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

No annotations are supplied, so the description carries the full behavioral burden. It never states that this is a read-only listing, whether it is scoped to the caller's team only, whether results are paginated or limited, or what authorization beyond api_key is needed. The only behavioral content is the enumeration of returned fields, which is thin for an unannotated 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?

It is a single short sentence with no wasted padding, which is good, but the front-loaded content is a noun phrase rather than a purpose statement, and the field list ('values, both checks, credits, results') is packed into ambiguous shorthand. Brevity here comes at the cost of comprehension.

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?

No output schema exists, so the description must explain return shape, and it only gestures at it with unexplained field names. Combined with the absence of annotations and any usage guidance among numerous math_* siblings, the definition leaves an agent unable to confidently decide when to call it or what to expect back.

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?

There is a single parameter and schema description coverage is 100%, with the api_key field already documented in the schema (including its origin and secrecy). The description adds nothing about the parameter, 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?

It identifies the resource ('Your team's math entries') and enumerates the kinds of data returned, but there is no verb and no indication of whether this lists, fetches, or summarizes entries. Terms like 'both checks' and 'vet' are domain jargon that an agent cannot resolve from the text alone. It is more informative than a tautology, but the purpose stays vague.

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 statement of when to call this versus the many plausible siblings (math_claims, math_problems, math_get_problem, math_vet). The trailing phrase 'which ones you can vet' hints at a relationship to math_vet but never says to use this first and then call math_vet. No prerequisites or exclusions are given.

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