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

With no annotations, the description carries the full burden. It usefully discloses the algorithm used and the access/pricing model (5 free trial calls per signed wallet), which implies a paid, wallet-authenticated service. It says nothing about behavior for large n, error cases, or performance limits, so disclosure is partial.

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 core purpose is front-loaded in a single tight clause, and the trailing free-trial note is short. Slightly diluted by the marketing emoji/promo, but overall efficient.

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 simple single-argument math tool this is close to adequate: the return value (partition count) is implied and the algorithm is named. However, the untyped/unbounded string parameter and absent output schema leave the agent guessing about valid input format and result shape.

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 the single parameter 'n' is an undescribed string. The description's 'p(n)' implies n is the integer argument, but it never clarifies that n must be supplied as a string, nor any bounds or format, so it does not compensate for the schema 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?

The description gives a specific verb and resource — 'Returns the integer partition count p(n)' — and even names the algorithm (Euler's pentagonal recurrence), which distinguishes it from generic math siblings. It does not, however, explicitly differentiate itself from the similarly named sibling 'x402-partition', leaving some ambiguity about which to call.

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 alternatives, no prerequisites, and no mention of input constraints or limits. The only extra clause is a promotional note about free trial calls, which is not usage guidance.

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