tetrahedral_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 calculation but does not mention performance characteristics (e.g., computational complexity for large n), error handling (e.g., for negative inputs), or output format. For a mathematical 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 highly concise and front-loaded: a single sentence that directly states the tool's purpose and includes domain/category in parentheses. There is no wasted verbiage, and every part of the sentence adds value, making it efficient and well-structured.

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 schema coverage, the description is incomplete. It lacks details on output format (e.g., integer result), error conditions, and practical usage examples. While concise, it does not provide enough context for reliable agent invocation 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 1 parameter (n) with 0% description coverage. The description adds meaning by explaining that n is the index for the tetrahedral number calculation, but does not specify constraints (e.g., n must be non-negative integer) or examples. Since schema coverage is low, the description partially compensates but not fully, 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 tetrahedral number (sum of first n triangular numbers).' It specifies the verb ('calculate'), resource ('tetrahedral number'), and mathematical definition. However, it does not explicitly differentiate from sibling tools like 'triangular_number' or 'triangular_sequence', which are related but distinct.

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 ('arithmetic') and category ('basic_sequences'), but does not specify use cases, prerequisites, or comparisons to sibling tools such as 'triangular_number' or 'triangular_sequence'. This leaves the agent without clear direction on tool selection.

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