ScorpTech x402 API

Stirling1

stirling1

Read-onlyIdempotent

The signed Stirling number of the first kind s(n, k). s(4, 2) is 11 and s(5, 2) is -50. s(n, 0) is 0 for n > 0. n runs from 0 to 64, and k must not pass n. 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/stirling1

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>",
      "k": "<k>"
    },
    "name": "stirling1"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.8/5.0

Behavior4/5

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

Annotations already establish that this is a read-only, idempotent, non-destructive operation. The description adds important behavioral context beyond the annotations: pricing ($0.001 USDC per successful x402 call), an HTTPS endpoint, and the fact that values beyond 15 digits are returned as decimal strings.

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 mathematical definition and then adds examples, constraints, precision behavior, and payment details. It is dense and mostly efficient, though the pricing and HTTPS endpoint details are operationally useful rather than strictly semantic.

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 mathematical function with no output schema and no schema descriptions, the definition is nearly complete: it covers the domain, special cases, examples, and output precision behavior. The main missing piece is explicit sibling routing guidance, which matters given many related Stirling-number tools.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

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 semantics, and it does. It explains n runs from 0 to 64, k must not exceed n, gives the edge case s(n, 0) = 0 for n > 0, and supplies concrete examples s(4, 2) = 11 and s(5, 2) = -50.

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 function: the signed Stirling number of the first kind s(n, k). It clearly distinguishes the signed variant from the unsigned sibling in the name space, but it never explicitly names or contrasts the related siblings such as stirling1_unsigned, stirling1_row, or stirling1_rec.

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 domain constraints and examples, but it does not say when to use this tool versus alternatives like stirling1_row, stirling1_rec, stirling1_unsigned, or stirling2. The agent must infer routing from the mathematical name alone.

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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