ScorpTech x402 Tools

Three Squares

three_squares

Read-onlyIdempotent

Whether n is a sum of three integer squares, and one nonnegative witness x <= y <= z when it is. It is impossible exactly when n = 4^power * odd with odd congruent to 7 mod 8. 3 is 1, 1, 1. 7 is impossible. n runs from 0 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/three-squares

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": "three_squares"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.7/5.0

Behavior4/5

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

Annotations already mark this as read-only, idempotent, non-destructive, and open-world. The description adds useful behavioral context beyond annotations: the exact impossibility condition, witness format, valid input range, examples, x402 price, and 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.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is front-loaded with the core mathematical purpose and witness definition, followed by the criterion, examples, bounds, and payment/endpoint details. It is appropriately sized, though the examples and operational notes could be tightened slightly.

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 explains the return concept as a truth value plus witness when possible, which is sufficient for this tool. It also covers bounds and payment access, leaving only minor gaps around exact output field names or error behavior.

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?

There is one parameter, n, and schema description coverage is 0%. The description compensates somewhat by saying n runs from 0 to 1000000 and giving examples, but it largely repeats the schema's min/max bounds and does not add deep semantics beyond the obvious integer input.

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 precise verb-like function: determining whether n is a sum of three integer squares and returning a nonnegative witness x <= y <= z. It is clearly distinct from siblings like two_squares and four_squares by the specific 'three squares' property, though it does not explicitly name alternatives.

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 question and the impossibility criterion, but there is no explicit guidance such as when to choose this over two_squares or four_squares. The HTTPS endpoint note is operational, not selection guidance.

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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