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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the safety profile is covered. The description adds useful behavioral context beyond annotations: the input range, per-call pricing, x402/Solana payment context, and an alternate HTTPS 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 front-loaded with the mathematical definition and examples, then adds only relevant constraints and access details. Every sentence contributes useful information for selecting or invoking 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 math tool with rich annotations and no output schema, the description supplies everything needed: exact definition, worked examples, valid input range, and call/payment details. An agent has enough information to invoke it correctly without consulting additional fields.

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, and it does by stating that n runs from 1 to 1000000000000 and supplying concrete examples. The schema itself supplies the integer type and min/max, so the description does not need to repeat those details.

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 precise mathematical operation: the product of n's distinct prime factors. Examples for rad(1), rad(12), and rad(36) make the operation unambiguous. It does not explicitly distinguish itself from nearby siblings such as squarefree_part or sopf, so it stops 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 gives the valid input range and examples, which imply when the tool is applicable. However, it never says when to use this tool versus related number-theory siblings, nor does it provide exclusions or alternative recommendations.

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