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

The annotations already establish that this is a read-only, idempotent, non-destructive operation. The description adds useful behavioral context beyond that: valid n range, example outputs, per-call pricing, and an HTTPS alternative 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 definition is front-loaded with the core behavior and examples, then adds range, price, and endpoint information compactly. Every sentence contributes practical calling or selection context.

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 deterministic function with no output schema, the description supplies enough to invoke it correctly: domain, examples, cost, and alternate transport. It could be slightly more complete with a brief definition of Moran numbers or error behavior.

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 must carry parameter meaning. It does this reasonably well by stating that n runs from 1 to 5000 and providing several concrete n-to-result examples, though it does not formally define the Moran-number property.

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 precise operation: returning the smallest Moran number that is at least n, with concrete input-output examples. It is clear what the tool computes, but it does not distinguish itself from sibling tools such as moran, moran_count, moran_ratio, or moran_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?

The description gives the input range and examples, but it does not say when to use this tool versus the many related Moran or sequence tools. There are no explicit exclusions, prerequisites, or alternative-selection guidance.

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