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

The annotations already declare read-only, idempotent, open-world, and non-destructive behavior, so the safety profile is covered. The description adds meaningful operational context beyond annotations: the $0.001 USDC x402 payment requirement on Solana and the equivalent HTTPS endpoint. It does not describe error behavior for invalid inputs, but it is substantially transparent for a paid endpoint.

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 description is front-loaded with the mathematical definition and identity, followed by a concrete example, constraints, range, and payment/endpoint details. Every sentence contributes either semantic clarification or operational information.

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 carries the burden of explaining the return value. It gives the closed form and a worked example, which strongly implies the integer sum result, and it covers parameter ranges, constraints, payment, and transport. It could be slightly more explicit about the return type or error behavior, but it is otherwise complete for a simple two-parameter math tool.

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. It identifies n and r as the summation bounds, states the cross-parameter constraint that r must not pass n, gives the valid range 0 to 1024, and provides a worked example with r=2 and n=5 yielding 20.

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 precise mathematical operation: the hockey-stick sum of binomial coefficients C(i, r) from i=r through n, and even gives its closed form C(n+1, r+1). This distinguishes it from sibling tools like binom by clearly describing a summation over a range rather than a single binomial coefficient.

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 description gives important usage constraints: r must not exceed n and both parameters run from 0 to 1024. However, it does not explicitly say when to use this tool versus alternatives such as binom or other summation tools, so the guidance is implied rather than comparative.

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