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

Annotations already declare readOnlyHint=true, destructiveHint=false and a closed world, so the safety profile is covered. The description adds scope context (one bounded mode, exhaustive classification including all direct-sum factorizations), but says nothing about input constraints, failure modes, or cost — it does not contradict annotations, just adds modest context.

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?

Front-loaded with the trigger, but the body is a single run-on sentence stacking many comma-separated analyses, and the licensing/ownership disclaimer is off-topic filler that dilutes the definition.

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 an output schema present, return values need not be explained, and annotations cover the safety profile, so the gaps are narrower. Still, for a tool taking two undocumented, constrained parameters, the description leaves an agent without enough to construct a valid call and adds a confusing non-technical caveat.

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% for both parameters, so the description must carry the burden. 'One bounded cyclic mode' faintly gestures at the modulus/interval-word boundedness, but nowhere clarifies what modulus or the integer intervalWord array represent or how they constrain a valid mode.

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?

Specific verb (classify) plus resource (one bounded cyclic mode) and an unusually concrete enumeration of the returned analyses (rotation/reversal/set classes, transposition kernel, reflection, interval/Fourier content, evenness, direct-sum factorizations). This is clear, but it never names or contrasts the closest sibling analyze_cyclic_scale, which an agent could easily confuse it with.

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?

'Use this when an agent needs to classify one bounded cyclic mode' gives a triggering condition but no when-not guidance and no alternatives among the sibling analysis/generation tools. The trailing 'Do not infer ownership, licensing, or unpublished availability' is a liability disclaimer, not usage guidance, and does not help selection.

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