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

Annotations already cover read-only, idempotent, non-destructive, and open-world behavior. The description adds important non-annotation behavior: a paid x402/Solana call at $0.001 per successful call and an HTTPS endpoint, plus the valid input range. It does not detail the payment/auth flow beyond that, so not a 5.

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 formula is front-loaded, followed by sample values and execution details, and the overall text is compact for a paid mathematical function. The examples are slightly dense and skip A(4), but no sentence is seriously wasteful.

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 mathematical function with no output schema, the description supplies the formula, sample outputs, input range, and payment/endpoint context. The main omissions are sibling differentiation and an explicit statement that the return value is A(n).

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% and the single parameter n has no schema description. The description compensates by defining n in the summation and stating that n runs from 0 to 11, though the min/max are already in the schema. It does not explicitly state the return type, but the sole parameter is well explained.

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?

Defines the Apery number with an exact summation formula and sample values, so the operation is unambiguous. It does not explicitly distinguish this direct A(n) tool from siblings such as apery_sum, apery_mod, apery_prime, or apery_term, preventing 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?

There is no explicit when-to-use guidance, no exclusions, and no mention of alternatives. The n range 0 to 11 is a constraint, not a usage rule; the agent must infer that this tool computes direct A(n) values rather than related apery_* variants.

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