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

Annotations already declare readOnly/idempotent/non-destructive, so safety is covered. The description adds genuinely useful context: the exact price ($0.001 USDC per successful call, x402 on Solana) and an equivalent HTTPS POST endpoint. That is precisely the payment/auth context annotations cannot convey, though it says nothing about failure behavior, timeouts, or error responses.

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?

Purpose is front-loaded in the first clause; the example table and endpoint/pricing precede nothing essential. Four looked-up values are more than strictly needed but they double as a self-check for the caller, so they earn their space; everything is compact prose with no filler.

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?

With one integer parameter, a hard upper bound, and no output schema, the agent has enough to call this correctly, and the sample counts substitute for a return-value description. Left open are error/edge behavior at n=5000 and whether the count is cumulative-inclusive, though the examples strongly imply it.

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?

A single parameter n at 0% schema description coverage, but the sentence 'How many arithmetic numbers are at most n' fixes its meaning (upper bound, inclusive) and the range 'n runs from 1 to 5000' matches the schema constraints. The worked examples further pin down boundary semantics such as through 1 there is 1.

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?

States a specific verb+resource: counting arithmetic numbers up to a bound n. The worked examples (through 6 there are 4, etc.) implicitly define the class of 'arithmetic numbers' and let an agent distinguish this from siblings like arithmetic_number, arithmetic_next, or arithmetic_sum. What's missing is an explicit one-line contrast with those siblings.

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?

No statement of when to use this versus arithmetic_sum, arithmetic_next, or arithmetic_number, all of which appear in the sibling list. The only constraint given is the n range 1..5000, which is already in the schema. The agent must infer selection from the name alone.

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