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

Annotations already declare read-only, idempotent, non-destructive, open-world behavior. Beyond that, the description discloses cost ($0.001 USDC per successful call via x402 on Solana), an HTTPS endpoint, and return semantics (k=0 when not multiperfect), which are operationally useful; it does not discuss failure modes or payment-error handling.

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 mathematical predicate and examples. Price, range, and endpoint details are compact and relevant; no sentence is wasted.

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 math predicate with no output schema, the description supplies return semantics, valid input range, and payment/transport details. It omits explicit sibling routing and a brief definition of sigma, so it is strong but not fully complete.

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 schema gives only type and bounds for n. The description supplies the range 1 to 100000 and examples of n values, but it largely repeats the schema's min/max rather than adding deeper parameter meaning such as defining sigma.

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 gives a specific predicate: whether sigma(n) is a multiple of n with multiplicity k >= 2, including examples and the k=0 case. It clearly identifies the multiperfect-number classification, though it never names sibling alternatives such as perfect_check or triperfect to sharpen differentiation.

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?

No sentence states when to use this tool instead of sibling number-theory classification tools, nor when not to use it. The range and examples describe input semantics, not usage conditions or alternatives.

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