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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, openWorld), so the description adds genuinely new behavioral facts: a per-call cost of $0.001 USDC via x402 on Solana, charged only on success, plus an equivalent HTTPS endpoint. That cost/payment detail is exactly the kind of context an agent cannot get from structured fields.

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 and examples are front-loaded, and each later sentence carries distinct information (domain, price, alternate endpoint). Slight redundancy in repeating the numeric bounds already present in the schema keeps it from a 5.

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, no-output-schema tool, the examples effectively stand in for a return-value description, and the cost/transport notes complete the picture. What is missing is minor: behavior at the top of the range (whether a result always exists for n up to 2000).

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 carry the parameter meaning — and it does, by defining n semantically and illustrating the mapping (1→14, 14→14, 15→19, 76→197), which shows both the lower-bound semantics and the boundary behavior. The stated range 1–2000 largely restates the schema min/max, so it adds little beyond the examples.

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 gives a precise verb+resource: the smallest Keith number that is at least n, backed by three concrete input/output examples. It is clearly distinct from the neighboring keith/keith_count/keith_row/keith_steps family in behavior, though it never names those siblings to contrast itself against.

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 by the worked examples and the stated domain (n from 1 to 2000), which is enough to know the tool suits 'next Keith number >= n' queries. However, there is no explicit routing guidance against keith, keith_count, keith_row or keith_steps, and no statement of when not to use it.

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