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

No annotations are present, so the description carries the full behavioral burden. It discloses that the tool performs formal verification and numerical-stability auditing, but it does not explain that audit behavior is gated by the audit_stability parameter or how tolerance and matrix participate. It adds some context but remains thin.

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 a single efficient sentence, front-loaded with the core purpose and followed by the audit scope. There is no fluff or redundant restatement of the tool name.

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?

With five parameters and no parameter-level documentation, an agent cannot determine why a matrix is relevant to an arithmetic equality claim, when to set audit_stability, or how tolerance affects verification. The description leaves too much to inference for a tool that includes optional audit features.

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 0%, and the description does not explain claim_lhs, claim_rhs, tolerance, audit_stability, or matrix. The phrase 'arithmetic equality claim' hints at the LHS/RHS pair, but the role of the optional matrix and tolerance is left entirely undefined.

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 operation: 'Formally verify an arithmetic equality claim' and names concrete audit concerns (numerical stability, condition number, cancellation risks). This clearly distinguishes it from solving/computation siblings like cognitive_solve_arithmetic.

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 verb 'verify' implies this is the checking counterpart to arithmetic-solving tools, but the description never names an alternative or states when to use it instead of cognitive_solve_arithmetic. Usage context is inferable rather than explicit.

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