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

The annotations already declare this as a read-only, idempotent, non-destructive operation. The description adds useful behavioral context beyond that: the price per successful call, the x402/Solana payment model, and the equivalent HTTPS endpoint. It does not explicitly state the return type, but 'Whether...' implies a boolean.

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 predicate, followed by illustrative examples, then practical range and payment details. It is compact, though the payment and endpoint information could be separated from the mathematical definition for clarity.

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 boolean predicate with annotations covering safety, the description gives enough to call the tool correctly: what it computes, examples, input range, cost, and endpoint. The main remaining gap is an explicit statement that the return value is a boolean.

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?

With one parameter and 0% schema description coverage, the description must carry the burden. It states that n runs from 1 to 1,000,000, but that range is already in the schema's minimum/maximum, and it does not further explain what n represents or add constraints beyond the schema.

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 mathematical predicate: whether the infinitary divisors of n sum to 2n. It gives concrete true/false examples, which sharpens the meaning. However, it does not explicitly differentiate this tool from nearby siblings such as infinitary_sigma or infinitary_abundant/deficient.

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 gives the valid domain of n (1 to 1,000,000) and examples, but it never says when to use this tool instead of infinitary_sigma, infinitary_abundant, infinitary_deficient, or perfect_check. There are no explicit exclusions or alternative-routing cues.

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