Applicability checklist

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It clearly states the behavior (decompose statement, check applicability) and warns about catching misapplications. The existence of an output schema (per context) compensates for lack of output details in the description. A slight deduction for not explicitly stating it is read-only.

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: two sentences that deliver purpose, usage, and a concrete example. Every sentence earns its place with no redundancy or fluff.

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 (one parameter, clear behavior, output schema exists), the description is complete. It explains why, when, and how to use the tool, and the example clarifies the value. No gaps remain.

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?

Schema coverage is 100% for the single parameter, and the schema description already explains it. The description adds context by calling it 'the result's statement text', reinforcing its role. This is adequate but not exceptional.

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 explicitly states it decomposes a candidate theorem into atomic preconditions and conclusion for verification, with a concrete example (closed-interval theorem misapplication). This clearly distinguishes it from sibling tools that focus on search, identification, or formal verification.

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 explicit usage guidance: 'Use after search, before relying on any candidate.' This tells the agent when to invoke this tool relative to other steps, effectively distinguishing it from sibling tools used at different stages.

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