ScorpTech x402 Tools

Franel

franel

Read-onlyIdempotent

The Franel number F(n), the sum of C(n,k)^3 for k from 0 to n. F(0) is 1, F(1) is 2, F(2) is 10, F(4) is 346, and F(5) is 2252. n runs from 0 to 16. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/franel

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": "franel"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.8/5.0

Behavior4/5

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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint=false. The description adds meaningful behavioral context beyond them: the $0.001 USDC per successful call pricing and the equivalent HTTPS endpoint. It does not discuss rate limits or error behavior, but the pricing and transport details are valuable.

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 is front-loaded, and the examples, range, price, and endpoint are all relevant to calling the tool correctly. Minor inefficiency: the examples skip F(3), and the pricing/URL information could be separated more cleanly, but overall it is appropriately sized.

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 single-parameter math tool, the description is largely complete: it defines the function, constrains n, shows example outputs, and states the cost and endpoint. It does not explicitly state the return type or out-of-range behavior, but the examples and schema cover those concerns adequately.

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 explains that n is the Franel index, gives the domain 'n runs from 0 to 16', and provides concrete mappings such as F(0)=1 and F(5)=2252, which clarify what n selects even though the schema already enforces min/max bounds.

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 defines the tool as computing the Franel number F(n) via the sum of C(n,k)^3, which is a specific mathematical resource. It does not mention sibling tools such as franel_mod, franel_sum, or franel_central, so the agent must rely on the name to distinguish them.

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 only implied: 'n runs from 0 to 16' establishes the valid domain, and the definition implies when the tool is useful. There is no explicit guidance on when to choose this tool versus sibling variants like franel_mod or franel_sum.

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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