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

Annotations already declare readOnlyHint, idempotentHint, and non-destructive behavior. The description adds useful behavioral details beyond those annotations: n's valid range, that entries past 15 digits are returned as decimal strings, the Bell-number inclusion, and the x402 pricing/Solana payment requirement.

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 short and front-loaded: it states the primary result, then the row bounds, numeric formatting, price, and HTTPS endpoint. Every sentence carries operational 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?

For a one-parameter computation tool with no output schema, the description is largely complete: it says what the row contains, includes the Bell number, explains large-integer serialization, and states the allowed n range. It could be slightly richer about the exact response shape, but an agent has enough to invoke it correctly.

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 explain the sole parameter. It does state that n is the row index and that n runs from 0 to 80, also clarifying that the row spans S(n,0) through S(n,n). The range partly duplicates the schema, but the row semantics add real meaning.

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 specific mathematical object and the exact extent of the result: row n of Stirling numbers of the second kind, S(n,0) through S(n,n), plus the Bell number. It implicitly distinguishes itself from single-value siblings like stirling2, but does not explicitly compare itself with stirling2_rec or stirling1_row.

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 defines what the tool returns and bounds n's range, but it gives no explicit guidance on when to choose this row-oriented tool over siblings such as stirling2 or stirling2_rec. Usage must be inferred from the tool name and the phrase 'Row n'.

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