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

Annotations already declare readOnly/idempotent/non-destructive, and the description adds material context the annotations cannot carry: per-call cost ($0.001 USDC via x402 on Solana) and an alternate HTTPS transport with a concrete URL. It stops short of describing the returned value's form (e.g., big decimal string vs integer).

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 operation is front-loaded in three characters, followed by worked examples, then constraints, then commercial terms. Every sentence either disambiguates semantics or discloses cost/transport; nothing is redundant.

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 pure-computation tool with no output schema, the description covers input validity, cost, and alternate access path. The only real omission is the shape of the return value, which matters given a 600-digit modulus.

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%, so the description must compensate, and it does: it clarifies that 'mod' is a positive decimal integer with zero rejected and bounds n to 0..100000. It does not explain that mod is passed as a string to allow up to 600 digits, which is the one non-obvious schema detail left implicit.

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 opens with the exact operation, 'n! mod m', plus two worked examples (0! mod 5 = 1, 10! mod 97 = 30) that pin down edge-case semantics. Among dozens of factorial-adjacent siblings (factorial_prime, factorial_valuation, alt_factorial, double_factorial), the verb+resource is unambiguous here.

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?

It gives domain constraints for the inputs (modulus must be positive, zero rejected, n in 0..100000), which effectively defines when the call is legal. However, it never states when to prefer this tool over a sibling or the HTTPS endpoint beyond naming the endpoint, and there are no explicit exclusions.

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