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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description adds genuinely non-structured behavior: a per-call price of $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint. The worked sample values also act as verifiable expected outputs, which is useful transparency. It stops short of saying what happens on out-of-range input or payment failure.

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?

Front-loads the definition in one sentence, then provides compact sample points, the domain constraint, and the payment/endpoint details. The five sample points are slightly list-heavy but each doubles as an output sanity check, so they mostly earn their place.

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 implies an integer count and the sample points make the return format unambiguous (through 30 there are 6). Cost, range, and an alternate transport are covered. The remaining gap is that the mathematical definition of a Zumkeller number is never given, so an agent relying solely on this tool cannot explain the result.

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% and the single parameter has no schema description, so the description carries the burden. It does clarify that n is an inclusive upper bound ('at most n') and repeats the 1..200 range already in the schema's min/max. That is meaningful but minimal — no note on how out-of-range values are handled or that n=200 is the ceiling of the precomputed table.

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 verb and resource: it counts Zumkeller numbers up to an inclusive bound n, which distinguishes it semantically from membership/subset siblings implied by its name (zumkeller, zumkeller_subset, zumkeller_odd). However, no sibling is named or contrasted, so the differentiation is left to the reader to infer from the name alone.

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?

Usage is implied rather than stated: by giving sample counts (through 6 is 1, through 12 is 2) it conveys this is the cumulative counting-function counterpart to a single-number test, but it never says 'use this instead of zumkeller when you need a cumulative count' or states any exclusions. An agent must infer the when-to-use from the samples.

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