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

No annotations are provided, so the description carries the full burden of disclosing behavior. It only repeats the tool name and does not mention side effects, determinism, return format, required inputs, or any execution characteristics.

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 tiny but tautological. 'Is Quadratic Residue: Is Quadratic Residue' is redundant rather than concise, and it leaves out the substantive content that would make a short description valuable.

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, no annotations, and no parameters, the agent must rely entirely on the description. The tautological text provides no way to know what input is expected, what condition is checked, or what result shape to anticipate.

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 declares zero properties and schema coverage is 100%, so there are no parameter semantics for the description to clarify. The zero-parameter baseline applies; the description does not contradict the schema, even though it adds no useful input 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 is exactly the tool's name with a colon: 'Is Quadratic Residue: Is Quadratic Residue'. This is a tautology that restates the title without saying what the tool does with any input or context. It does not distinguish itself from related number-theory predicates in the sibling list.

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?

The description provides no guidance on when to use this tool, when not to use it, or which alternative tools might be appropriate. The sibling list contains many similar mathematical predicates, but the description offers no routing information at all.

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