ScorpTech x402 Tools

Stirling2

stirling2

Read-onlyIdempotent

The Stirling number of the second kind S(n,k), the number of ways to partition n objects into k nonempty unlabeled sets. S(5,2) is 15. S(n,k) is 0 when k is greater than n. n and k run from 0 to 80. 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/stirling2

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": "stirling2"
  }
}

Input Schema

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

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior5/5

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

Annotations already cover read-only, idempotent, non-destructive, but the description adds genuinely new behavioral facts: paid access at $0.001 USDC per successful call via x402 on Solana, an alternate HTTPS endpoint, the >15-digit decimal-string return format, and the k>n zero case. Cost/auth-adjacent information of this kind is exactly what annotations cannot convey.

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?

Front-loaded with the definition and example, then the boundary behavior, output format, and pricing/endpoint. Every sentence carries information, though the pricing/URL tail makes it slightly list-like rather than tightly woven.

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-integer math tool with no output schema, the definition, input range, k>n edge case, return-format threshold, and payment terms cover what an agent needs to call it correctly. The one real gap is sibling routing (stirling2_row / stirling2_rec) in an extremely dense sibling namespace.

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 coverage is 0%, so the description must carry the load; it does define what n and k mean semantically (n objects, k nonempty unlabeled sets) and gives the k>n edge case. The '0 to 80' restatement duplicates the schema bounds rather than adding meaning, keeping it below a 5.

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?

States the exact mathematical object ('the Stirling number of the second kind S(n,k)'), defines it as the count of partitions into k nonempty unlabeled sets, and grounds it with 'S(5,2) is 15'. Clear verb-equivalent and resource, but it never differentiates from the close siblings stirling2_row, stirling2_rec, or stirling1_unsigned.

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 only implied: the singular S(n,k) framing suggests single-value use versus the row/rec variants, and 'S(n,k) is 0 when k is greater than n' warns of a degenerate case. There is no explicit when-to-use or when-to-prefer-a-sibling statement despite stirling2_row and stirling2_rec existing.

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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