ScorpTech x402 Tools

Josephus K2

josephus_k2

Read-onlyIdempotent

The Josephus survivor when every 2nd person is eliminated. Write n = 2^m + l with l < 2^m. The survivor is 2*l + 1. 5 gives 3, 10 gives 5, and 41 gives 19. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/josephus-k2

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": "josephus_k2"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.6/5.0

Behavior4/5

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

Annotations already declare the operation is read-only, idempotent, open-world, and non-destructive. The description adds important behavioral context beyond annotations: the $0.001 USDC x402 payment on Solana and the equivalent HTTPS endpoint. It could still say more about output format or rate limits, but the payment disclosure is 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 with the core purpose and formula, followed by examples, range, and payment details. It is dense but every element is relevant; the HTTPS endpoint and price could be separated from the mathematical description for cleaner structure, but there is little wasted text.

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 single-parameter mathematical tool with no output schema, the description is largely complete: it defines the computation, gives examples, states the input range, and discloses payment mechanics. The main missing piece is sibling differentiation among the many Josephus-related tools.

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?

With zero schema description coverage, the description compensates by defining n via the formula and giving concrete examples such as n=5 → 3 and n=41 → 19. The stated range 1 to 1,000,000 also clarifies the parameter, though it duplicates the schema's min/max rather than adding new constraints.

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 states a specific mathematical operation: the Josephus survivor when every 2nd person is eliminated, with an explicit formula and examples. It is clear what the tool computes, but it does not differentiate itself from sibling Josephus tools such as josephus, josephus_first, or josephus_place.

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

Usage Guidelines2/5

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

The description provides no explicit guidance on when to use this tool versus alternatives, nor does it name or exclude related siblings. Usage is only implied by the mathematical definition and the k=2 naming.

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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