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

Annotations already cover safety (readOnly, idempotent, non-destructive), and the description adds genuinely new context: a per-call price of $0.001 USDC via x402 on Solana and an equivalent HTTPS endpoint. It does not state whether out-of-range n errors or clamps, which is the main remaining behavioral gap.

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 pricing/endpoint. Four sentences each carrying information; only the enumeration of four example values borders on excess.

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?

No output schema exists, and the examples effectively communicate return values (a single integer sum), which is the key missing piece. Pricing and alternate transport are covered. Only edge-case behavior for n outside range or at boundary values is left unstated.

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 compensate. It does clarify that n is an inclusive upper bound ('at most n') and restates the 1–10000 range, but adds no format/type/edge-case detail beyond the schema's min/max.

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+resource: the sum of Carmichael numbers at most n, and gives worked examples (561→561, 1105→1666) that pin down exactly what is being summed. It never names the closest siblings (carmichael, carmichael_count, carmichael_number), so the agent must infer the distinction from 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?

The domain constraint ('n runs from 1 to 10000') and the examples imply intended usage, but there is no explicit when-to-use or when-not-to-use guidance relative to carmichael_count or carmichael_next. No prerequisites or failure conditions are described.

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