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

With no annotations, the description must carry the behavioral burden. It discloses what content is returned—open problems, values to beat with source/date, construction formats, points, and team role shares—and the effect of the optional api_key. It does not state that the operation is read-only, mention pagination or result size, or otherwise describe side effects. The disclosure is useful but incomplete for a no-annotation tool.

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?

The description is compact and front-loads 'Math Record Hunt' before detailing the data. It packs several concepts into a single long sentence but avoids filler or repetition. Minor restructuring could improve readability, but every clause conveys relevant scope.

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 listing tool with no output schema, the description is fairly complete: it names the problem types, data included, and optional api_key behavior. It omits pagination and result ordering, which would be useful for an agent, but the core return content is well covered. No annotations are present, so it does enough without overclaiming.

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 schema already fully documents the single api_key parameter, including its format and security warning. The description adds meaning beyond the schema by explaining that with api_key the caller receives their team's best per problem, clarifying the parameter's functional effect. This makes the parameter semantics clearer than the schema alone.

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 clearly identifies a list of math problems, distinguishing open record-hunt problems from practice problems and listing the data fields included. It does not use an explicit verb like 'list', but the resource and scope are specific enough for an agent to understand what the tool returns. It is distinguishable from math_get_problem, which fetches a single problem, though it does not name 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?

The description implies usage by contrasting open problems with practice problems and explaining that an api_key adds team-specific best results. However, it gives no explicit when-to-use versus alternatives such as math_get_problem or math_claims, and no when-not-to-use guidance. The guidance is inferred rather than stated.

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