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

Annotations already declare a read-only, idempotent, non-destructive operation. The description adds useful non-schema context: the $0.001 USDC x402 charge per successful call, the Solana payment rail, and an equivalent HTTPS POST 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 operation, then examples, range, and payment/transport details. It is compact and every element is relevant to invoking or interpreting 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 mathematical count with no output schema, the description provides the operation, input range, sample outputs, and cost/transport details. The main omission is a formal definition of 'complexity,' but the examples and the sibling complexity tool make the intent recoverable.

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?

There is one required parameter, n, with 0% schema description coverage. The description compensates by defining n as both the upper bound and the reference integer ('from 1 through n have the same complexity as n') and illustrating behavior with examples, though it does not formally define 'complexity'.

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 operation—counting integers from 1 through n that have the same complexity as n—and gives concrete outputs for n=5, 6, 10, and 12. It is distinguishable from siblings like complexity and complexity_sum by its counting behavior, though it does not explicitly name those alternatives.

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 applicable input range (1–1000) and examples, so the use case is inferable. However, it never says when to prefer this tool over complexity, complexity_sum, complexity_max, or complexity_least, and it provides no explicit exclusions.

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