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

Annotations already declare read-only, idempotent, open-world, and non-destructive behavior. The description adds important behavioral context beyond annotations: it is a paid x402/Solana call costing $0.001 per successful invocation and is also available over HTTPS at a specific 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 tool's purpose and remains reasonably tight. The examples and payment/endpoint details are useful, though the four-example enumeration is slightly dense.

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 count tool with one bounded parameter and no output schema, the definition is nearly complete: it explains the quantity computed, the input bound, and gives examples that implicitly convey return values. A brief explicit return-type statement would make it fully complete.

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 does so by defining n as the upper bound ('at most n'), restating the 1–2000 range, and providing worked examples that map specific n values to counts.

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 counting operation: how many Higgs primes with exponent 2 are at most n. The phrasing and examples clearly distinguish this counting tool from sibling generation/index tools such as higgs_next or higgs_index.

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 gives the valid domain for n (1 to 2000) and worked examples, which implies when the tool is applicable. However, it does not explicitly say when to use this instead of sibling tools like higgs or higgs_next, nor does it state exclusions.

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