ScorpTech x402 Tools

Cototient

cototient

Read-onlyIdempotent

The cototient n - totient(n): how many integers from 1 to n share a factor with n. 1 gives 0, 6 gives 4, 9 gives 3, and 10 gives 6. n runs from 1 to 100000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cototient

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": "cototient"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.1/5.0

Behavior4/5

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

Annotations already declare readOnly, idempotent, openWorld, and non-destructive behavior. The description adds useful invocation context: input range, pricing per successful call, and an HTTPS endpoint alternative.

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 examples, range, pricing, and endpoint. Every sentence contributes useful information without redundancy.

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?

For a simple read-only math function with no output schema, the definition is complete: it explains the result, gives sample outputs, states valid n range, and discloses cost and transport details.

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%, but the single parameter is simple and the description gives its allowed range plus concrete input-output examples. Those examples add meaning beyond the raw integer type and min/max constraints.

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?

Defines the cototient precisely with a formula (n - totient(n)) and concrete examples, making the computed quantity unambiguous. It also implicitly distinguishes itself from the sibling totient tool by naming totient(n) in the definition.

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?

Provides no explicit guidance on when to choose this tool over alternatives or when not to use it. The mathematical definition implies usage, but there is no routing guidance among the many sibling math tools.

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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