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

Annotations already establish that this is a read-only, idempotent, non-destructive operation. The description adds useful behavioral context beyond that: the cost per successful call, the x402/Solana payment mechanism, and an HTTPS endpoint alternative. It does not detail rate limits or failure behavior, but the added cost/auth context is meaningful.

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 purpose is front-loaded, followed by terse examples, range, and operational details. There is little waste, though the pricing and HTTPS endpoint information is auxiliary to the core classification task.

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?

For a simple read-only classifier with no output schema, the description is nearly sufficient: it states the operation, gives the input range, provides illustrative examples, and discloses cost/payment context. A formal definition of the Wythoff sequences or an explicit output-shape statement would make it complete.

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 compensate. It repeats the 1..1000000 range and provides examples mapping m values to sequence/index results, but it does not define the lower/upper Wythoff sequences or fully specify the return semantics. This is partial compensation rather than rich parameter documentation.

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 task: determine which Wythoff sequence contains m and its index. The examples ('1 is lower index 1', '2 is upper index 1') reinforce the operation. It does not explicitly differentiate from siblings such as wythoff_lower, wythoff_upper, or wythoff_inverse, but the core purpose is clear.

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 no explicit when-to-use or when-not-to-use guidance, and it never names an alternative sibling tool. Usage is only indirectly implied by the opening question.

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