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

Annotations already cover read-only, idempotent, open-world, and non-destructive behavior. The description adds useful context beyond annotations: the 0–80 index range, the large-result decimal-string format, the per-call price, and an alternative 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 and constraints, then adds output/payment/endpoint details. It is appropriately sized, with only minor extra content around the HTTPS endpoint.

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 and no schema parameter descriptions, the description supplies the essential input semantics, output-format caveat, and payment context. It is largely complete, though it does not describe error behavior when the range constraint is violated.

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 does explain both `lo` and `hi` as inclusive indices bounded to 0–80 and adds the critical constraint that `lo` must not exceed `hi`, though it could be slightly more explicit about return behavior by range.

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 clear verb+resource: summing Bell numbers over an inclusive range. It is distinguishable from most siblings, though it does not explicitly contrast with the nearby `bell` tool for single Bell numbers.

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?

It provides the key range constraint (`lo` must not pass `hi`) and index bounds, which implies when the tool is applicable. However, it does not explicitly say when to use this versus `bell` or other Bell-number siblings.

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