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 genuinely useful behavioral context: the input domain cap of 1,000,000, the per-call price of $0.001 USDC, and an alternate HTTPS endpoint. It does not state the explicit return shape, but 'whether ... sum to 2n' strongly implies a boolean.

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?

Three tight sentences: the predicate first, then confirming and refuting examples, then domain, price, and endpoint. Front-loaded with the core definition and no filler.

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 one-parameter predicate with no output schema, the description covers the definition, domain, cost, and transport, which is enough to call it correctly. The only minor gap is not explicitly saying the result is a boolean value rather than a sigma sum.

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 bears the burden; it compensates by stating 'n runs from 1 to 1000000', clarifying the domain of the single parameter even though the schema only encodes it as min/max. It adds no detail on what n represents beyond the mathematical definition already given.

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 opening sentence gives a specific definition ('bi-unitary divisors of n sum to 2n') and the concrete true/false examples (6, 60, 90 vs 16, 24, 36, 48) make the predicate unambiguous. It does not explicitly contrast with nearby siblings like biunitary_sigma, biunitary_abundant, or perfect_check, so sibling differentiation is left implicit.

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 1000000' and the worked examples imply when the tool applies, and the price line signals cost-sensitive usage. There is no explicit guidance on when to use this versus biunitary_sigma or the general perfect_check, so routing still requires inference.

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