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

Annotations provide readOnlyHint=true, idempotentHint=true, and destructiveHint=false, so the tool is known to be safe and non-destructive. The description adds value by mentioning the operation's non-commutative nature implicitly through operand ordering (name_a vs name_b) but does not explicitly state that cross product is anti-commutative, which is relevant behavior. It also mentions the error condition (ValueError) but that provides minimal extra beyond schema. Overall, since annotations cover safety, the description adds moderate value with error handling details.

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 concise with a clear purpose statement, parameter descriptions, return type, and error conditions. It follows a docstring format that is well-structured: purpose first, then args, returns, and raises. No extraneous information. Each 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?

Given the tool complexity (mathematical operation on stored vectors), the description is a bit sparse. It lacks critical usage details such as vector dimensions required (cross product typically only for 3D), dimensionality constraints, and what happens if the vectors are not 3D. While the output schema exists (though not provided in full), the description doesn't explain return format beyond 'Tensor'. Considering the sibling tools are all mathematical operations, more context on applicability would improve completeness.

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 100% with clear descriptions for both parameters: each is 'Name of the first/second stored vector' and left/right operand. The description adds minimal value, essentially repeating the same information. However, it does clarify that the tool operates on stored vectors (by name), which is slightly beyond schema. Baseline 3 is appropriate as the schema already covers parameter meaning.

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 states that the tool computes the cross product of two stored vectors, specifying the operands as name references in the tensor store. It distinguishes from siblings like vector_dot_product and vector_project by explicitly naming 'cross product'. However, it doesn't explicitly differentiate from other vector operations, but the verb 'cross product' is specific enough.

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: it requires two vectors stored in the tensor store)Skip, but does not explicitly state when to use this tool versus alternatives (e.g., for 3D vectors only, not for dot product). It doesn't mention constraints like vector dimensionality (cross product is typically only defined for 3D vectors), which is a notable gap for correct usage.

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