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

Annotations already declare readOnly, idempotent, non-destructive, and open-world behavior. The description adds valuable behavioral context beyond annotations: per-call pricing, x402/Solana payment, an HTTPS endpoint, and that values longer than 15 digits are returned as decimal strings.

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 compact and front-loads the defining identity before field mapping, input constraints, formatting, and access details. Every sentence contributes useful information with 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 one-parameter read-only math tool with no output schema, the description covers the core operation, returned fields, input range, large-result formatting, payment, and transport. It could be slightly more complete by explicitly distinguishing itself from nearby Jacobsthal tools, but no critical invocation information is missing.

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 explain the single parameter. It does so by stating that n runs from 0 to 8191 and why (so n+1 stays in range), and by tying n to J(n) and J(n+1), adding meaning beyond the min/max constraints in 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 clearly identifies the mathematical operation via the Jacobsthal identity and maps the returned fields: left=J(n), right=J(n+1), value=sum. It is specific, but it does not explicitly distinguish this tool from sibling Jacobsthal tools such as jacobsthal, jacobsthal_add, jacobsthal_lucas, or jacobsthal_sum.

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 states the valid range for n and the paid/HTTPS access details, but gives no guidance on when to use this tool instead of the sibling Jacobsthal tools. The formula implies its use, but no alternatives or exclusions are named.

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