ScorpTech x402 API

Cullen

cullen

Read-onlyIdempotent

The nth Cullen number, n*2^n + 1. The 1st is 3, the 2nd is 9, and the 5th is 161. n runs from 1 to 256. 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/cullen

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": "cullen"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.1/5.0

Behavior4/5

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

Annotations already declare this a read-only, idempotent, open-world computation, so the description does not need to re-explain safety. It adds genuinely new context: large results return as decimal strings past 15 digits, each successful call costs $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint is provided. Those are things the annotations cannot express.

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?

Three tight sentences, each doing distinct work: definition, examples/range, output format and payment/transport details. Front-loaded with the mathematical definition so the agent gets the core meaning first.

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?

With no output schema, the description responsibly covers return format (integer vs decimal string past 15 digits), input domain, and cost. The only gap is unspecified behavior for invalid n (e.g., n=0 or n>256), a minor omission for a single-parameter math tool.

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 the parameter burden, and it does: it explains that n is the Cullen index, defines the formula it feeds, and states the valid range 1–256 (matching the schema bounds). It stops short of describing error behavior at the boundaries.

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?

States the exact closed-form definition (n*2^n + 1), anchors it with concrete example values for n=1, 2, and 5, and gives the domain of n. An agent can distinguish this from the many sibling sequence tools (woodall, proth, etc.) without any extra lookup.

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 formula and the stated range (n from 1 to 256), but there is no explicit when-to-use guidance, no mention of sibling tools, and no statement about what happens for out-of-range n. The constraint on n is the only routing signal offered.

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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