ScorpTech x402 API

Domb Term

domb_term

Read-onlyIdempotent

One summand of the Domb number, C(n,k)^2 * C(2k,k) * C(2n-2k,n-k). The k=1 summand of D(2) is 16 and the k=0 summand of D(3) is 20. A k past n is 0. n and k run from 0 to 12. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/domb-term

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": "domb_term"
  }
}

Input Schema

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

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.2/5.0

Behavior4/5

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

Annotations already establish read-only, idempotent, non-destructive behavior, while the description adds important operational details: a $0.001 USDC x402 payment on Solana, an HTTPS endpoint, and the zero result when k exceeds n. It stops short of describing error handling or explicitly stating the return type, though the formula and examples imply an integer value.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The definition is front-loaded, followed by examples, the edge case, range limits, cost, and endpoint. Every sentence carries relevant information for selecting or invoking the tool.

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 math function with no output schema and no parameter descriptions, the description supplies the formula, examples, edge-case behavior, and access details. A brief statement of the return type would make it fully self-contained.

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 parameter meaning. It does well by giving the formula showing how n and k enter the binomial coefficients, restating the 0–12 range, and specifying that k > n yields 0. It could be slightly stronger by defining n's role in plain language.

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?

The description gives a precise mathematical definition: one summand of the Domb number, with the exact binomial formula. This clearly distinguishes it from sibling tools like domb_sum or domb, which operate on the whole sequence/sum rather than an individual term.

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 'One summand' and the worked examples, but the description never explicitly names alternatives such as domb_sum or states when not to use this tool. An agent can infer the right context, but routing guidance is limited.

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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