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

No annotations exist, so the description carries the full behavioral burden. It discloses the free-trial-per-signed-wallet pricing trait, which is real added context, but says nothing about required input format, error behavior, or return shape for a computation tool.

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 compact sentence, front-loaded with the operation and its return, with no filler. The emoji-flagged trial note is mildly noisy but short and informative.

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 two-parameter numeric tool with no annotations and no output schema, the description omits the parameter format (why strings?), expected output representation, and any domain hint about what a Stirling number of the second kind means or when an agent should reach for it.

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 coverage is 0% and both parameters are typed as strings, which is surprising for a numeric math function. The description merely echoes the parameter names ('for n and k') without explaining meaning, accepted format, or valid ranges, so it fails to compensate for the coverage gap.

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?

States a specific verb ('Returns') and a precise mathematical resource ('the Stirling number of the second kind'), which is unambiguous and distinguishable from numeric siblings like x402-bell-number or x402-partition-number. It stops short of explicitly naming or contrasting any sibling, but the resource itself is sharply defined.

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 offers no when-to-use guidance, no preconditions, and no alternatives among the many combinatorics siblings (bell-number, catalan-number, binomial-coefficient). The only contextual note is the pricing/trial line, which is unrelated to selection.

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