Applicability checklist

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

Annotations already declare readOnlyHint=true and idempotentHint=true, so the tool is safe and idempotent. The description adds that the tool decomposes statements into preconditions and conclusion for the agent to verify, disclosing that the tool outputs a checklist rather than performing verification itself.

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?

Two sentences with no extraneous information. The core action is front-loaded, followed by a concise usage instruction. Every sentence serves a clear purpose.

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 that an output schema exists, the description does not need to explain return values. It covers purpose, usage context, and parameter semantics adequately for a simple tool with one parameter.

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 description coverage is 100%, and the description reiterates the parameter's meaning as 'the candidate result's statement text', adding no extra semantic context beyond what the schema already provides. Baseline of 3 is appropriate.

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 verb 'Decompose' and the resource 'candidate theorem's statement into atomic preconditions + conclusion'. It distinguishes the tool from siblings by specifying its role in checking applicability after search, before relying on a candidate, which sets it apart from search and verification tools.

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?

Explicitly says 'Use after search, before relying on any candidate,' providing clear when-to-use guidance. It does not explicitly mention alternatives or when not to use, but the context is sufficiently clear for an agent to select this tool appropriately.

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