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

With no annotations, the description carries the full behavioral burden, and it discloses little: it does not say what happens for k <= 1 (where the bound goes to zero or negative), whether the result is a float or formatted string, or any error behavior. It does reveal the tool is a pure deterministic computation and mentions a 5-call free trial per signed wallet, which is minor added context.

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?

One front-loaded sentence that states the operation and the exact output formula, followed by a short promotional note. Nothing is padded out, though the free-trial boilerplate is not operationally useful.

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 trivial one-parameter math function, the description is adequate: it states the input and the returned formula. It still leaves the input type/domain and output representation unspecified, and there is no output schema to fall back on, so an agent guessing at k's format would be doing so blind.

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 0% and the single parameter k is typed only as a string with no documentation. The description implies k is numeric via the formula k*k, but adds no format, range, or validity constraints to compensate for the undocumented schema.

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 names a specific computation (the Chebyshev inequality bound) and even gives the exact formula 1 - 1/(k*k) applied to k, so the agent knows precisely what comes back. It stops short of distinguishing itself from the similar-named siblings x402-chebyshev and x402-chebyshev-distance, which an agent could easily confuse.

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 statement of when to use this tool versus the adjacent Chebyshev tools, nor any prerequisite such as k needing to be greater than 1. The only extra sentence concerns free trial quota, which is commercial framing rather than usage guidance.

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