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

Annotations already declare read-only, idempotent, non-destructive, and open-world behavior. The description adds useful behavioral context: input rejection for base-4 digits above 1, the valid n range, per-call pricing, and the 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 short and front-loaded: purpose first, then examples, validation rule, range, and operational details. Every sentence adds useful information without repetition.

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, read-only mathematical lookup with no output schema, the description provides enough to select and invoke the tool correctly: what it computes, examples, valid input range, rejection rule, cost, and endpoint.

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?

With 0% schema description coverage, the description compensates well by defining n's valid range, giving concrete example mappings, and explaining that n must have only 0 or 1 in base 4. It does not spell out every edge case, but the parameter meaning is substantially clarified.

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 inverse computation: the index whose Moser-de Bruijn number is n. Examples like 5 -> 3 clarify the mapping, though it does not explicitly differentiate itself from sibling tools such as moser or moser_check.

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 implies the use case through the inverse mapping but gives no explicit guidance on when to use this tool versus sibling tools like moser, moser_check, moser_count, or moser_sum. It also does not state when not to use it.

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