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

With no annotations, the description carries the full burden of behavioral disclosure. It does indicate the set of mathematical operations the tool can perform, implying a pure computation, but it says nothing about how results are presented, what happens for invalid or missing parameters, how operations are selected, or whether there are side effects. The agent only learns a list of math topics, not the behavior of the tool.

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 compact sentence that front-loads the domain ('Number theory') and then lists supported computations in a scannable comma-separated form. It wastes no words and is easy to parse quickly. The conciseness is commendable, though it comes at the cost of omitting the explanatory detail needed for parameter mapping.

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 tool with 9 parameters, no annotations, and 0% schema description coverage, this description is not complete enough for an agent to invoke correctly. The output schema covers return values, but the description still fails to document allowed operation values, required parameters per operation, or parameter constraints. It names the feature set without providing the per-operation contract needed to construct a valid call.

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%, so the description must compensate by linking parameters to operations. It offers only weak hints: 'CRT' suggests moduli and remainders, 'extended GCD' suggests a and b, and 'modular inverse' suggests a and m. But it never explicitly maps each of the nine parameters to a specific operation, explains how they combine, or defines the valid operation string values. An agent must guess the invocation contract.

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 identifies the resource (number theory) and enumerates specific computations (primality, factoring, extended GCD, CRT, etc.), which distinguishes it from arithmetic, matrix algebra, or equation-system siblings. However, it lacks an explicit verb such as 'computes' or 'solves' — the action is only implied by the tool name and the domain label. It reads as a topic list rather than a statement of what the tool does.

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?

No usage guidance is provided. The description never states when to prefer this tool over closely related siblings like cognitive.solve_arithmetic, cognitive.verify_arithmetic_claim, or cognitive.matrix_algebra, nor does it give conditions or exclusions. The only implicit signal is the topic list, which is insufficient for an agent deciding between competing tools.

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