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

With no annotations provided, the description carries the full burden of behavioral disclosure. It reveals nothing about what the tool does, what it returns, whether it has side effects, or what inputs it expects.

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 text is short, but this is under-specification rather than effective conciseness. It simply echoes the tool name without front-loading any meaningful semantic 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?

Even though the tool has no parameters and no output schema, the description supplies no operational context whatsoever. In a large catalog of similar math/signal tools, an agent cannot infer what invocation would accomplish.

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 input schema has zero properties, so there are no parameter semantics for the description to add; the schema fully documents the absence of parameters. Baseline for zero-parameter tools is 4.

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, 'Triangle Wave: Triangle Wave', is a tautology that merely restates the tool name and provides no verb, resource, or action. An agent cannot tell whether this generates, computes, or analyzes a triangle wave, and it is indistinguishable from siblings like x402-sawtooth-wave and x402-square-wave.

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 provides no guidance on when to use this tool or how it differs from alternatives. An agent has no basis for choosing triangle-wave over sawtooth-wave or square-wave.

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