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

Annotations already declare readOnly/idempotent/non-destructive, so the description's real contribution is disclosing the paid-call model ($0.001 USDC per successful call via x402 on Solana) and the equivalent HTTPS endpoint — operationally important context an agent would otherwise miss. It does not describe error or rate-limit behavior, keeping it just short of 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?

Purpose is front-loaded in the first clause, followed by disambiguating examples, the valid range, then pricing/endpoint details. Every sentence carries distinct information 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 no output schema, the 'Whether ...' phrasing plus the worked examples make the boolean return clear, and annotations cover the safety profile. Only the payment-failure/error semantics are left unstated, a minor gap for a single-parameter predicate.

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 coverage is 0%, so the description must carry the load. It establishes that n is the integer being tested and restates the 1..1000000 domain that the schema already enforces, but adds no format or edge-case meaning beyond that.

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 predicate: whether the infinitary divisor sum of n exceeds 2n, and backs it with concrete true/false examples (24, 30 vs 6, 16, 36, 48). The word 'infinitary' distinguishes it from the plain abundance/abundancy siblings, though it never explicitly names 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 examples and the 1..1000000 range imply when the tool applies, but there is no explicit when-to-use or when-not guidance and no named alternative such as infinitary_sigma (for the actual sum) or abundance (for the ordinary-divisor version). Usage must be inferred.

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