ScorpTech x402 Tools

Brocard

brocard

Read-onlyIdempotent

Whether n! + 1 is a perfect square. 4! + 1 = 5^2, 5! + 1 = 11^2, and 7! + 1 = 71^2. The root is 0 when it is not a square. n runs from 1 to 12. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/brocard

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": "brocard"
  }
}

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?

The annotations already establish read-only, idempotent, and non-destructive behavior. The description adds useful context beyond that: it explains that the return value is the root, with 0 when not a square, and it discloses the n range, x402 price, and 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 description is front-loaded with the definition, then adds examples, return behavior, range, and payment/access details without filler. Its length is appropriate for a one-parameter math tool that also includes pricing metadata.

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?

Given the simple one-parameter schema and absence of an output schema, the description supplies the operation, examples, return sentinel, valid input bounds, and access/payment details. Nothing critical for correct invocation is missing.

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 the semantic load. It ties the single parameter n to the factorial expression, gives worked examples, and restates the 1-to-12 domain, which is sufficient for this one-integer tool.

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 specific mathematical test — whether n! + 1 is a perfect square — and gives concrete examples plus the zero-root sentinel. It is clear, but it does not explicitly name Brocard's problem or distinguish this from nearby math tools such as perfect_check or isquare.

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?

There is no explicit when-to-use, when-not-to-use, or alternative-tool guidance, despite the large sibling set of math utilities. The valid n range and examples imply valid input, but they do not help an agent choose this tool over related ones.

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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