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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the safety profile is covered. The description adds useful behavioral context: payment cost via x402/Solana, the HTTPS endpoint, zero-rejection behavior, and the residue being smaller than the modulus. It does not describe error responses or rate limits, so it is not fully comprehensive.

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 description front-loads the operation and then compactly states constraints, output bound, price, and endpoint. The sentences are short and largely purposeful, though the pricing and HTTPS endpoint add operational rather than mathematical detail.

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 two-parameter mathematical tool with no output schema, the description defines the computation, valid n range, modulus restrictions, output bound, and payment endpoint. It leaves some error-case behavior to schema enforcement but provides enough information for an agent to call the tool correctly.

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 description coverage is 0%, so the description must compensate. It clarifies that n runs from 1 to 80 and that the modulus must be a positive decimal integer with zero rejected — notably, the schema pattern allows "0" but the description rules it out. However, it omits the 600-digit maximum and string representation details for mod, leaving some semantic gaps.

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 clearly states the mathematical operation (a(n) mod m) and the named sequence (Wedderburn-Etherington numbers), so the resource and computation are identifiable. It does not explicitly contrast with siblings such as wedderburn, wedderburn_sum, or other *_mod tools, so it falls short of a 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 operating constraints (n from 1 to 80, positive decimal modulus, zero rejected), but it does not explicitly say when to choose this tool over wedderburn, wedderburn_sum, or other modular-arithmetic siblings. Usage is implied by the modulo operation, with no stated alternatives or exclusions.

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