly appended rather than integrated.

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 two-parameter mathematical tool with no output schema, the description covers what is computed, valid input ranges, output representation (decimal string past 15 digits), cost, and an alternate transport. It is nearly complete, missing only deeper combinatorial context for p and explicit error behavior.

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 does so by defining both parameters through the formula and example, showing that p parameterizes the Fuss-Catalan generalization and n is the index. The stated ranges duplicate the schema's min/max, and the combinatorial meaning of p beyond p=2 is not explained, but the description substantially compensates for the schema 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 states the exact formula C(p*n+1, n)/(p*n+1) and gives a concrete example (FC(2,5)=42). It also explicitly links the tool to its Catalan sibling via 'FC(2,n) is the Catalan number', so an agent can distinguish it from the many combinatorial siblings.

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 valid ranges for p and n are stated, which implies usage, and the Catalan relationship hints at when this overlaps with the catalan tool. However, there is no explicit guidance on when to prefer this tool over catalan or fuss_check, and no exclusions or prerequisites are given.

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