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

Annotations already declare the tool as read-only, idempotent, non-destructive, and open-world, so the safety profile is covered. The description adds useful behavioral context by disclosing the cost per successful call, the x402/Solana payment context, the HTTPS endpoint, the accepted n range, and sample return values.

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 compact examples, range, price, and endpoint information. Every sentence carries useful information 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 one-parameter mathematical tool with rich annotations and no output schema, the description is nearly complete: it defines the result, gives examples, states the valid range, and discloses payment/transport details. The only minor gap is not explicitly stating the return type, though the examples make it clear.

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 has to compensate for the single undocumented parameter. It does so by saying n runs from 0 to 80 and by giving example inputs and outputs, though it largely repeats the schema's min/max bounds rather than adding richer parameter semantics.

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 overpartitions of n, and defines the object well enough to distinguish it from ordinary partition tools by noting the first part may be overlined. It also anchors the meaning with concrete values such as 1, 2, 4, 8, 14, 24 and examples for n=4 and n=10.

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 to use the tool by defining the overpartition function and giving the valid n range, but it does not explicitly compare it with sibling tools such as partition or partition_distinct. The usage context is inferable rather than stated.

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