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

With no annotations and no output schema, the description carries the full burden of behavioral disclosure. It says nothing about return format (e.g., boolean), input constraints, or how values like zero, negatives, or non-integers are handled.

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 but redundant and under-specified. It repeats the same phrase after a colon without adding any useful information, so it does not earn its place.

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 predicate tool with no annotations and no output schema, the description should at least define 'ugly number' and indicate that a boolean result is returned. It is completely inadequate for an agent to call the tool 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?

The schema has 100% description coverage, so the baseline is 3. However, the schema description 'Value to process' is generic, and the tool description adds no additional meaning about the expected numeric format or constraints.

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 Ugly Number: Is Ugly Number' merely repeats the tool name and title without explaining what an ugly number is or what the tool checks for. It is a tautology, not a specific verb+resource definition.

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?

No guidance is given about when to use this tool, what inputs are expected, or how it relates to adjacent number-checking tools like x402-is-prime or x402-is-perfect.

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