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

Annotations already declare read-only, idempotent, non-destructive, and open-world behavior. The description adds useful behavioral context beyond annotations: n is capped at 100, results past 15 digits are returned as a decimal string, and each successful call costs $0.001 USDC via x402 on Solana.

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 front-loaded with the core definition and recurrence, followed by examples, bounds, output formatting, and operational details. It is dense but every sentence adds either mathematical or invocation-relevant 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?

For a single-parameter math tool with no output schema, the description covers the domain, expected output format for large values, pricing, and an alternate HTTPS endpoint. It is nearly complete, though it omits explicit sibling differentiation and error behavior for invalid or out-of-range inputs.

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, and it does: it defines n as the number of objects, gives the valid range 0–100, and provides worked examples for n=5 and n=10. It does not explicitly restate that n is an integer, but the schema covers type constraints.

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 specific computation clearly: the number of involutions of n objects, including the recurrence and concrete examples I(5)=26 and I(10)=9496. It does not explicitly differentiate from sibling variants such as involution_fixed, involution_mod, or involution_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?

The description explains the mathematical definition and valid n range but gives no guidance on when to use this tool versus sibling alternatives. There are no exclusions or routing hints even though involution_fixed, involution_mod, and involution_sum exist.

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