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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, and the description adds genuinely new operational context: a $0.001 USDC charge per successful call via x402 on Solana and an equivalent HTTPS endpoint. It also implicitly guarantees determinism by giving closed-form outputs per case.

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 and the case split, then worked examples, then commercial/reachability details — a sensible ordering with no filler. Slightly dense run-on sentences ('Phi_4(1) is 2, Phi_6(1) is 1, and Phi_9(1) is 3') cost it the top mark.

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, side-effect-free numeric function with no output schema, the description supplies the definition, the edge-case result, example outputs, input bounds, and cost/transport. The only residual gap is the return type, which is implied by the integer examples rather than stated.

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 burden, and it does: n is identified as the index of the cyclotomic polynomial, its domain is restated (1 to 1000000), and the boundary case n=1 is explicitly called out as returning 0. This compensates for the undocumented schema property without fully explaining behavior for the prime-power case.

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 pins down exactly which quantity is computed (Φ_n(1)) and even enumerates the value by case (0 for n=1, p for prime powers, 1 otherwise), which is far more specific than the bare name. It does not, however, distinguish this from close siblings like cyclotomic, cyclotomic_coeff, or cyclotomic_neg, so an agent must infer that this is the 'evaluate at 1' specialization.

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?

There is no statement of when to prefer this over cyclotomic or cyclotomic_coeff, nor any prerequisites or exclusions. The only usage-adjacent facts are the domain of n (repeating the schema's 1..1000000 bounds) and the price/endpoint, none of which tell an agent when to select this tool.

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