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

With no annotations, the description carries the full burden of behavioral disclosure. It fails entirely—there is no mention of what the tool computes, what output it produces, or any side effects. The description does not contradict annotations only because there are no annotations.

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 extremely short, but this is under-specification rather than conciseness. The redundant repetition of 'Bell Number' adds no value and lacks any meaningful structure.

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?

The description is completely inadequate. An agent cannot determine whether this tool returns the nth Bell number, a sequence, a constant, or something else. It lacks any context that would allow a correct selection or invocation.

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?

The input schema has zero properties, so there are no parameter semantics to document. Per the baseline for a 0-parameter tool, the schema is already complete (coverage 100%), and the description adds no necessary parameter information.

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 'Bell Number: Bell Number' is a pure tautology—it restates the tool name with no verb or action. It does not specify what the tool does (e.g., compute, return, or generate a Bell number) and is indistinguishable from the name itself.

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?

There is no guidance whatsoever about when to use this tool. Among hundreds of siblings, including closely related math tools like x402-catalan-number, x402-fibonacci, and x402-partition-number, an agent receives no information to select this tool over alternatives.

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