ScorpTech x402 Tools

Prufer Degree

prufer_degree

Read-onlyIdempotent

The degree of a vertex in the tree described by a Prüfer code. Degree is one plus the number of times the vertex appears. In code 2,3, vertex 2 has degree 2 and vertex 1 has degree 1. The vertex must lie from 1 to n. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/prufer-degree

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": {
      "code": "<code>",
      "vertex": "<vertex>"
    },
    "name": "prufer_degree"
  }
}

Input Schema

Name	Required	Description	Default
`code`	Yes
`vertex`	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 cover read-only, idempotent, non-destructive behavior. The description adds useful context beyond annotations: cost per successful call, x402/Solana payment, and an equivalent HTTPS endpoint. It does not describe error handling for invalid input, but that is minor for this pure calculation tool.

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 and compact. Every sentence serves a purpose: core definition, formula, example, range constraint, pricing, and alternate access path.

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?

With no output schema, the description appropriately explains the return value through the degree formula and example. It also covers payment and access, but omits the explicit relationship between code length and the valid vertex range n.

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 description coverage is 0%, so the description must carry parameter meaning, and it does: code is a Prüfer code, degree equals one plus the vertex's occurrences, and vertex must lie from 1 to n. The main gap is that n is not explicitly defined as len(code)+2.

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?

Opens with a precise operation and resource: computes the degree of a vertex in the tree described by a Prüfer code. The formula and worked example make the purpose distinct from sibling tools such as prufer_encode and prufer_decode.

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?

The description implies when the tool is useful, but it does not explicitly say when to use it instead of prufer_decode or prufer_encode, nor does it state exclusions or prerequisites. Usage is inferable from the definition rather than directly guided.

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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