Is Edge Binvariant

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

The description mentions the additional output ('Also returns the nontrivial barriers of G - e'), which informs the user about what to expect. As a query tool, it likely has no side effects, but since there are no annotations, it would benefit from explicitly stating read-only behavior. Still, the provided output details add transparency.

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 very short and to the point, with no redundant wording. It conveys the core function and an additional return value in two concise sentences, making it easy to quickly understand.

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 specialized domain and the presence of sibling tools, the description is sufficient for an expert user. It does not define b-invariant or quasi-b-invariant, but such definitions are likely standard in this context. The additional return value is noted, rounding out the tool's behavior.

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 provides basic descriptions for each parameter (endpoint, graph6 string). The tool description adds minimal extra meaning beyond stating that the graph is a brick. It does not elaborate on the format or domain of the parameters, so the schema carries the main burden.

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 checks whether an edge in a brick is b-invariant or quasi-b-invariant. It uses a specific verb and identifies the resource, though it does not explicitly differentiate from sibling tools, the specialized terminology makes the purpose unambiguous.

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 provides a condition ('Only defined for bricks') that tells when the tool is applicable, but does not explicitly contrast with sibling tools or state when to prefer alternatives. This gives partial guidance but leaves the selection criteria implicit.

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