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

Annotations already cover safety (readOnly, idempotent, non-destructive), so the description earns credit for adding what annotations cannot: explicit rejection behavior for non-terms and leading zeros, the 600-digit input ceiling, per-call pricing ($0.001 USDC via x402/Solana), and an alternate HTTPS endpoint. It does not describe the error response shape or confirmation of returned index, a minor gap.

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 core definition is front-loaded in the first sentence, followed by clarifying examples (index 1 -> 1, index 6 -> 6) and then constraint/price/payment details. The pricing and endpoint sentences are slightly extraneous to task selection but are operationally relevant; nothing is repeated wastefully.

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 single-parameter lookup with no output schema, the description covers input format, error conditions, cost, and transport alternative, and the opening sentence implies the return value is the index n itself. It would be complete at 5 if it explicitly stated what is returned on rejection (error vs empty) or clarified that output is n as a decimal string.

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 carries the load: it explains that value is a decimal integer capped at 600 digits and adds a constraint the schema pattern (^[0-9]{1,600}$) does NOT capture – that leading zeros are rejected. That is genuine meaning beyond the structured field; it could go further by describing the value as 'a Wedderburn-Etherington number a(n)' explicitly tied to the parameter.

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 precise verb-free but specific mathematical relation: 'the smallest index n with Wedderburn-Etherington number a(n) equal to value' – an agent immediately knows this is the inverse lookup for the Wedderburn-Etherington sequence, distinct from wedderburn/wedderburn_sum/wedderburn_mod siblings. It stops short of naming a sibling to redirect to (e.g. use wedderburn to enumerate terms), so it lands at 4 rather than 5.

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 conditional rules for valid input ('a number that is not a term, or a leading zero, is rejected'), which implicitly bounds when the call will succeed. However, it never states when to prefer this over siblings like wedderburn or wedderburn_mod, nor any prerequisites beyond the input format, leaving usage context to inference.

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