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

Annotations already cover read-only, idempotent, and non-destructive behavior, so the description does not need to restate those. It adds useful non-schema behavior: a per-call price ($0.001 USDC via x402 on Solana) and an alternate HTTPS endpoint. It does not give full return-format details beyond the worked example, keeping it from a 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?

The description is front-loaded with the recurrence and an example, followed by compact range, pricing, and endpoint information. Every sentence adds useful context for invoking or paying for the tool, with no redundant restatement of annotations or schema fields.

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 provides the recurrence, a worked example showing the return value, valid ranges, pricing, and an alternate endpoint. It is largely complete, though it does not explicitly state the return type or error behavior for out-of-range inputs.

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 add meaning for n and k. It does so by giving the valid range (1–64 for n) and the important relation k ≤ n, which is not captured in the schema, plus a concrete example. It still relies on the formula notation rather than plainly defining what n and k represent in prose, so a 4 is appropriate.

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 specific recurrence formula ('One step of s(n, k) = s(n-1, k-1) - (n-1)*s(n-1, k)') and an example, making it clearly a single recursive step for signed Stirling numbers of the first kind. It does not explicitly name the sequence or directly distinguish itself from siblings such as stirling1, stirling1_row, or stirling1_unsigned, so it falls short of a 5.

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 supplies valid input ranges ('n runs from 1 to 64 and k from 1 to n') and an example, which gives implied usage context. However, it never states when an agent should choose this recursive-step tool over stirling1, stirling1_row, or stirling1_unsigned, nor does it mention exclusions or alternatives.

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