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

Annotations already declare read-only, idempotent, open-world, non-destructive behavior. The description adds important context beyond annotations: invalid inputs are rejected, the accepted range is bounded, and each successful call costs $0.001 USDC via x402 on Solana, with an HTTPS alternative endpoint.

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 compact and front-loaded: the defining formula and examples come first, followed by rejection behavior, range, price, and endpoint. Every sentence contributes useful information for calling or understanding the tool.

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 simple one-parameter mathematical tool with no output schema, the description sufficiently explains the return concept as a pair (a,b) and gives examples. It could be more explicit about the exact output encoding and rejection format, but overall it is complete enough to invoke correctly.

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 defining n through the equation n = 2^a * 3^b + 1, giving four concrete n-to-pair examples, and stating the accepted range, which clarifies what the single required integer represents.

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 identifies a specific mathematical operation: given n, find the exponents a,b such that n = 2^a * 3^b + 1, illustrated with examples. It is clear enough to distinguish the tool from generic Pierpont-related siblings, though it does not explicitly name or contrast those alternatives.

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 implies usage by stating that a number not of the Pierpont-power form is rejected and by giving the valid range 1 to 999999999999999. However, it gives no explicit guidance on when to choose this tool over siblings such as pierpont, pierpont_next, or pierpont_prime.

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