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

Annotations already declare readOnly, idempotent, openWorld and non-destructive, so the description rightly focuses elsewhere — it discloses the cost ($0.001 USDC per successful call), the x402/Solana payment mechanism, and an equivalent HTTPS endpoint. Pricing and payment requirements are exactly the kind of behavioral context annotations cannot convey; only the return-value shape is left unstated.

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?

Front-loaded with the definition, then the examples that disambiguate it, then constraints, then pricing and endpoint. Four short sentences, none wasted; only the endpoint URL line is verbose but it carries real operational value.

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 predicate with no output schema, the description covers domain, semantics, cost and access method well. It stops short of stating the response format (boolean vs. {result: bool}), which an agent must infer from 'Whether…'.

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 carry the burden, and it does specify the input domain (n runs from 1 to 1000000), matching the schema's min/max. It does not restate that n is the integer being tested or that the result is a boolean, leaving a small gap.

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, well-defined mathematical predicate — whether the average of n's divisors is an integer — and backs it with worked examples (1, 3, 6, 15, 20 yes; 2, 4, 8, 12 no). The property is distinct from neighbours like arithmetic_sum or arithmetic_count, though the description never names those siblings to sharpen the distinction.

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 domain of n and the example sets imply when to reach for this tool (testing membership in the arithmetic-number sequence), but there is no explicit when-to-use/when-not guidance and no pointer to alternatives such as arithmetic_sum or arithmetic_next, which appear in the sibling list and could easily be confused with it.

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