ScorpTech x402 Tools

Franel Central

franel_central

Read-onlyIdempotent

The middle summand of the Franel number, C(n, floor(n/2))^3. n=0 gives 1, n=2 gives 8, n=4 gives 216, n=5 gives 1000, and n=6 gives 8000. 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-central

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_central"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior4/5

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

Annotations already declare read-only, idempotent, non-destructive behavior. The description adds meaningful context beyond them: the x402/Solana pricing model and an 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.

Conciseness5/5

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

The definition is front-loaded, followed by examples, range, price, and endpoint. Every sentence adds useful information and there is no filler.

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 one-parameter pure computation with no output schema, the definition is complete enough: formula, domain, sample outputs, cost, and endpoint are all provided.

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 coverage is 0%, but the description compensates well by defining n as the index from 0 to 16 and giving concrete input-output examples such as n=0→1 and n=6→8000. It could be slightly stronger by stating the return type explicitly, though the examples make it clear.

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?

It states a specific mathematical object and exact formula: the middle summand C(n, floor(n/2))^3 of the Franel number. That is enough to distinguish it in practice from franel and franel_sum, but it never explicitly names those alternatives or explains when this one is preferred.

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 by the formula and examples; there is no explicit 'use this when' guidance or comparison with sibling tools such as franel, franel_sum, franel_mod, or franel_gcd.

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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