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

Annotations already declare readOnly, idempotent, non-destructive behavior. The description adds genuinely new context the annotations cannot: the valid domain (1 to 1,000,000), a per-call price ($0.001 USDC via x402 on Solana), and an equivalent HTTPS endpoint. The one gap is no mention of the return value, but with these annotations the behavioral bar is appropriately lowered.

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 definition is front-loaded, followed by compact examples, the domain, then the operational cost and endpoint. The five examples are slightly more than needed but illustrative, and the pricing/endpoint sentences earn their place for a paid x402 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 single-parameter pure math function with no output schema, the description supplies the operation, worked examples, valid input range, and payment mechanics—enough for an agent to call it correctly. The only omission is an explicit statement of the return type, which is minor given the examples imply an integer.

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 0% schema description coverage, the description must carry the parameter burden. It does partially: 'n runs from 1 to 1000000' restates the min/max and the five worked examples clarify what value n produces. However, it never explicitly defines n as the integer whose infinitary divisor sum is computed, so it only marginally compensates for the coverage gap.

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 opening sentence, 'The sum of the infinitary divisors of n', states a specific mathematical operation and resource clearly, distinct from siblings like unitary_sigma or biunitary_sigma by naming the infinitary variant. Worked examples reinforce exactly what is computed. It stops short of explicitly contrasting with those sibling tools, but the purpose is unambiguous.

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 examples and a domain but never states when to choose this over related tools such as unitary_sigma, biunitary_sigma, divisor_sum, or sigma_k. There are no when/when-not conditions or alternative routing; the agent must infer that 'infinitary' is the distinguishing selector.

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