ScorpTech x402 API

Euler Zigzag

euler_zigzag

Read-onlyIdempotent

The nth Euler zigzag number, the number of up-down permutations of n. a(0) is 1, a(3) is 2, a(4) is 5, and a(5) is 16. For n at least 1 it is the Entringer number E(n, n). n runs from 0 to 40. 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/euler-zigzag

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>"
    },
    "name": "euler_zigzag"
  }
}

Input Schema

Name	Required	Description	Default
`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 declare the tool as read-only, idempotent, non-destructive, and open-world. The description adds valuable behavioral context: pricing per successful call, x402/Solana payment, HTTPS endpoint availability, and 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 definition is front-loaded and packed with useful facts: mathematical meaning, examples, bounds, output representation, pricing, and endpoint. Pricing and HTTPS details are slightly ancillary for an invocation-focused description, but they are relevant and not wasteful.

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 simple one-parameter math tool with no output schema, the description covers the domain, bounds, examples, and special output representation for large values. It does not fully specify the return type for values under 15 digits or error behavior, but the key invocation information is present.

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?

The schema has 0% parameter description coverage, so the description must compensate. It defines n as the index of the Euler zigzag number, gives the valid range 0 to 40, supplies examples such as a(0)=1 and a(5)=16, and relates n >= 1 to the Entringer number E(n, n).

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 resource: the nth Euler zigzag number, defined as the number of up-down permutations of n. It gives concrete examples and a range, making the purpose clear. It does not explicitly distinguish when to choose this over sibling tools such as entringer or euler_zigzag_sum, though it mentions the Entringer relation.

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 the definition and the stated range n = 0 to 40, but there is no explicit guidance on when to use this tool versus alternatives like entringer or euler_zigzag_sum. The pricing and HTTPS endpoint are useful context but do not clarify tool selection.

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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