review_math_model

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

No annotations are provided, so the description carries the full burden; it discloses the audit dimensions and the return status tokens ('REVIEW_STATUS: PASSED'/'FAILED'), which is useful. However, it omits whether the check is read-only, deterministic, what a FAILED result contains, and what input format the formulation must take.

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 sentences, zero filler, with the audit scope front-loaded before the return-value statement. Every clause 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?

An output schema exists, so explaining return values is not strictly required, yet the description already covers the status outcome. The only real gap for a single-string audit tool is the expected input format, which is a minor but noticeable omission.

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?

Only one parameter ('formulation') with 0% schema description coverage, so the description must compensate. It names the object being audited but gives no expected format (LaTeX, code, structured text) or size constraints, leaving the sole required parameter underspecified.

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?

Specific verb ('Audits') plus a precise resource ('mathematical optimization formulation') with enumerated check dimensions: index consistency, variable domains, bounds, objective alignment, constraint correctness. This clearly distinguishes it from siblings like review_model_code and review_requirements.

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 never states when to use this tool versus review_requirements, review_model_code, or formulate_math_model, nor any prerequisites or sequencing. The audit dimensions hint at a post-formulation stage, but no explicit guidance 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.