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

Annotations already declare the read-only, idempotent, non-destructive profile, so the description's job is lighter. It adds genuinely useful non-schema behavior: a per-call price of $0.001 USDC via x402 on Solana and an alternative HTTPS endpoint. It does not mention rate limits or error behavior, keeping it short of a 5.

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 definition, then examples, then the valid range, then pricing and the HTTP mirror — every sentence carries information. Slightly denser than necessary because pricing and endpoint metadata sit in the same block, but nothing is wasted.

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?

A one-parameter, annotation-covered math query with no output schema; the description supplies the return meaning plus concrete example outputs (2, 11, 13), which is enough for an agent to call and verify. Missing only explicit sibling routing and failure/pagination-style behavior, which are minor here.

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 must carry the parameter's meaning, and it does define n as the order of the Farey sequence and give its range 1–100000 (matching the schema's min/max). It does not restate the integer type or explain any computational caveats, so compensation is adequate but not rich.

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 computation: the number of reduced fractions in the Farey sequence of order n, spanning 0/1 to 1/1. That is clearly distinct from farey_adjacent and farey_child in substance, but the description never names those siblings, so differentiation is left implicit.

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?

Provides worked examples (order 1 → 2, order 5 → 11, order 6 → 13) that let an agent sanity-check a call, and states the identity with the totient sum. It never says when to prefer this over farey_adjacent/farey_child or what the tool is unsuitable for, so usage is only implied.

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