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

Annotations already supply the safety profile (readOnly, idempotent, non-destructive, openWorld), so this adds real extra context: the comma-separated return shape, the off-cycle rejection behavior, and per-call pricing that is charged only on successful calls, plus an alternate HTTPS endpoint. It stops short of explaining cycle detection edge cases or any auth flow beyond implying x402 payment.

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 core definition and output format, then examples, bounds, and pricing in a logical order. The multiple worked examples are slightly repetitive but each demonstrates a distinct case (2-cycle, fixed point, long cycle), so they mostly earn their place.

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 math tool with no output schema, the description fully specifies output format (comma-separated cycle starting at n), valid input range, invalid-input behavior, and cost. An agent has everything needed to call it and interpret the result correctly.

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 coverage is 0%, so the description carries the burden, and it does well: it explains that n is the starting number of the aliquot cycle, bounds it to 1..20000, and states the rejection condition for off-cycle inputs. The examples (220, 6, 12496) further clarify what counts as a valid n.

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 a specific verb/resource (return the aliquot cycle containing n) plus concrete output examples, so an agent knows exactly what it produces. However, it never distinguishes itself from the sibling tools sociable, sociable_length, sociable_min, and sociable_sum, which likely return related but different slices of the same data.

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?

It gives useful input guidance (n must be on a cycle, otherwise rejected; n in 1..20000), which steers selection somewhat. But there is no explicit statement of when to prefer this over the closely-named sociable/sociable_length/sociable_sum siblings, leaving the alternative-routing implicit.

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