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 failure behavior ('null when none exists') and the payment model ('5 free trial calls per signed wallet'), which an agent cannot infer from the schema. However, it omits permission/auth details and any note on input constraints or output format.

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 defines the operation and its edge case, with the trial-call note appended. Both are short and earn their place; only the emoji and promotional phrasing are mild noise.

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 math tool with no annotations and no output schema, the description covers purpose and the null return, which is the most important unknown. It still leaves input format, valid ranges, and coprime requirements unstated, so it is adequate but not complete.

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%, so the description must compensate. The formula 'inverse of a modulo m' does map both parameters to their roles (value vs modulus), which is the essential semantics. But it gives no format guidance despite both parameters being typed as strings, leaving an agent unsure whether to send decimal, hex, or big-integer text.

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 precise verb and mathematical resource ('Finds the modular multiplicative inverse of a modulo m') plus the failure outcome ('or null when none exists'). This is far more specific than the bare tool name, but it does not differentiate itself from related siblings such as x402-extended-gcd, which computes the same inverse as a byproduct.

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 guidance on when to call this versus x402-extended-gcd, x402-pow-mod, x402-chinese-remainder, or any other modular-arithmetic sibling. Usage is only implied by the mathematical statement, and no prerequisites (e.g. a and m must be coprime) are mentioned.

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