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

With no annotations the description carries the full burden, and it does add the algorithmic method (trial division over prime factors up to sqrt) plus the paid-call context ('5 free trial calls per signed wallet'). It still omits input bounds, error behavior, and the return format, so it is only partially transparent.

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?

A single front-loaded sentence states the operation and method, followed by a short pricing note. Nothing is redundant, though the trailing emoji/price banner is not strictly part of the functional description.

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-parameter math routine with no output schema, the description covers what it computes and how, which is most of what is needed. It falls short on the expected return representation and input constraints, which an agent must infer.

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?

One parameter at 0% schema description coverage, so the description must compensate. It does clarify that n is an integer, but the schema types n as a string, which is left unexplained, and no constraints on magnitude or allowed form are given.

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 and resource ('Computes Euler's totient of integer n') and even names the algorithm, so the purpose is unambiguous. However, it does not differentiate itself from near-identical siblings like x402-euler and x402-euler-totient, leaving the agent to guess which one to pick.

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 prerequisites, and no reference to alternative totient tools. The math context implies its domain, but nothing tells an agent when this rather than x402-euler-totient is the right call.

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