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

Annotations already declare readOnly, idempotent, openWorld, and non-destructive behavior. Beyond that, the description adds important behavioral context: a per-successful-call x402 price and an alternate HTTPS POST endpoint. It does not contradict the annotations.

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 definition is front-loaded with the core operation and then supplies only relevant supporting facts: lower/upper encoding, uniqueness of positive integers, valid range, and payment/endpoint details. Every sentence contributes to correct invocation and no unnecessary prose is present.

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?

Given one parameter, no output schema, and annotations covering safety traits, the description is nearly complete. It explains the conceptual return value and encoding, though it does not specify the exact response field names or payload shape.

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 parameter meaning. It explains that m is the positive integer whose containing Wythoff sequence and index are found, which is more than the schema's bare integer/min/max definition. It does not add formatting details beyond that, but the single parameter is semantically clear.

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 specific inverse operation: given m, it returns which Wythoff sequence contains it and at which index. It also defines the lower/upper encoding, making the purpose clear. It does not explicitly differentiate itself from all nearby siblings such as wythoff_kind, but the inverse framing is understandable.

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 implies usage by saying it answers which sequence contains m, and it validates the domain with m from 1 to 1,600,000. However, it does not explicitly state when to use this instead of sibling tools like wythoff_kind or wythoff_pair, leaving sibling selection partly inferential.

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