find_social_numbers

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 tool finds sociable numbers but gives no information about computational limits, performance characteristics, error handling, or output format. For a tool with two parameters and no output schema, this lack of behavioral context is a significant gap, leaving the agent with insufficient information to predict the tool's behavior.

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 very concise—a single sentence followed by domain/category tags. It avoids unnecessary words and gets straight to the point. However, the domain/category tags might be considered slightly redundant if the server context already implies arithmetic/special numbers, but they don't significantly detract from conciseness.

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 complexity (finding mathematical sequences with two parameters), the lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to explain parameters, behavioral traits, or output expectations. For a tool in a server with many mathematical functions, more context is needed to guide effective use.

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 schema description coverage is 0%, meaning the input schema provides no descriptions for the parameters 'limit' and 'max_chain_length'. The tool description does not mention these parameters at all, failing to compensate for the schema's lack of documentation. This leaves the agent guessing about what 'limit' and 'max_chain_length' mean in the context of finding sociable numbers.

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: 'Find sociable numbers (amicable chains of length > 2).' It specifies the mathematical concept (sociable numbers) and distinguishes them from amicable pairs by noting chains of length > 2. However, it does not explicitly differentiate from sibling tools like 'find_amicable_pairs' beyond the domain/category tags, which is why it doesn't reach 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 includes domain and category tags ('Domain: arithmetic, Category: special_numbers'), but these are generic and don't help an agent choose between this and similar sibling tools (e.g., 'find_amicable_pairs', 'amicable_numbers', 'aliquot_sequence_analysis'). There's no mention of prerequisites, constraints, or typical use cases.

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