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

Annotations already declare readOnlyHint, idempotentHint and destructiveHint=false, so the safety profile is covered. The description does add non-schema operational context — a $0.001 USDC x402 charge per successful call and an equivalent HTTPS endpoint — which an agent needs before invoking it, though it doesn't say whether failed calls are billed or how the count is returned.

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?

Purpose is front-loaded in the first sentence, followed by quick exemplars, then bounds and pricing. Every clause carries information an agent can act on; nothing is filler despite packing definition, examples, domain, cost and transport into a short block.

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, side-effect-free computation with no output schema, the definition supplies the mathematical semantics, the domain, sample values and the payment/transport details. The only gap is that it never states the return shape (a non-negative integer count), which the agent must infer.

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% (the single property 'n' has no description), so the description must compensate: it defines n as the inclusive upper bound on the integers counted and restates its 0–5000 domain. That is a real semantic addition over the bare integer schema, with only the inclusive/exclusive reading left implicit.

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 counting operation over a precisely defined mathematical property ('how many positive integers through n have at least two writings as a sum of two positive cubes'), which unambiguously separates it from the sibling taxicab (which would return the number itself, not a count). An agent knows exactly what is being computed without opening the schema.

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 range 'n runs from 0 to 5000' and the worked examples (none through 100, 1 through 1729, 2 through 4104) give the agent a sense of scale and let it sanity-check a result, but there is no statement of when to prefer this tool over the sibling taxicab or other cube-related tools (two_cubes, cube_ways).

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