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Prufer Decode

prufer_decode
Read-onlyIdempotent

The tree edges for a Prüfer code, as a flat list of sorted pairs. Code 2,3 is the path 1-2-3-4. Code 1,1 is the star at 1. An empty code is the edge 1-2. Code entries run from 1 to 30. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/prufer-decode

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>"
    },
    "name": "prufer_decode"
  }
}

Input Schema

NameRequiredDescriptionDefault
codeYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A3.6/5.0
Behavior4/5

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

Annotations cover read-only, idempotent, and non-destructive behavior. The description adds useful context: output format (flat list of sorted pairs), edge-case semantics (empty code → edge 1-2), input range (1–30), pricing, and an HTTPS alternative endpoint.

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 front-loaded with the core operation and examples, then adds pricing and endpoint information. All sentences are informative, though the pricing detail is auxiliary.

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

Completeness5/5

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

For a simple, single-parameter decode tool with no output schema, the description provides sufficient detail: examples, edge cases, input range, and output format. Nothing essential is missing.

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

Parameters3/5

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

Schema coverage is 0%, so the description partially compensates by giving examples and stating the value range (1–30). It omits the maximum array length (28) and does not explain the output structure in more detail.

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 that it returns tree edges for a Prüfer code as a flat list of sorted pairs, with concrete examples. It clearly identifies the decode operation but does not explicitly contrast with sibling tools like prufer_encode or prufer_degree.

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 explicit guidance on when to use this tool versus alternatives such as prufer_encode. Usage is only implied by the examples and the tool name.

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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