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 behavioral disclosure, and it discloses nothing: not the formula applied, not what k represents, not the return shape, not any constraints. The annotation-free mutation/computation profile is left entirely opaque.

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?

It is short, but that brevity reflects under-specification rather than efficient structure. The duplicated phrase earns no place and communicates no information.

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 annotations, no output schema, and a one-line tautology, an agent has essentially no information needed to call this tool correctly or interpret its result.

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?

Schema description coverage is 100%, so the baseline is 3 even though the description adds no parameter meaning. Note the schema text itself ("K to process") is uninformative for a statistics tool, so this is only marginally adequate.

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 the tautology "Chebyshev Inequality: Chebyshev Inequality", restating the tool name verbatim without a verb, an output, or any indication of what the tool computes. An agent cannot distinguish it from the dozens of other x402 math/statistics siblings such as x402-chebyshev, x402-chebyshev-distance, or x402-empirical-rule.

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 when-to-use guidance, no exclusion criteria, and no mention of any alternative tool. The reader is given nothing to route on beyond the bare name.

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