ScorpTech x402 API

Jordan Totient

jordan_totient

Read-onlyIdempotent

The Jordan totient J(k, n). J(1, n) is Euler's totient. J(1, 6) is 2 and J(2, 6) is 24. k runs from 1 to 12 and n runs from 1 to 1000000. 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/jordan-totient

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": {
      "k": "<k>",
      "n": "<n>"
    },
    "name": "jordan_totient"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.4/5.0

Behavior5/5

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

Annotations cover the safety profile (readOnly, idempotent, non-destructive), so the description's job is to add behavior, which it does substantially: it discloses that results past 15 digits come back as a decimal string (critical with no output schema), states the price ($0.001 USDC per successful call), the x402/Solana payment requirement, and the equivalent 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 definition and examples are front-loaded, and each subsequent clause (ranges, large-value encoding, price, HTTPS mirror) contributes something an agent cannot get from structured fields. Slightly dense prose but no filler sentences.

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

Completeness5/5

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

For a two-parameter pure-computation tool with no output schema, the description covers the math, the valid domains, the return-type edge case, the cost, and the alternate transport. Nothing essential to correct invocation is missing.

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% and the schema only supplies bare integer bounds for k and n, so the description must carry the meaning. It defines k as the totient order (via the Euler-totient identity) and shows concrete input/output pairs that reveal how both parameters map to a result, though it adds nothing about error behavior for out-of-range inputs.

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 names the exact mathematical object (Jordan totient J(k, n)) and anchors it with the identity J(1, n) = Euler's totient plus two worked values (J(1,6)=2, J(2,6)=24). That makes it distinguishable from the sibling 'totient' at a glance, since a reader immediately sees the k-parameter generalization.

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?

Usage is implied by the definition: request J(k, n) for the stated parameter ranges. The note that J(1, n) equals Euler's totient hints that the simpler 'totient' sibling covers the k=1 case, but the description never states when to pick this tool over that one, and gives no exclusions or failure guidance.

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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