ScorpTech x402 Tools

Stirling2 Rec

stirling2_rec

Read-onlyIdempotent

The Stirling recurrence S(n,k) = k*S(n-1,k) + S(n-1,k-1). term is the first summand and diag is the second. n and k run from 1 to 80. Past 15 digits a part 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-rec

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_rec"
  }
}

Input Schema

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

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

B3/5.0

Behavior4/5

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

Annotations already cover safety (readOnly, idempotent, non-destructive), so the description focuses on useful extras: the 1..80 domain, the big-number rule ('past 15 digits a part is a decimal string'), the per-call price, and an alternate HTTPS endpoint. It also names the two output components ('term' and 'diag') in place of a missing output schema. The only gap is that it remains unclear whether the call returns the summed value or just the two parts.

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?

Short and front-loaded with the core recurrence, then domain bounds, number representation, pricing, and the alternate endpoint. Every sentence carries information, though leading with a bare formula rather than a plain statement makes the opening slightly less accessible.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a two-parameter math function with no output schema, the description covers domain, large-number formatting, pricing, and output component names. However, it leaves the return shape and the mathematical meaning of n and k unspecified, so an agent could still format a call or interpret a result incorrectly.

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

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description bears full responsibility for parameter meaning. It only restates the range 'n and k run from 1 to 80', which the schema already enforces via minimum/maximum. It never explains that n is the size of the set and k the number of blocks, which an agent needs to avoid swapping or misusing the parameters.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description gives the Stirling recurrence formula rather than a plain-language verb+resource statement ('computes the Stirling number of the second kind'). An agent with math knowledge can infer the purpose, but it never explicitly says what value is produced, and the mention of 'term' and 'diag' muddies whether the tool returns S(n,k) or its two components. It also does not distinguish itself from siblings like stirling1_rec, stirling2, or stirling2_row.

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?

No when-to-use guidance is given: nothing says to prefer this recurrence variant over stirling2 or stirling2_row, and no conditions or prerequisites are stated. Usage is only implied by the formula itself.

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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