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

Annotations already cover safety and idempotence, but the description adds meaningful behavior: invalid non-cycle inputs are rejected, n is bounded to 1–20000, calls cost $0.001 USDC on success, and an HTTPS/x402 endpoint is provided. It does not contradict the read-only, non-destructive annotations.

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 definition is front-loaded and compact, followed by rejection behavior, input range, pricing, and endpoint. Each sentence or fragment provides useful information for selecting or invoking the tool, with 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 mathematical tool with no output schema, the description supplies the core semantics, valid input range, rejection behavior, examples, cost, and alternate endpoint. The only minor gap is that return format is shown by example rather than explicitly described.

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?

With 0% schema description coverage, the description must carry parameter meaning, and it does: n is the number whose aliquot cycle is queried, must be in 1–20000, and must actually lie on a cycle or the call is rejected. The examples clarify expected return values, though the underlying cycle concept is left fairly terse.

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 first sentence precisely states the operation: return the smallest member of the aliquot cycle containing n. This differentiates it from sibling tools such as sociable_length, sociable_sum, and sociable_chain by focusing on the minimum member rather than the full chain or aggregate.

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 description implies when the tool applies by specifying that n must be on an aliquot cycle and that non-cycle inputs are rejected. However, it does not explicitly name alternatives like sociable_chain or sociable_length, nor does it explain when an agent should choose this minimum-member tool over those siblings.

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