ScorpTech x402 Tools

Cyclotomic Height

cyclotomic_height

Read-onlyIdempotent

The largest absolute coefficient of Phi_n. Phi_1 through Phi_15 have height 1. Phi_105 has height 2. n runs from 1 to 120. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cyclotomic-height

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": "cyclotomic_height"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.5/5.0

Behavior4/5

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

Annotations already declare read-only, idempotent, non-destructive, and open-world behavior. The description adds useful behavioral context beyond annotations: a per-success price, the x402/Solana payment model, and an equivalent 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.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The definition is front-loaded and the sentences are short and purposeful. Examples, range, price, and endpoint information are all relevant, though the two example sentences could be tightened.

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?

With no output schema, the description explains the returned quantity as the largest absolute coefficient of Phi_n and gives examples. For a one-parameter mathematical tool with annotated safety behavior, this is complete enough, though it could explicitly state the return type.

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 description coverage is 0%, so the description must carry parameter meaning. It supplies the valid range and illustrative values such as Phi_1 through Phi_15 and Phi_105, but it does not fully explain the index semantics beyond the Phi_n notation.

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 precisely defines the computed quantity as the largest absolute coefficient of Phi_n, which is more specific than merely restating the title. It does not explicitly name sibling alternatives such as cyclotomic_coeff, but the stated metric is distinctive enough to infer the difference.

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?

The description gives the valid range n = 1 to 120 and sample values, but it does not say when to use this tool instead of related cyclotomic tools. There are no explicit alternatives, exclusions, or usage conditions.

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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