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

Annotations already cover safety (readOnly, idempotent, non-destructive), so the description is free to add what they can't: a per-call price of $0.001 USDC via x402 on Solana, and the output-shape rule that values past 15 digits come back as a decimal string. That pricing detail is exactly the kind of behavioral fact an agent needs before calling a paid endpoint.

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, then examples, then the disambiguation, then constraints, then economics and access path — five dense sentences with no filler. Nothing is repeated that the schema or annotations already state verbatim.

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 carries the return-value burden and does so for the large-value case (decimal string), though it doesn't say what a small value looks like (presumably an integer). Together with the range, the cost, and the alternate transport, an agent has enough to call this 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 coverage is 0%, but with a single integer parameter bounded 1-200 in the schema the description's restatement of that range adds little. Its only genuine semantic contribution is embedding n in the formula definition (k runs 0 to n-1), which clarifies what n actually indexes.

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: computes the Kurepa function K(n) as the sum of k! for k=0..n-1, with concrete examples (K(5)=34) and an explicit disambiguation from the subfactorial. What keeps it from a 5 is that it never references the closest sibling, kurepa_mod, so an agent scanning the catalog must infer which of the two is the plain-value variant.

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 bounds the domain (n from 1 to 200) and discloses the cost and an HTTPS alternative, which tells the agent it is viable for direct calls. It gives no explicit guidance on when to prefer this over kurepa_mod or any other factorial-sum tool, so usage is only implied.

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