ScorpTech x402 Tools

Eulerian Sum

eulerian_sum

Read-onlyIdempotent

The sum of Eulerian numbers A(n, k) for k from lo through hi. The whole row sums to n!. A(4, 0) through A(4, 1) is 12. lo must not pass hi, and hi must be an ascent of n. n runs from 1 to 60. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/eulerian-sum

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>",
      "lo": "<lo>",
      "hi": "<hi>"
    },
    "name": "eulerian_sum"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`hi`	Yes
`lo`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.1/5.0

Behavior4/5

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

Annotations already cover read-only, idempotent, non-destructive, and open-world behavior. The description adds important constraints (lo<=hi, hi must be an ascent of n, n range), a paid-call price, and an alternate HTTPS endpoint, which is useful context beyond annotations.

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 compact and front-loaded with the mathematical definition, then constraints, example, pricing, and endpoint. Every sentence is relevant, though the pricing and endpoint details make it slightly longer than strictly necessary for every use case.

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?

Given rich annotations, no output schema, and three bare schema parameters, the description supplies enough mathematical context, range constraints, and pricing to invoke the tool correctly. It could more explicitly define valid ascent values, but the core behavior is clear.

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 explain parameters. It defines n's range, explains that lo and hi bound the k range for A(n,k), gives an example, and states constraints such as lo<=hi and hi being an ascent of n, though it does not fully define what qualifies as an ascent.

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 states a specific mathematical operation: summing Eulerian numbers A(n,k) over a range k=lo..hi. It distinguishes itself from the full-row sibling by emphasizing partial sums, reinforced by the example A(4,0)..A(4,1)=12.

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 through the partial-range sum definition and example, but there is no explicit guidance on when to use this instead of eulerian_row or eulerian. The agent must infer the alternative from the tool name and sibling list.

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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