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

With no annotations and no substantive description, there is zero disclosure of behavioral traits such as input format, result semantics, or side effects. The description merely repeats the name and provides no context beyond the tool title.

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?

While the description is extremely short, it is not meaningful conciseness—it is under-specification. It contains no useful content and does not earn its place in any way.

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?

Given the lack of annotations, output schema, and any explanatory text, the description is wholly inadequate. An agent cannot know what the tool does, how to interpret its output, or when to call it among hundreds of similar math predicates.

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 schema has zero parameters, so there is nothing for the description to clarify. Per the rubric, zero params means a baseline of 4 is appropriate, though the description still fails to explain what the tool actually evaluates.

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 'Is Carmichael: Is Carmichael' is a pure tautology—it restates the tool name without any verb describing an action or resource. It gives no indication of what the tool computes or returns, and it cannot be distinguished from the many sibling math/number tools.

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 on when to use this tool versus alternatives like x402-carmichael-function or x402-is-prime. No context, prerequisites, or exclusions are provided, leaving the agent to guess.

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