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

Annotations already cover safety (readOnly, idempotent, non-destructive), and the description adds real behavioral context beyond them: the cross-consistency requirement between the two modes, rejection of unreduced fractions, a per-call price ($0.001 USDC via x402 on Solana), and an equivalent HTTPS endpoint. These are exactly the operational facts an agent cannot infer 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?

Front-loaded with the tool's identity and the two usage modes in the first two sentences, then constraints, then commerce details. Every sentence carries information; only the trailing endpoint sentence is slightly bulky, though it remains useful.

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 does convey what is returned (an nth rational, or an index) and the invariants around it. It leaves open the exact return shape (e.g., 'a/b' string vs object) and the input bounds, which are small but real gaps.

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 has to carry the semantics, and it does: n is the tree index, num/den are the reduced fraction used for the inverse lookup, and they must agree when both are sent. It omits the schema's numeric bounds (n up to ~1e15, num/den capped at 2000), which would matter for validity.

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?

States a specific mathematical resource (the Calkin-Wilf tree) with both directions spelled out: n → nth positive rational starting at 1/1, or num/den → index. An agent can tell it is a bidirectional enumeration map, though it never distinguishes itself from related siblings like stern, farey_child, or mediant.

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?

Clearly says which input mode to use: pass n for the nth rational, or a reduced num and den for the index, and that both must agree when supplied together. It also states a rejection rule (unreduced fractions) but names no alternative tools or when-not-to-use conditions.

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