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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint=false, and destructiveHint=false, so the safety profile is covered. The description adds substantial behavioral detail beyond that: it returns actual problem IDs, evaluation version, and a verification fingerprint, excludes stale evaluations, distinguishes pattern shortage from per-pattern problem shortage, and refuses to auto-relax conditions.

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 purpose is front-loaded in the first clause, and each following sentence adds a distinct rule (evaluation filtering, shortage distinction, no auto-loosening, band-match caveat). The prose is dense but every sentence 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?

For a read-only inspection tool with no output schema, the description covers what is returned (problem IDs, evaluation version, fingerprint) and the behavioral rules well. It stops short of explaining how this feeds into create_math_difficulty_worksheets, which is the main remaining gap.

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 coverage is only 60%, and nested items fields (variantId, patternCount, problemsPerPattern) have no schema descriptions. The description explains conceptually what bands and items represent (patterns per difficulty and problems per pattern) but adds nothing about seed reuse semantics, grade defaults, or the MV-id format, so it does not compensate for the coverage gap.

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 states a specific action: inspect existing stock for the same learning objective and confirm how many patterns exist per difficulty band and how many problems exist per pattern. It clearly marks itself as the read-and-verify counterpart to create_math_difficulty_worksheets, though it never names that sibling 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?

It implies when the tool applies by saying unevaluated, needs-review, or stale evaluations are not used as basis, and that conditions are not automatically loosened. However, it never states when to choose this versus create_math_difficulty_worksheets or find_math_problem_types, leaving the workflow position inferred.

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