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

readOnlyHint=true already tells the agent this is a safe read. The description adds real behavioral context beyond the annotation: the account requirement and the session/auth flow that must happen before the call succeeds. It does not describe return shape, but the safety profile is covered.

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, purpose front-loaded and the access caveat clearly separated. Nothing is redundant, though the authentication aside is somewhat verbose relative to the tool's simplicity.

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 output schema, the description still conveys what the tool reports (sending setup status plus DNS record progress) and the prerequisite to get a result. For a single-parameter read-only status check this is close to complete, with only the exact return fields left unspecified.

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% and there is only one parameter (id, 'Domain ID'), so the schema carries the parameter meaning. The description's phrase 'for a domain' corroborates but adds no syntax, format, or lookup detail beyond what the schema provides, making baseline 3 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 states a specific verb (check) and resource (email sending setup status for a domain) and adds scope detail (DNS record configuration progress). It is distinguishable from verification-oriented siblings like check_domain_verification or get_user_domain_verification_status, though it never names those neighbors explicitly.

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?

It explains the access prerequisite (needs a Proof account, authenticate or use start_login then retry), which is genuinely useful context. However, it offers no guidance on when to prefer this over adjacent tools such as check_domain_credentials, check_domain_verification, or get_domain.

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