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

With no annotations, the description must carry the behavioral burden. It simply restates the purpose without disclosing whether this is a pure calculation, what the output format is, or any constraints. For a math utility with no annotations and no output schema, this is inadequate.

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 short sentence, which is concise but under-specified rather than efficient. It doesn't front-load any useful detail beyond the 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?

For a tool with 2 parameters, no annotations, and no output schema, the description is too minimal. It doesn't explain the calculation formula (density = mass / volume) or how it relates to sphere volume, leaving significant gaps for an agent to call it correctly.

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 100%, so the schema already documents both parameters ('Mass to process', 'Radius to process'). The description adds no meaning beyond what the schema provides. Baseline 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 'Sphere Density: Density of sphere' names a verb-less resource (density of a sphere), which is more specific than the tool name but still tautological. Given the many math siblings like x402-density and x402-sphere-volume, the description doesn't clarify what makes this tool distinct.

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 guidance on when to use this tool vs alternatives like x402-density or x402-sphere-volume. The description provides no context about scenarios or prerequisites.

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