square_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 computational characteristics (e.g., performance with large n, error handling, or output format). For a mathematical function with no 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 concise and front-loaded, with the core purpose stated first. The domain/category annotation is brief and doesn't add unnecessary length. However, the lack of usage or parameter details means it's under-specified rather than optimally concise, slightly reducing the score.

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 parameter coverage, the description is incomplete. It doesn't explain the return value (e.g., integer result), error conditions, or mathematical definition of square pyramidal numbers. For a tool with minimal structured data, more descriptive context is needed.

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, documenting only the parameter type (integer n). The description adds no parameter semantics beyond the name 'n' implying an index. It doesn't explain valid ranges (e.g., n ≥ 1), units, or examples. With low schema coverage, the description fails to compensate adequately, resulting in 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 square pyramidal number.' It specifies the verb ('calculate') and resource ('square pyramidal number'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'triangular_pyramidal_number' or 'pentagonal_pyramidal_number' beyond the name, which prevents 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 ('arithmetic') and category ('figurate_numbers'), but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'triangular_number' or 'polygonal_number'. This leaves the agent with insufficient context for tool selection.

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