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

With no annotations, the description carries the full burden of disclosing behavior, and it discloses nothing. It does not explain what the tool does with inputs, how results are returned, or whether it relies on conversation context. This is equivalent to an empty behavioral description.

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 not helpfully concise; it is under-specified. It contains only a title-like phrase and a vague subordinate clause, providing no operational meaning despite being only a few words.

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 tool with no parameters, no output schema, and no annotations, the description absolutely must explain what the tool computes and how to invoke it. 'Mean of geometric' gives an agent no way to know what input to supply or what result to expect, making the definition severely incomplete.

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 parameters, so there are no parameter semantics for the description to clarify. The rubric establishes a baseline of 4 for zero-parameter tools; the description does not harm this because no parameters exist to document.

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 nearly tautological: 'Geometric Mean: Mean of geometric.' restates the tool name and adds no actionable verb or resource clarity. It fails to distinguish the tool from closely related siblings like x402-harmonic-mean or x402-mean-of.

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 instead of alternatives such as x402-geometric-series, x402-geometric-pmf, or x402-mean-of. The only implied usage comes from the tool name itself, not from any stated context or conditions.

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