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

Annotations already declare readOnly/idempotent/non-destructive, so the description's main added value is the pricing model ($0.001 USDC per successful call via x402 on Solana) and the alternative HTTPS endpoint — genuinely important context an agent would otherwise not have. It does not describe error or failure-charging behavior beyond 'per successful call'.

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?

Front-loaded with the core formula, then examples, bounds, price, and endpoint — each sentence carries information. Three worked examples is slightly more than needed when one or two would fix the mapping.

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 description should clarify the return value; the examples imply a non-negative integer in [0, m) but this is never stated. The bigger gap is the undefined trinomial sequence definition for a tool whose output depends entirely on it.

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 the description does explain that n indexes T (0–30) and m is the modulus (1–1,000,000), plus examples showing result format. But the stated ranges merely restate the schema's min/max, and the meaning of T itself remains undefined, so compensation is partial.

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 gives a formula shape ('T(n) modulo m') plus three worked examples that partially pin down the sequence, which distinguishes it from trinomial_sum/trinomial_term. However, it never states what T actually is (trinomial coefficient vs. central trinomial coefficient), so an agent must infer the sequence from examples or the sibling 'trinomial' tool.

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?

No statement of when to use this versus the many related siblings (trinomial, trinomial_sum, trinomial_term, trib_mod, central_mod). The only context is the input domain and the note that the same tool exists over HTTPS, which is deployment info rather than selection guidance.

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