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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description adds substantial context beyond them: rejection of a zero modulus, the 15-digit threshold after which the result becomes a decimal string, the per-call price of $0.001 USDC via x402 on Solana, and an alternate HTTPS endpoint. Output-format and cost disclosure are exactly the kind of behavior an agent cannot get from structured fields.

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?

Five short sentences, each contributing distinct information; the core identity is front-loaded, followed by constraints, output format, and payment/transport details. Nothing is redundant or padded.

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 three-parameter pure function with no output schema, the description supplies everything an agent needs: input validity rules, modulus behavior, the caveat that large results return as decimal strings, and the payment/endpoint requirement. No material gap remains.

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 carry parameter meaning, and it does: it explains the n/k index range and the k<=n relation, and describes the optional modulus and that zero is rejected. It does not note that mod is passed as a decimal string (up to 200 digits) per the schema pattern, leaving a small gap.

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 mathematical operation, 'The binomial coefficient C(n, k)', which is a specific verb+resource and immediately understandable. It does not, however, distinguish itself from near-neighbors in the large sibling list such as central_binomial, multichoose, or vandermonde, so an agent must infer the boundary itself.

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?

The text gives input constraints (k must not exceed n, indexes up to 4096) but never states when to use this tool versus alternatives like multichoose or central_binomial, nor any preconditions beyond the argument rules. There is no explicit when/when-not guidance, only validity rules.

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