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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false. The description adds useful behavioral context beyond those annotations: the input bound, the $0.001 USDC charge per successful call, x402/Solana payment, and the HTTPS access path. It does not contradict the annotations.

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 definition and stays appropriately sized for a one-parameter predicate tool. The theorem and examples are slightly redundant but useful for clarity; the pricing and HTTPS details are relevant but make the ending list-like.

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 read-only predicate with no output schema and rich annotations, the description is nearly complete: it defines politeness, gives examples, states the input range, and discloses cost and access details. It implies a boolean return via 'Whether n is polite' but does not explicitly state the return format.

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 compensate. It does so by defining n as the candidate number and stating that n runs from 1 to 1000000, with examples such as 3, 6, and 9 being polite and 1, 2, 4, and 8 not. The schema already carries the integer type and min/max constraints, so some overlap remains, but the predicate meaning is clear.

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 n is a sum of two or more consecutive positive integers. It gives an equivalent characterization and examples, so the resource and operation are clear. It does not mention the closely related sibling polite_split, so it falls short of full sibling 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?

The description defines the property and gives examples, but does not say when to use this tool instead of alternatives. There is no mention of polite_split or of when to prefer the HTTPS endpoint over the MCP tool. Usage is only implied by the mathematical definition.

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