ScorpTech x402 Tools

Crt

crt

Read-onlyIdempotent

Solve simultaneous congruences x ≡ a_i (mod m_i). Shared factors are allowed when the system is consistent; an inconsistent system is rejected. The result is the smallest non-negative solution and the lcm of the moduli. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/crt

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": {
      "a": "<a>",
      "m": "<m>"
    },
    "name": "crt"
  }
}

Input Schema

Name	Required	Description	Default
`a`	Yes
`m`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior4/5

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

Annotations already cover read-only, idempotent, non-destructive behavior. The description adds useful operational context: inconsistent systems are rejected, the result includes the smallest non-negative solution and lcm, and calls are paid via x402 on Solana.

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 tightly front-loaded around the mathematical operation, followed by edge-case behavior, return values, and payment/endpoint details. Every sentence adds relevant information without unnecessary prose.

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 read-only math tool with no output schema, the description gives the core result semantics and consistency behavior. It is nearly complete, though it could explicitly tie the a and m arrays to the required paired-input shape and input constraints.

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 does connect a_i to residues and m_i to moduli through the congruence notation, but it does not clarify array constraints such as equal lengths, accepted string integer formats, or the max of 12 elements.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description gives a specific verb and mathematical resource: solving simultaneous congruences x ≡ a_i (mod m_i). This is distinguishable from the many sibling math tools because CRT is a unique operation, not a generic arithmetic helper.

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?

It explains the consistency condition and rejection behavior, which implicitly defines valid use. However, it does not explicitly say when to choose this tool over neighboring modular-arithmetic tools or when not to use it.

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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