centered_triangular_number

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates a value, implying it is a read-only operation, but does not specify computational complexity, error handling (e.g., for negative inputs), or output format. The description lacks details on whether it handles large integers, returns a specific data type, or has any side effects, which are gaps for a tool with no annotation coverage.

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 concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information is brief and relevant. There is no wasted verbiage, making it efficient for quick understanding, though it could benefit from more detailed usage or parameter guidance.

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?

Given the tool's mathematical nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain the formula or behavior, provide examples, or clarify the output. For a tool that performs a specific calculation, more context on the mathematical definition and expected result is needed to be fully helpful to an agent.

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?

The input schema has one parameter 'n' with 0% description coverage, and the tool description does not add any semantic information about 'n'. It does not explain what 'n' represents (e.g., integer index starting from 1), valid ranges, or examples. With low schema coverage, the description fails to compensate, leaving the parameter's meaning unclear beyond its type.

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 states the tool's purpose: 'Calculate the nth centered triangular number.' It specifies the verb ('calculate') and the resource ('centered triangular number'), and distinguishes it from other triangular number tools (e.g., 'triangular_number', 'triangular_numbers') by specifying the 'centered' variant. However, it does not explicitly differentiate from 'centered_polygonal_number' or 'centered_square_number' among siblings, which are similar figurate numbers.

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 provides minimal usage guidance. It includes a domain ('arithmetic') and category ('figurate_numbers'), which implies context but does not specify when to use this tool versus alternatives like 'triangular_number' or 'centered_polygonal_number'. There is no explicit mention of when-not-to-use or prerequisites, leaving the agent to infer based on the tool name alone.

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