centered_square_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 only states what the tool calculates without mentioning any behavioral traits such as input validation (e.g., handling negative integers), performance characteristics, error handling, or output format. For a tool with no annotation coverage, this leaves significant gaps in understanding how the tool behaves beyond its basic function.

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. It avoids unnecessary details and wastes no words, making it efficient for quick understanding. However, the inclusion of domain and category in parentheses, while helpful, slightly detracts from absolute minimalism.

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 complexity (a mathematical calculation with one parameter), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what a centered square number is, provide examples, describe the output, or address potential edge cases. For a tool with no structured support, more contextual information is needed for effective use.

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 0% description coverage, with a single parameter 'n' of type integer. The description does not add any semantic meaning beyond the schema—it doesn't explain what 'n' represents (e.g., the index of the centered square number), valid ranges, or examples. With low schema coverage, the description fails to compensate, leaving the parameter's purpose unclear.

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 square number.' It specifies the verb ('calculate') and resource ('centered square number'), and distinguishes it from siblings by mentioning the domain 'arithmetic' and category 'figurate_numbers', which helps differentiate it from other mathematical tools. However, it doesn't explicitly contrast with similar tools like 'centered_hexagonal_number' or 'centered_polygonal_number', preventing a perfect score.

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 no guidance on when to use this tool versus alternatives. It mentions the domain and category but doesn't specify scenarios where centered square numbers are applicable, nor does it refer to sibling tools like 'centered_hexagonal_number' or 'polygonal_number' for comparison. Without any usage context or exclusions, the agent lacks direction on appropriate application.

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