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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description adds real behavioral context beyond them: exact vs estimated verdicts, the undetermined fallback condition, and a versioned integrity digest. It also discloses scope limits (no unit or model-meaning validation), which is genuinely useful for interpreting results.

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?

Three dense, front-loaded sentences with no filler; the core action leads and the caveats follow. It is efficient, though the final clause about units/model meaning is slightly compressed.

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?

An output schema exists, so return values need not be explained, and annotations carry the safety profile. However, with 5 parameters at 0% schema coverage, the description should say more about the values array and the two tolerance parameters to be complete.

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 0% across 5 parameters, and the description only gestures at 'expression, claim and tolerances' without explaining the values array, tolerance_absolute vs tolerance_relative, or any format/semantic details. It fails to compensate for the documentation gap it is the only source for.

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?

States a specific verb and resource ('Check an explicit arithmetic claim') and bounds the scope by declaring it does no unit or model-meaning checks. It is clearly distinct in kind from siblings like verify_claim, though it never names that sibling to sharpen the boundary.

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?

Usage is implied through capability boundaries: representable i128 rational expressions yield exact verdicts, while unsupported functions or overflow fall back to an estimate with an 'undetermined' verdict. There is no explicit when-to-use-this-vs-verify_claim guidance or stated prerequisites.

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