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

Annotations already declare readOnly, idempotent, openWorld, and non-destructive, so the safety profile is covered. The description adds real context beyond them: the hard cap of n <= 1,000,000, the per-call price of $0.001 USDC via x402 on Solana, and that the same operation is reachable over HTTPS. It does not explain failure behavior for out-of-range n or payment failure, which keeps it below 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 and formulas, then examples, then constraints, then pricing/endpoint. Every sentence is doing work; the only mild duplication is the range restated from the schema, which is justified given the schema has no descriptions.

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?

There is no output schema, so the description must describe the return shape — and it does, naming the two fields (lower, upper) and their relationship. Combined with the index range, examples, and payment model, nothing an agent needs to call it correctly is missing.

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% (bare integer 1..1000000), so the description carries the full burden and does: it defines n as the pair index, states the valid range, and gives worked examples for n=1 and n=5 that let an agent sanity-check a call before or after invoking it. Meaningful compensation for the empty schema.

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 resource ('the nth Wythoff pair') and gives the exact defining formulas (lower = floor(n*phi), upper = lower+n), so an agent knows precisely what is returned. Against siblings like wythoff_lower, wythoff_upper, wythoff_inverse, and wythoff_kind, the definition makes clear this returns both members of the pair at once.

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?

Usage is only implied: an agent can infer this is the tool for getting both pair values together rather than calling wythoff_lower and wythoff_upper separately, but no sibling is named and no when-to-use/when-not guidance is given. Adequate for a self-describing math primitive, but not explicit routing.

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