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 real context beyond them: explicit rejection of non-Keith inputs, a $0.001 USDC per-successful-call x402/Solana pricing model, and an HTTPS endpoint alternative. It does not describe the error shape returned on rejection or latency/confirmation behavior, so it stops short of a 5.

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 definition leads with the semantics and examples before constraints and pricing, and every sentence carries information. The 'Same tool over HTTPS: POST ...' line is useful but placed last where it is slightly awkward, and the first sentence's phrasing is denser than it needs to be.

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 must convey what comes back, and it does via the step-count definition and the 14→3 / 197→5 examples, plus rejection behavior and cost. Missing only explicit error/response shape for the rejected case and any note about the paid-call failure mode, which are minor for a single-integer pure function.

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?

The single parameter n has 0% schema description coverage, so the description must compensate. It gives the range (1 to 1000000, duplicating the schema min/max) and demonstrates meaning through the 14 and 197 examples, but never says plainly that n is the integer to test for Keith-ness. Partial compensation, not full.

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 states a specific computation ('how many new terms are generated... before a Keith number reaches itself') and grounds it with two worked examples (14→3, 197→5), which is far more concrete than a bare 'Keith steps'. It implicitly distinguishes itself from siblings like keith/keith_count/keith_next by returning a step count rather than a boolean, count, or next value, but it never names those siblings explicitly.

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 only implied: 'A number that is not Keith is rejected' and the 1–1000000 bound tell the agent what inputs are valid, but there is no statement of when to choose this over keith, keith_count, keith_next, or keith_row. The agent must infer the selection rule from the phrase 'how many new terms'.

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