Is Efec

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

With no annotations, the description carries the burden of behavioral disclosure. It does well by explaining the True condition and, notably, that a False result includes the disconnecting witness triple. It does not mention edge cases like disconnected graphs or invalid inputs, but the core behavior is clearly disclosed.

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 compact and efficient: a direct question, a one-sentence definition of the property, and a one-sentence note about the False output. No filler or redundant 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?

The description defines the property, states the True condition, and explains the False-case witness, which covers the essential behavior for a single-parameter predicate. With an output schema present, this is mostly complete, though it leaves minor gaps around prerequisites or behavior on degenerate graphs.

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 schema already documents the only parameter ('graph') as 'a graph6 string or a registry name', with 100% coverage. The description adds no additional parameter semantics, so the baseline score of 3 is appropriate.

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 the tool's purpose: it checks whether a graph is essentially 4-edge-connected (efec) and gives a precise criterion ('no three pairwise non-adjacent edges disconnect the graph'). It does not explicitly distinguish itself from the sibling is_efec_cubic_brick, so it falls short of a 5.

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?

There is no guidance about when to use this tool versus alternatives, such as is_efec_cubic_brick or is_brick. The definition of the property is provided, but no context on prerequisites, exclusions, or preferred use cases.

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