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

Annotations already declare readOnly, idempotent, openWorld, and non-destructive, so safety is covered. The description adds genuinely new behavioral context the annotations lack: a per-call price ($0.001 USDC via x402 on Solana) and an alternate HTTPS endpoint, plus the integer-comparison method used to avoid float error.

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, followed by examples and the comparison-method note, with cost and endpoint details last. Every sentence is relevant, though the pricing/endpoint line is appended rather than integrated.

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-integer predicate tool with no output schema, the description is nearly complete: it defines the predicate, gives examples, and states the range and cost. The only gap is that it never explicitly says the return value is a boolean result, though 'Whether...' strongly implies it.

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 for the single parameter n. It states the range 1 to 10000, but that merely repeats the schema's min/max; it does not explain the semantic role of n beyond the surrounding definition of the predicate.

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 precise mathematical predicate (sigma(n)/n strictly larger than sigma(m)/m for every m below n), not just a restatement of the name. The worked examples (1,2,4,6,12 are; 3,8,16 are not) let an agent distinguish it from nearby siblings like abundancy, abundance, and highly_abundant without opening the schema.

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 10000) is stated, which effectively tells the agent the valid input range. However, there is no explicit when-to-use guidance or routing to alternative siblings such as abundancy or highly_abundant, so usage is only implied.

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