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

Annotations already declare readOnly, idempotent, non-destructive, so the safety profile is covered. The description adds genuinely new behavioral context beyond annotations: a per-call price of $0.001 USDC, that billing applies only to successful calls, the x402/Solana payment rail, and an equivalent HTTPS endpoint. It does not describe the return type, though the worked examples imply an integer.

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?

Three tight sentences: definition first, examples and bounds second, commercial/transport detail last. The bound is stated twice (implicitly in the examples and explicitly in 'n runs from 0 to 15'), a minor redundancy, but nothing is wasted.

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-integer deterministic math tool with no output schema, the description supplies the domain, sample outputs, and the payment/transport mechanics an agent needs before calling. The only gap is the absence of any output-type statement, which the examples largely mitigate.

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 carries the full burden and does so adequately: it names the parameter (n), states the domain 0 to 15 (matching schema min/max), and supplies three concrete input→output pairs that fix the mapping. It could have added a note on out-of-range behavior, which is why it is not a 5.

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 mathematical operation: the greatest common divisor of two consecutive Franel numbers F(n) and F(n+1). The verb+resource is unambiguous and the worked examples (n=0→1, n=1→2, n=6→16) confirm the exact function. It does not explicitly contrast with siblings such as franel_sum or franel_mod, so an agent must infer the distinction from the name, but the computation itself is precisely defined.

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?

No explicit when-to-use or when-not-to-use guidance relative to the four sibling franel_* tools. Usage is implied by the narrow domain (n from 0 to 15) and the pricing note, but an agent is left to infer that franel_sum or franel computes the underlying sequence instead.

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