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

Annotations already declare read-only, idempotent, open-world behavior and non-destructiveness. The description adds valuable context beyond annotations: pricing ($0.001 USDC per successful call via x402 on Solana), an alternative HTTPS endpoint, and the valid input range (1 to 1000000).

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 formula and examples, followed by range and operational details. Every sentence contributes something useful, though the pricing and endpoint information, while helpful, could be considered auxiliary.

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 adequately conveys that the tool returns an integer (the nth upper Wythoff number) and provides examples that clarify the mapping. The range, cost, and endpoint details complete the picture for an agent calling this tool.

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?

With 0% schema description coverage and one required parameter, the description compensates by defining n as the index (1 to 1000000) and giving concrete input-output examples (B(1)=2, etc.). This clarifies the parameter's meaning beyond the bare schema type and min/max.

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 function: the nth upper Wythoff number with formula floor(n*phi^2), plus concrete examples (B(1)=2, B(2)=5, B(5)=13). The word 'upper' distinguishes it from the sibling wythoff_lower, though no sibling is named explicitly.

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 no guidance on when to use this tool versus alternatives like wythoff, wythoff_lower, or wythoff_pair. It describes what the tool computes but not the context or conditions that should lead an agent to select it.

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