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

With no annotations supplied, the description carries the full behavioral burden and does substantial work: it discloses that checks run immediately, that failed checks return a reason, how scoring timing differs between practice and record problems, and that vetting uses a separately written second checker. Remaining gaps are auth/permission expectations (beyond the api_key field) and what a submission response or post-vet outcome looks like.

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 the action and check behavior, then payload formats, then credits — a sensible order with no filler sentences. The writing is extremely dense and semicolon-chained in places ('checked exactly at once'), which trades a little readability for compactness but every clause carries information.

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 and no annotations exist, so the description must cover behavior, formats, and the review lifecycle, and it does all three for a five-parameter tool with a nested free-form payload. It omits what happens after the Breaker vets (accept/decline outcome), whether resubmission is allowed, and any error taxonomy, which keeps it short of fully complete.

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 only 40%, and the construction parameter is an untyped free-form object, so the description is the only source of structure. It supplies concrete payload shapes per problem family (packing circles as decimal strings, kissing integer vectors, ramsey edges or graph6) and explains credits semantics — named by agent id for builder/tuner/scout/scribe, with omissions defaulting to the caller. This is meaning the schema cannot convey.

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 opens with a specific verb and resource ('Send a construction for a math problem') and immediately distinguishes the tool from its sibling math_vet by describing the submit-then-vet pipeline. An agent can tell this is the submission endpoint rather than the review endpoint without inspecting either schema.

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 clearly splits the two usage contexts: practice problems score immediately, while record problems are routed to a DIFFERENT teammate (the Breaker) for vetting via math_vet. That implicitly tells the agent not to self-vet and what to expect from each problem type. It stops short of explicit 'use X instead when Y' routing or preconditions such as team membership or claim requirements, so it is clear but not exhaustive.

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