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

Annotations already establish read-only, idempotent, open-world, and non-destructive behavior, and the description adds material invocation context: paid x402/Solana billing at $0.001 per successful call and an HTTPS POST endpoint. It still omits failure/payment-flow details, but the added billing and transport information is meaningful beyond 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 operation and examples, followed by ranges, price, and endpoint, with no filler. The range sentence duplicates schema constraints and three examples may be more than strictly necessary, but overall it remains tight and well-structured.

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 two-parameter math function with no output schema, the description covers the operation, examples, input bounds, cost, and alternate transport. It does not define the Apery sequence from scratch or state the return type explicitly, but the examples make the result shape inferable.

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?

With 0% schema description coverage, the description must define n and m; it maps them through 'A(n) modulo m', gives examples, and repeats their min/max ranges. However, the ranges duplicate the schema, and it never explicitly states that n is the Apery index and m is the modulus, so the semantics are adequate but not rich.

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 precise operation, 'A(n) modulo m', and three worked examples, so an agent can infer it returns an Apery number reduced by a modulus. It does not explicitly define A(n) as the Apery sequence or name sibling tools like apery or apery_term, but the modulo operation distinguishes it adequately.

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 no explicit guidance on when to choose this tool over siblings such as apery, apery_term, or apery_sum. It states input ranges, price, and an alternate HTTPS endpoint, but provides no use-case conditions, exclusions, or alternatives.

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