triangular_pyramidal_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. The description only states what the tool calculates without mentioning any behavioral traits such as input validation, error handling, performance characteristics, or output format. For a mathematical function with no annotation coverage, this leaves significant gaps in understanding how the tool behaves.

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 with zero wasted words. The single sentence efficiently conveys the core purpose, and the parenthetical domain/category information is appropriately brief. It's front-loaded with the main functionality and doesn't contain any redundant or unnecessary information.

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 lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. While the tool is mathematically simple, the description doesn't address what the tool returns, how it handles edge cases (negative n, large n), or any mathematical properties of triangular pyramidal numbers. For a tool with no structured documentation, more context would be helpful.

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 description mentions 'nth' which corresponds to the single parameter 'n' in the schema, but provides no additional semantic context beyond what's implied by the tool name. With 0% schema description coverage and only one parameter, the description doesn't compensate by explaining what 'n' represents (e.g., that it should be a non-negative integer, or its mathematical meaning). The baseline is appropriate given the single parameter.

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 calculates the nth triangular pyramidal number (tetrahedral), providing a specific verb ('calculate') and resource ('triangular pyramidal number'). It distinguishes from siblings by specifying the mathematical domain (arithmetic) and category (figurate_numbers), though it doesn't explicitly differentiate from similar figurate number tools like 'tetrahedral_number' or 'square_pyramidal_number' in the sibling list.

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. While it mentions the domain and category, it doesn't indicate scenarios where this specific figurate number calculation is appropriate or suggest alternative tools for related calculations. There's no mention of prerequisites, constraints, or comparison with sibling tools.

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