ScorpTech x402 Tools

Duffinian Gcd

duffinian_gcd

Read-onlyIdempotent

The greatest common divisor of n and its divisor sum. 4 gives 1, 6 gives 6, 9 gives 1, and 15 gives 3. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/duffinian-gcd

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": "duffinian_gcd"
  }
}

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 readOnly/idempotent/non-destructive, and the description adds genuinely new behavioral context: a per-call cost ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint. It does not mention failure behavior or what happens outside the range, so it is strong but not exhaustive.

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?

Definition first, then concrete examples, then domain, then pricing/endpoint — well front-loaded with no filler. Every sentence carries information, though the HTTPS duplication and price sentence could arguably be merged.

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 single-parameter pure math function with no output schema, the description supplies enough: formula, sample outputs, valid domain, and cost. Only execution-edge details (errors at boundaries, response shape) are absent, which is minor for this tool class.

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 carry the load, and it does explain that n is the integer whose divisor sum is taken and that it is bounded to 1..1000000 (repeating the schema min/max but adding semantic role). The worked examples further pin down what a valid n looks like.

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?

States the exact computation: 'The greatest common divisor of n and its divisor sum', which is a precise verb+resource combination, and the worked examples (4→1, 6→6) remove ambiguity about what is being gcd'ed. It does not differentiate from near-neighbours such as duffinian, duffinian_sum, or gcd_sum, so it falls short of a 5.

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 domain constraint ('n runs from 1 to 1000000') and the examples imply when the tool applies, but there is no explicit guidance on when to choose this over duffinian_sum or gcd_sum, and no stated exclusions or preconditions beyond the range. Usage is inferable but not directed.

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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