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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false, so the safety profile is covered. The description adds the return shape (pass rate with CI, cost figure), which matters because there is no output schema, but it says nothing about data freshness, scope, or whose cases are included. Adequate but thin against the annotated baseline.

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?

A single sentence, front-loaded with the deliverable and followed by its exact contents. There is no filler, hedging, or repetition of the title.

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?

With no parameters and no output schema, the description must carry the return-value burden, and it does specify the three measurements returned plus their statistic (95% CI). What is missing is scope framing — what "claimed" cases are and over what period. Reasonably complete for a trivial-signature tool.

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 tool takes zero parameters, which is the baseline-4 case. The description correctly adds no parameter detail and instead spends its words on payload semantics. Nothing misleading is introduced.

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 names the concrete deliverable ("your proof packet") and enumerates its contents: pass rate per workflow, 95% CI, and human unit cost. That is far more specific than the bare name "proof" and tells an agent what it will get. It does not, however, distinguish this from any sibling such as list_resolved_examples or calculate, so a 4 rather than 5.

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?

There is no when-to-use statement, no prerequisites, and no named alternative. The phrase "the cases you claimed" hints at a post-hoc verification scenario, but the agent must infer when this tool is the right choice versus list_resolved_examples or calculate. Implied-only guidance merits a 2.

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