Classify Edges

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

With no annotations, the description must carry behavioral disclosure. It discloses the core behavior: classification of every edge and reporting quasi-b-invariant edges with the two nontrivial barriers of G - e. However, it does not explicitly state that the operation is non-mutating, what happens for non-brick inputs, or any performance/error characteristics, leaving some burden on the agent.

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 two tight sentences, each earning its place. The primary operation is front-loaded, and the additional barrier-reporting detail and brick precondition are provided without waste.

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 one-parameter graph-theory tool with an output schema, the description is largely complete: it defines the operation, the one precondition, and the key output detail. It could be more complete by naming sibling tools or explaining behavior on invalid/non-brick inputs, but those are modest gaps.

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?

The input schema already fully describes graph as 'a graph6 string or a registry name' (100% coverage). The description adds important extra semantic context by stating the graph must be a brick, which constrains valid parameter values beyond the schema.

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 begins with a specific action and scope: 'Split every edge of a brick into b-invariant and quasi-b-invariant.' This clearly distinguishes classify_edges from siblings like is_edge_binvariant (a single-property test) and has_qbinv_edges (an existence check), since it handles all edges and produces both categories.

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 states a clear precondition: 'Only defined for bricks,' which tells an agent not to call it on non-brick graphs and suggests verifying brickness (e.g., via is_brick) first. It does not explicitly name alternatives or when-not cases such as using has_qbinv_edges for a quick existence check.

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