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

With no annotations at all, the description carries the full burden: it usefully discloses that the endpoint is public and encodes the status lifecycle ('unconfirmed until a person reviews it and the record keeper accepts it'), which is genuinely non-obvious domain behavior. It still omits ordering, pagination, or volume for 'every' claim, and error behavior when claim_id does not resolve.

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 compact sentences with the default (list-all) behavior front-loaded and the parameter-driven variant second; nearly every phrase carries information. The nested parenthetical explaining claim status is slightly dense but earns its place by defining the lifecycle.

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?

For a simple read-only listing tool with one optional parameter and no output schema, the description covers the modes and the meaning of the returned status field. It leaves gaps around result size/ordering and pagination, which matter given the tool promises 'every' claim.

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% and the schema only types claim_id as a string, so the description is doing real work by explaining that supplying claim_id switches to a single-claim lookup that additionally returns the claim's 'construction'. The name and semantics of the parameter are conveyed, though its format/ID shape is not.

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 resource and two retrieval modes: all math record claims with status and reporting location, or a single claim including its 'construction' when claim_id is supplied. It is clearly distinct from sibling mutation/review tools like math_submit, math_vet, and math_house_vet, though it never names those siblings 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?

The 'Public:' prefix implies no authentication and the second sentence implies the two usage modes (list all vs. fetch one), so an agent can infer how to call it. However, there is no explicit statement of when to prefer this over related tools such as math_problems or math_vet, and no stated exclusions or prerequisites.

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