ScorpTech x402 API

Mertens Max

mertens_max

Read-onlyIdempotent

The largest absolute value of the Mertens function M(k) for k from 1 through n, and the smallest k where it occurs. Through 10 the maximum is 2 at k = 5. Through 100 it is 4 at k = 31. 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-max

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_max"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.9/5.0

Behavior4/5

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

Annotations already cover read-only, idempotent, open-world, and non-destructive behavior. The description adds useful context beyond annotations: price per successful call, x402/Solana payment, an HTTPS endpoint, and the maximum n. It does not disclose latency, error behavior, or exact response fields, but those are secondary for this simple computation.

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 definition is front-loaded, followed by examples, constraints, and payment/endpoint details. The two numerical examples are useful but slightly expand the text; overall every part serves a purpose.

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 simple one-parameter mathematical tool with no output schema, the description adequately explains what is computed, the input range, and examples of the output values. It leaves minor ambiguity about exact response field names and whether the returned maximum is signed or absolute, but the core call semantics are clear.

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 there is only one parameter. The description explains that n is the upper bound for k from 1 through n and repeats the 1..1000000 range, adding mathematical meaning beyond the bare integer schema; examples further clarify behavior.

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 states a precise computation: the largest absolute value of the Mertens function over k=1..n and the smallest k where it occurs. It gives concrete examples and is clearly distinguishable from the sibling mertens tool, which presumably computes a single Mertens value.

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?

It gives the valid range of n and examples, but does not say when to choose this tool over siblings such as mertens or other number-theoretic tools. There are no explicit when-to-use, when-not-to-use, or alternative-routing instructions.

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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