ScorpTech x402 API

Liouville

liouville

Read-onlyIdempotent

Liouville's function lambda(n) = (-1) to the number of prime factors of n, counted with multiplicity. lambda(1) is 1, lambda(2) is -1, and lambda(4) is 1. n runs from 1 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/liouville

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n": "<n>"
    },
    "name": "liouville"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.7/5.0

Behavior4/5

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

Annotations already mark the tool as read-only, idempotent, non-destructive, and open-world. The description adds useful behavioral context by disclosing the x402 payment model, cost per successful call, and a direct HTTPS endpoint.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description front-loads the mathematical definition and examples, then adds domain and payment details. It is reasonably compact, though the pricing and endpoint information could be structured more clearly.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple one-parameter math tool with annotations covering safety and no output schema, the description covers the function, domain, examples, and payment context. It could explicitly state the return value, but the mathematical definition makes that clear enough.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must carry parameter meaning. It defines n as the argument to lambda, gives the same 1-to-1e12 range as the schema, and provides example evaluations, but it does not add much beyond the mathematical definition and schema constraints.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states that the tool computes Liouville's function lambda(n), including its formula and concrete example values. It is specific enough for an agent to identify the mathematical operation, though it does not explicitly contrast itself with sibling tools such as liouville_sum.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description gives the valid domain for n and pricing/endpoint details, implying the tool is used to evaluate lambda at a single integer. However, it does not say when to use this tool versus alternatives like liouville_sum or other number-theory siblings.

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

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