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

Annotations already cover read-only, idempotent, open-world, and non-destructive behavior. The description adds important context beyond annotations: a $0.001 USDC charge per successful call via x402 on Solana and an HTTPS endpoint, which materially affects how an agent should invoke it.

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 definition is front-loaded in the first sentence, followed by compact examples, parameter ranges, and payment/access details. The ranges partly duplicate the schema, but overall the description is appropriately sized and every sentence adds useful context.

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 math tool with no output schema, the description supplies examples, valid domains, payment cost, and an HTTPS alternative. It could explicitly say the result is an integer, but the examples make the return value clear enough for correct invocation.

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 stating the domains ('n runs from 0 to 16 and m runs from 1 to 1000000') and giving examples that map n and m to the modulo result, though it does not formally define the Franel sequence or the return type.

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 a specific computation, 'F(n) modulo m', and reinforces it with concrete examples such as 'F(4) mod 7 is 3'. It distinguishes itself from a plain Franel-number tool by explicitly including the modulus, though it does not name sibling tools like franel or franel_sum.

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?

Usage is implied by the computation and parameter ranges, but the description does not explicitly say when to prefer this over franel, franel_sum, or other siblings. It does note an alternative access path ('Same tool over HTTPS'), which is useful but not sibling-selection guidance.

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