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

Annotations already establish read-only, idempotent, open-world, and non-destructive behavior, so the description is not carrying the full burden. It adds useful context beyond annotations: a $0.001 USDC per successful call cost, x402/Solana payment context, an HTTPS endpoint, input bounds, and concrete example outputs.

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 formula and examples are front-loaded, and the payment/endpoint details are relevant for invoking a paid x402 tool rather than filler. Every sentence contributes useful information, with no redundancy.

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 arithmetic tool with annotations covering safety and side effects, the formula, classification, examples, and bounds are enough to call it correctly. It could be stronger by explicitly defining sigma(n) and stating the return type, since there is no output schema.

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%, and the only parameter is n with min/max bounds already present in the schema. The description repeats the range and adds useful input-output examples, which partly compensates, but it does not define sigma(n) or otherwise explain n beyond the formula.

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 gives an exact formula (2n - sigma(n)) and concrete examples mapping n to outputs (4 -> 1, 6 -> 0, 12 -> -4), so the mathematical purpose is clear. It stops short of a 5 because it does not explicitly say 'computes' or 'returns' and does not name the sibling tool abundance/abundancy as the opposite operation.

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 explicit when-to-use guidance, no condition for choosing this over sibling abundance or abundancy tools, and no exclusions. The classification context ('deficient positive, perfect 0, abundant negative') is informative but does not tell an agent when this tool is the right choice.

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