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

Annotations already declare read-only, idempotent, open-world, and non-destructive behavior. The description adds meaningful context beyond that: pricing per successful call, payment/access details, and the zero-modulus rejection rule. It does not contradict the annotations.

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 definition is front-loaded with the core computation and example, followed by constraints and access details. It is appropriately sized and contains no filler.

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?

With no output schema, the example result C(10) mod 7 = 5 helps indicate the return value. Input constraints and payment/access context are also included. An explicit return-type statement would make it fully complete, but the description is sufficient for correct invocation.

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 explain parameters, and it does: n is bounded to 0-200, and mod is a positive decimal integer with zero rejected. It does not mention the 600-digit maximum or string representation, but the core semantics are covered.

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 states a specific operation, C(n) mod m for central binomial coefficients, and gives a concrete example. This clearly distinguishes it from siblings such as central_binomial and central_sum by the modulo operation.

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 provides useful invocation constraints: n runs from 0 to 200, the modulus must be a positive decimal integer, and zero is rejected. However, it does not explicitly say when to choose this tool over related siblings like central_binomial or factorial_mod.

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