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 disclose the return contents (gcd, x, y) plus the cost/rate-limit model ('5 free trial calls per signed wallet'). It says nothing about how non-integer strings, zero, or negative inputs are handled, which matters given both inputs are typed as strings.

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 tight sentence that front-loads the computation and its outputs, with the trial-call note appended. The emoji and marketing clause add minor noise but also carry real information about cost.

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?

The description compensates for the missing output schema by naming the three return values, but with zero annotation coverage, 0% parameter documentation, and no error/input-format guidance, an agent still lacks enough to call it confidently.

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 neither 'a' nor 'b' is documented anywhere. The phrase 'two integers' is the only hint, and it actually corrects the schema's string typing, but it does not explain which operand is which or the required format, so a caller must guess.

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 the extended GCD of two integers') and even names the outputs (gcd plus Bezout coefficients x and y), so the agent knows exactly what it gets. It does not distinguish itself from the many adjacent number-theory siblings (x402-euler-phi, x402-prime-factors, x402-chinese-remainder), so it stops short of a 5.

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 statement of prerequisites, and no pointer to an alternative for plain GCD or for other number-theory operations. The only contextual line is the promotional '5 free trial calls per signed wallet', which is pricing, not usage direction.

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