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

Beyond the readOnly/idempotent annotations it discloses the paid x402 flow ($0.001 USDC per successful call on Solana), an equivalent HTTPS endpoint, and the return representation (decimal string beyond 15 digits). Payment/auth requirements and output typing are exactly the kind of behavior annotations cannot convey.

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?

Front-loads the definition, then edge case, then worked examples, then domain, then output format and billing. Slightly dense with two example values that could be trimmed, but every sentence adds usable information.

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?

No output schema exists, and the description usefully explains that results become decimal strings past 15 digits, covering the main return-value ambiguity for a tool that can produce huge integers. It does not state behavior for out-of-range input or error cases, a minor residual gap.

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, and it does: n is the object count and k the exact number of fixed points, with the cross-parameter constraint k <= n that the schema alone does not impose. The 0-100 ranges merely repeat the schema bounds.

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 a specific combinatorial quantity: the number of involutions of n objects with exactly k fixed points. That is enough to distinguish it from neighbors such as involution, involution_mod and involution_sum, though the description never explicitly contrasts with them.

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?

Gives concrete operating context: n spans 0-100, k spans 0 to n, and the result is 0 whenever n-k is odd, so the agent knows the valid domain and one important no-op case. It does not name an alternative tool or say when a sibling should be preferred instead.

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