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

The annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so safety behavior is covered. The description adds useful behavioral context: pricing at $0.001 USDC per successful call via x402 on Solana, plus an equivalent HTTPS endpoint.

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 description is front-loaded with the core mathematical definition and examples, then appends domain, price, and endpoint details. Every sentence is useful and there is 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 simple read-only pure computation with no output schema, the definition, examples, valid input range, pricing, and alternate endpoint give an agent everything needed to invoke it correctly. Return semantics are clear from the mathematical definition and examples.

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%, so the description must carry parameter meaning. It defines n through the omega function and states that n runs from 1 to 1000000000000, reinforced by examples; this is sufficient for the single required parameter, though type information is left to the schema.

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 specific mathematical function, 'the number of distinct prime factors of n,' and gives concrete examples: omega(1)=0, omega(4)=1, omega(30)=3. This is clear, but it does not explicitly distinguish the tool from the sibling big_omega, which likely counts prime factors with multiplicity.

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 explains what the function computes and gives its valid range, but it does not say when an agent should choose this tool over alternatives such as big_omega. It also provides no explicit usage conditions beyond the input domain.

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