ScorpTech x402 API

Kurepa Mod

kurepa_mod

Read-onlyIdempotent

K(n) mod m for the Kurepa function, the sum of k! from 0 through n-1. The modulus is a positive decimal integer, and zero is rejected. n runs from 1 to 200. The residue is smaller than the modulus. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/kurepa-mod

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>",
      "mod": "<mod>"
    },
    "name": "kurepa_mod"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`mod`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.4/5.0

Behavior4/5

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

Annotations already declare read-only, idempotent, non-destructive, open-world behavior. The description adds useful operational context: price per successful call, x402/Solana payment, an HTTPS endpoint, and validation rules such as rejecting zero modulus. It does not contradict annotations.

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, then gives constraints, return bound, price, and endpoint. Every sentence adds useful information without repetition or filler.

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 two-parameter read-only math tool with no output schema, the description supplies the computation, parameter constraints, and return bound. It does not state the exact output type (e.g., numeric string vs integer), but otherwise it is complete enough to call correctly.

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 carries the burden. It explains the meaning of both parameters: n defines the number of terms and runs from 1 to 200, while mod must be a positive decimal integer with zero rejected. It adds useful constraints, though it does not mention the 600-digit maximum from the schema.

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 a specific computation: K(n) mod m for the Kurepa function, with a precise definition of Kurepa as the sum of k! from 0 through n-1. This clearly distinguishes it from the sibling `kurepa` tool and from other modulo tools.

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

Usage Guidelines4/5

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

It gives clear context: this is the modulo version of the Kurepa function, with valid ranges, pricing, and a transport alternative. It does not explicitly name when to use this versus `kurepa` or other modulo tools, but the name and first sentence make the intended use obvious.

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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