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

Annotations already cover safety (readOnly, idempotent, non-destructive), and the description adds genuinely new behavioral context: cost of $0.001 USDC per successful call via x402 on Solana, implying billing only occurs on success. It also discloses an equivalent HTTPS endpoint, which is practical deployment context not present in any structured field.

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 predicate, then examples, bounds, and pricing/endpoint — every sentence contributes. Slightly telegraphic ('16 gives sigma 31') but that terseness conveys real information about the sigma convention rather than wasting space.

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 boolean predicate with read-only annotations and no output schema, the description gives the definition, domain, and cost. The main residual gap is that it never states the return shape (boolean vs. sigma value) or out-of-range behavior, though 'Whether ...' strongly implies a boolean result.

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 state the valid range (1 to 1000000) matching the schema bounds plus example inputs (16, 6, 10) that show what n means in practice. It does not explicitly restate that n is the integer whose divisor sum is compared, but the predicate phrasing makes that clear.

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 states a precise mathematical predicate (sigma(n) = 2*n - 1) with concrete worked examples ('16 gives sigma 31', '6 and 10 are not'), which pins down the sigma convention and the operation unambiguously. It never names near-siblings such as perfect_check or semiperfect, so differentiation relies on the agent knowing the underlying math term.

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?

Usage is implied by the definition rather than stated: the agent can infer it should call this to test the almost-perfect property for a single integer. The domain bound 'n runs from 1 to 1000000' is a useful precondition, but there is no explicit when-not-to-use or routing to alternatives like perfect_check.

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