ScorpTech x402 Tools

Fubini

fubini

Read-onlyIdempotent

The nth Fubini number, the ordered partitions of an n-element set. a(0) is 1, a(2) is 3, a(3) is 13, and a(5) is 541. n runs from 0 to 20. 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/fubini

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": "fubini"
  }
}

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 cover read-only, idempotent, and open-world behavior, so the bar is lower. The description adds valuable context: pricing ($0.001 USDC per call), payment method (x402, Solana), an HTTPS alternative, and output format (decimal string past 15 digits). These are meaningful behavioral traits beyond structured data.

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 description is front-loaded with the core definition and examples, then moves to constraints and payment details. It is efficient but includes some slightly tangential payment information that could be compressed, though it remains relevant for a paid API.

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 explains the return type (integer for small results, decimal string past 15 digits) and provides example outputs. Annotations cover safety, and the pricing and HTTPS endpoint are included. Error behavior for out-of-range n is left to the schema constraints, which is acceptable.

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 compensate. It explains that n is the size of the set (ordered partitions of an n-element set), reiterates the range 0–20, and gives concrete output examples for specific n values, adding meaning beyond the bare integer schema.

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 states it returns the nth Fubini number and defines it as the ordered partitions of an n-element set, with examples. It does not explicitly differentiate this tool from sibling tools like fubini_mod or fubini_sum, but the core purpose is unambiguous.

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 gives no guidance on when to use this tool versus alternatives, nor does it mention preconditions or exclusions. The range constraint (n from 0 to 20) is present but is essentially parameter semantics, not usage guidance.

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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