centered_hexagonal_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 but does not describe any behavioral traits such as input validation (e.g., handling negative 'n'), performance characteristics, error conditions, or output format. For a computational tool with zero annotation coverage, this is a significant gap in transparency.

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 extremely concise and front-loaded: a single sentence stating the core purpose, followed by domain/category in parentheses. Every word earns its place with no redundancy or unnecessary elaboration, making it efficient for quick comprehension.

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 computational nature, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on behavior, parameter semantics, output format, and usage context. While concise, it does not provide sufficient information for an agent to confidently invoke the tool without additional assumptions.

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, so the schema provides no semantic context. The description adds minimal value by implying 'n' is an index ('nth'), but does not explain its meaning (e.g., integer position in the sequence), constraints (e.g., non-negative), or examples. With low schema coverage, the description compensates inadequately, warranting a baseline score.

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 hexagonal number.' It specifies the verb ('calculate') and resource ('centered hexagonal number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'centered_polygonal_number' or 'centered_square_number', which would require more specific guidance on when to use this particular figurate number tool.

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 does not specify scenarios, prerequisites, or comparisons with sibling tools (e.g., 'centered_polygonal_number', 'centered_square_number'). Without explicit when-to-use or when-not-to-use instructions, the agent lacks contextual direction.

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