ScorpTech x402 Tools

Mertens

mertens

Read-onlyIdempotent

The Mertens function M(n), the sum of the Mobius function mu(k) from 1 through n. M(1) is 1, M(10) is -1, and M(100) is 1. 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/mertens

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": "mertens"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.3/5.0

Behavior4/5

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

The annotations already declare read-only, idempotent, open-world, and non-destructive behavior. The description adds meaningful context beyond that: pricing at $0.001 USDC per successful call via x402 on Solana, plus an HTTPS endpoint alternative, and example return values that imply integer output.

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 mathematical definition, followed by concrete examples, valid range, and payment/transport details. Every sentence is relevant and there is no wasted verbiage.

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 one-parameter mathematical function, the description supplies the definition, examples that imply output format, input bounds, cost model, and alternate endpoint. With annotations covering safety and no output schema needed beyond the integer examples, nothing essential 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 parameter meaning. It defines n as the upper bound of the summation from 1 through n and states the range 1 to 1000000, which compensates well for the bare schema, though it does not explicitly restate the integer type.

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 precisely defines the tool as computing the Mertens function M(n), the summatory function of the Mobius function. It distinguishes the operation from the sibling `mobius` tool by making clear that this returns the cumulative sum, not the individual mu(k) value.

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 description gives a clear mathematical context and valid input range but does not explicitly state when to use this tool versus related siblings such as `mobius` or `mertens_max`. Usage is implied by the function definition rather than spelled out as 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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