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

Annotations already declare readOnly/idempotent/non-destructive, so the description's real value-add is operational: $0.001 USDC per successful call via x402 on Solana, plus a plain HTTPS fallback endpoint. That payment/auth detail is not derivable from annotations. It omits return type/pagination, but for a scalar count that gap is minor.

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-loaded with the definition, then examples, then bounds, then payment/logistics, which is a sensible order. Dense but no filler; the URL and price could arguably be split out, but they earn their place for billing awareness.

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 pure math function with no output schema, the description covers semantics, domain, examples, and access/cost. The only omission is an explicit statement that the result is a single integer.

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 only parameter name 'n' is opaque on its own. The description defines n as the square side length, supplies the range and three concrete outputs, which materially improves the agent's ability to pick a valid value.

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 computed quantity: the count of lattice points (x,y) with 1<=x,y<=n and gcd(x,y)=1, i.e. visible from the origin. The mathematical definition plus worked examples (1, 3, 19) make it unmistakable against siblings like totient or squarefree_count.

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?

Gives a clear domain ('n runs from 1 to 100000') and sample values an agent can use to sanity-check calls, which is enough context to invoke confidently. It does not name alternative siblings or say when not to use it, so it stops short of explicit routing.

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