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

Annotations cover openness and idempotency (openWorldHint, idempotentHint, destructiveHint=false), and the description adds real behavioral detail beyond them: the pending/paid state machine, a retry interval, the 'Authorization: Bearer <key>' usage convention after success, and an activation link. There is a mild tension between the read-only framing ('Checks whether...') and readOnlyHint=false, but the mention of a pass key and an activating link makes clear the call is not purely observational, so this is not a direct contradiction.

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?

Front-loaded with purpose and only two sentences, with no filler. The second sentence is densely packed (nesting the Bearer-header convention and the activation link inside the 'paid' case), which slightly hurts scannability but all content earns its place.

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?

There is no output schema, so the description carrying the return values (pending with retry interval, paid with pass key, activation link) is necessary and it delivers. It leaves out failure/expiry states (e.g. what happens if payment never completes or fails) and any auth requirement, which are the remaining gaps for a polling 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?

Schema description coverage is 100% and the single parameter is fully documented in the schema, including its origin ('reference from start_pass_purchase (ag_…)'). The description repeats 'purchase reference' but adds no format or constraint detail beyond the schema, so the baseline of 3 applies.

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 and resource ('Checks whether the payment for a purchase reference has completed') and names the exact outcome states (pending / paid with pass key). Combined with the schema's pointer to start_pass_purchase, an agent can place this tool precisely at the end of the purchase flow and distinguish it from start_pass_purchase and the unrelated marine siblings.

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 strongly implied: it is a post-payment status/collection step ('pending (with a retry interval)' signals polling after start_pass_purchase, and the title says 'after the user has paid'). The description never explicitly names start_pass_purchase as the prerequisite call or states when not to use it, so it stops short of full routing guidance.

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