pentagonal_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. It only states what the tool calculates, without mentioning any behavioral traits such as input validation (e.g., whether 'n' must be positive), performance characteristics, error handling, or output format. For a tool with no annotations, this leaves significant gaps in understanding how it 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 and front-loaded: a single sentence that directly states the tool's purpose, followed by a brief domain/category note. Every word earns its place with no redundancy or unnecessary elaboration, making it efficient for quick understanding.

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 insufficient. It doesn't explain what a pentagonal pyramidal number is, the formula or method used, valid input ranges, or what the output represents (e.g., integer result). For a tool with these contextual gaps, more detail is needed to be complete.

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 adds minimal semantics by implying 'n' is an index ('nth'), but does not clarify its meaning (e.g., that it represents position in the sequence) or constraints (e.g., non-negative). This provides some value over the bare schema, but doesn't fully compensate for the low coverage, aligning with the baseline for partial compensation.

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 pentagonal pyramidal number.' It specifies the verb ('calculate'), resource ('pentagonal pyramidal number'), and parameter ('nth'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'pentagonal_number' or 'square_pyramidal_number' beyond the domain/category note, which limits full sibling distinction.

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 ('figurate_numbers'), but this is generic context that doesn't help an agent choose between similar tools like 'pentagonal_number' or other pyramidal number calculators. There are no explicit when/when-not instructions or named alternatives.

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