ScorpTech x402 API

Subfactorial

subfactorial

Read-onlyIdempotent

The subfactorial !n, the number of derangements of n objects. !0 is 1, !1 is 0, !2 is 1, and !5 is 44. n runs from 0 to 4096. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/subfactorial

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": "subfactorial"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.2/5.0

Behavior4/5

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

Annotations already cover read-only, idempotent, non-destructive behavior. The description adds useful behavioral context beyond annotations: the $0.001 USDC x402 payment model, the HTTPS endpoint, and the important output-format rule that values past 15 digits are returned as a decimal string.

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

Conciseness5/5

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

The description is front-loaded with the mathematical definition, followed by examples, range, output representation, and payment/endpoint details. Every sentence contributes useful information and there is no obvious padding.

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?

With no output schema, the description partially explains return behavior by noting the decimal-string threshold and showing example outputs. It does not explicitly state the return type for values under 15 digits or the full response shape, but for a simple one-parameter math function this is nearly complete.

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

Parameters4/5

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 does so adequately: it defines n via 'n objects', specifies the valid range 0..4096, and gives concrete examples for n=0, 1, 2, and 5.

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

Purpose5/5

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

The description states exactly what the tool computes: the subfactorial !n, defined as the number of derangements of n objects. This is a specific mathematical resource with a precise name and meaning, making it distinguishable from the many adjacent combinatorics siblings.

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 definition and examples imply when to use the tool, and the valid domain n = 0..4096 is stated. However, it gives no explicit guidance versus related siblings such as rencontres, which also involves derangements, and no when-not-to-use context.

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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