ScorpTech x402 Tools

Partition Conjugate

partition_conjugate

Read-onlyIdempotent

The conjugate of an integer partition, read down the columns of its Ferrers diagram. Parts must be positive and nonincreasing. The empty partition is its own conjugate. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/partition-conjugate

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": {
      "parts": "<parts>"
    },
    "name": "partition_conjugate"
  }
}

Input Schema

Name	Required	Description	Default
`parts`	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 establish read-only, idempotent, non-destructive behavior. The description adds useful context: input invariants, the empty-partition edge case, x402 pricing, and an alternate HTTPS endpoint.

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 constraints, edge case, and access details. The description is compact with no filler.

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 mathematical transformation with annotations and no output schema, the description gives enough to call it correctly. The only minor gap is not explicitly stating the return representation, though the first sentence implies it.

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 must carry parameter meaning. It usefully states that parts must be positive and nonincreasing and covers the empty partition, but it does not fully describe the array representation or reconcile the schema's allowance of zeros.

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 names a specific mathematical operation, the conjugate of an integer partition, and explains it via Ferrers diagram columns. It is clear what the tool computes, though it does not explicitly distinguish itself from sibling partition-related tools.

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 mathematical definition and the input constraints, but there is no explicit when-to-use guidance or comparison to alternatives such as partition or partition_parts.

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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