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

No annotations are provided, so the description must carry the full behavioral burden. It does disclose the payment/auth model ('5 free trial calls per signed wallet'), which is real added context, but omits units of the decay constant, expected input format (schema types it only as an undocumented string), required/optional status, and what the result looks like.

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 purpose is front-loaded in a single tight sentence, but it is followed by a promotional trial-pricing clause with an emoji, which adds clutter without helping the agent compute anything.

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 one-parameter math utility with no output schema and no annotations, the formula makes the result derivable and reasonably complete. The main gap is the absence of unit/format expectations for the decay constant, which matters for correctness in a physics calculation.

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. It names the 'decay constant' and its role in the formula, which partially maps to decayConstant, but it gives no units or format despite the parameter being typed merely as a string and not even marked required.

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?

States a specific verb and resource ('Computes half-life') and even gives the exact formula (ln 2 / decay constant), so an agent immediately knows the operation and its direction. It does not name or differentiate from near siblings like x402-decay-constant (the inverse) or x402-radioactive-decay, so it falls short of a 5.

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?

There is no when-to-use/when-not guidance and no mention of alternatives such as x402-decay-constant for the reverse calculation. The formula implies the input direction but gives no conditions for choosing this tool over its siblings.

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