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

Annotations already declare readOnly, idempotent, non-destructive, open-world behavior. The description adds useful context beyond annotations: output indexing from s(n,0) through s(n,n), the absolute-value sum identity, a concrete row example, valid n range, price, and alternate HTTPS endpoint.

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 core operation, then gives bounds, example, price, and endpoint. Every sentence adds practical information for invoking the tool, with no redundant repetition of the title.

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 description still explains the returned row structure, indexing convention, and sign pattern via an example. Combined with annotations covering safety and idempotency, it is complete enough for an agent to invoke 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 carry parameter meaning. It defines n as the row index, constrains it to 0 through 64, and shows the resulting row for n=4, which sufficiently compensates for the bare schema.

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 verb/resource: it returns row n of the signed Stirling numbers of the first kind, with explicit bounds and an example row. It is clear what the tool computes, but it does not explicitly distinguish itself from nearby siblings such as stirling1, stirling1_rec, stirling1_unsigned, or stirling2_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 explains the mathematical result and valid n range, but it gives no explicit guidance on when to use this row tool instead of stirling1, stirling1_unsigned, stirling1_rec, or stirling2_row. The agent must infer the use case from the name and output shape.

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