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

Annotations already declare readOnly, idempotent, and non-destructive, so the description adds material value: it discloses the algorithmic cutoff (chains past 30 steps or one million are rejected as 'open'), the input domain, and the per-call price. What it leaves ambiguous is whether an 'open' verdict returns false or an error, which matters for interpreting results.

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 core definition is front-loaded in the first sentence, with examples and computation bounds following logically. The x402 pricing and HTTPS endpoint sentence is boilerplate but genuinely useful for callers. No sentence is redundant with another, though the example list is slightly padded.

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 boolean predicate with no output schema, the description covers the definition, examples, domain bound, algorithmic limit, and payment requirements. The only real gap is the unspecified outcome for out-of-range n or for chains classified as open, which an agent would want to know before relying on the return value.

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%, but the single parameter is trivial and the description adds that n is the number under test plus the range 1-2000. The range merely restates the schema's min/max, adding little semantic value beyond the schema. Baseline for one simple, bounded param is 3, and nothing here exceeds it.

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 states a precise predicate: whether n lies on an aliquot cycle of length at least 3, with concrete examples (12496 qualifies; 6, 220, 25 do not). The phrasing 'Whether' makes the boolean-check nature clear enough to distinguish it from chain-returning siblings like sociable_chain or sociable_list-style tools. It does not name a sibling explicitly, so it stops short of a 5.

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?

Usage is implied by the predicate framing — call it to test membership in an aliquot cycle of length >= 3 for a given n. There is no explicit when-to-use guidance, no when-not, and no routing to sibling tools like sociable_chain or sociable_length that also concern sociable numbers. The selection burden is left to the agent.

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