ford_circle_properties

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 mentions what the tool analyzes (properties of Ford circles) but doesn't disclose any behavioral traits such as computational complexity, output format, whether it's read-only or has side effects, error conditions, or performance characteristics. For a tool with no annotation coverage, this is insufficient.

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 appropriately concise with a single sentence that states the core purpose, followed by domain/category metadata in parentheses. There's no wasted verbiage, and the main purpose is front-loaded. However, the parentheses content could be integrated more smoothly.

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 has no annotations, no output schema, and 0% schema description coverage for its single parameter, the description is incomplete. It doesn't explain what properties are analyzed beyond tangency, what the output looks like, or what the parameter 'n' means. For a mathematical tool with specific domain knowledge required, this leaves significant gaps for an AI agent to understand how to use it correctly.

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% schema description coverage, meaning the parameter is completely undocumented in the schema. The description provides no information about what 'n' represents (e.g., maximum denominator, sequence index, or other context). The description fails to compensate for the complete lack of parameter documentation in the schema.

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 states the tool 'Analyze properties of Ford circles including tangency relationships', which provides a general purpose (analyze properties) and resource (Ford circles). However, it's vague about what specific properties are analyzed beyond tangency relationships, and it doesn't differentiate from sibling tools like 'ford_circles' which might have overlapping functionality.

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 a domain (arithmetic) and category (farey_sequences) in parentheses, but this doesn't constitute practical usage guidance. There's no mention of prerequisites, when-not-to-use scenarios, or explicit alternatives among the many sibling tools.

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