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

Annotations already declare read-only, idempotent, non-destructive behavior, and the description adds genuinely non-obvious context: a per-successful-call price in USDC via x402 on Solana and an equivalent HTTPS endpoint. It also discloses the output representation switch to a decimal string past 15 digits. It stops short of describing the response envelope or failure/refund behavior.

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-loaded with the mathematical definition and worked examples, then range, then output-format caveat, then commercial/transport details. Every sentence adds information; nothing is padded.

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?

With no output schema, the description handles return values adequately by noting the decimal-string behavior for large results, and the formula lets the agent predict the value. It does not state the JSON field name or envelope shape, which is the only remaining gap for a one-parameter compute tool.

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 coverage is 0%, so the description carries the burden, and it does define n as the index into the Woodall sequence and restates the 1..256 bound. That is close to the maximum useful semantic content for a single integer index, though it adds little beyond the schema's own min/max.

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 exact closed-form definition (n*2^n - 1) plus the first three values, so the tool is unambiguously distinguishable from near-neighbours like cullen (n*2^n + 1). A specific verb-equivalent (compute the nth term) and resource (Woodall number) are both present.

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?

It gives the valid domain (n from 1 to 256), which implicitly tells the agent when the tool is applicable, but never names an alternative such as cullen or a general math_eval substitute, and gives no explicit when-not guidance. Usage must be inferred from the formula.

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