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

Annotations already cover safety properties (read-only, idempotent, non-destructive, open-world), so the description's added details about cost, payment mechanism, and HTTPS endpoint are valuable. It discloses the per-successful-call price and alternative API path, which go beyond structured annotations. It does not explicitly state the return type, though the phrasing 'Whether...' implies a boolean result.

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, then examples, then input range, then cost and endpoint. Every part is relevant for a paid API-backed tool, though the range sentence partly repeats schema constraints and the HTTPS endpoint is ancillary for MCP invocation.

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 predicate with no output schema, the description gives enough to call it correctly: the tested condition, example inputs, valid range, cost, and endpoint. It could be slightly stronger by explicitly saying it returns a boolean, but 'Whether...' already implies that.

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?

The single parameter n has 0% schema description coverage, so the description must carry meaning. It states that n runs from 1 to 1000000 and gives examples, but this largely duplicates the schema's minimum and maximum constraints. It does not further define the parameter beyond its role in the infinitary-divisor predicate.

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 clearly states a specific mathematical predicate: whether the infinitary divisors of n sum to less than 2n. It gives examples of true and false cases, making the operation concrete. It does not explicitly distinguish itself from sibling tools like infinitary_abundant or infinitary_perfect, so it falls short of a 5.

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 defines what the tool computes but gives no explicit guidance on when to use it versus alternatives such as infinitary_abundant, infinitary_perfect, or infinitary_sigma. The examples and input range are useful context but do not constitute usage guidelines.

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