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

With no annotations provided, the description carries the full transparency burden. It discloses that the tool returns a constant value, provides the approximate value, and states that no input is required. It does not specify the exact numeric precision or return format, but for a zero-input constant-returning tool this is adequately transparent.

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 one compact sentence that front-loads the core information — returning Euler's number e — and then adds the clarifying mathematical context and no-input note. There is no redundant or filler content.

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 simple constant-returning tool with no input schema and no output schema, the description fully explains what the tool does, what value it produces, and that no input is needed. No critical information is missing.

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 tool has zero parameters and the schema already fully documents this with an empty properties object. The description reinforces this with 'No input needed,' which is consistent though it adds little beyond the schema. The baseline of 4 for zero-parameter tools 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 uses a specific verb ('Return') and identifies the exact resource: Euler's number e, with its value and mathematical meaning ('base of natural logarithms'). This clearly differentiates it from sibling tools like x402-euler-phi and x402-euler-totient.

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 description makes the use case clear: call this when you need Euler's number e. The phrase 'No input needed' also signals there are no prerequisites or configuration choices. It does not explicitly name alternative tools, but the mathematical clarification is sufficient to avoid confusion.

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