ScorpTech x402 API

Cyclotomic

cyclotomic

Read-onlyIdempotent

The cyclotomic value Phi_n(a) for an integer a at least 2. Phi_1(2) is 1, Phi_5(2) is 31, Phi_6(3) is 7, and Phi_1(5) is 4. n runs from 1 to 40 and a from 2 to 20. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cyclotomic

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>",
      "a": "<a>"
    },
    "name": "cyclotomic"
  }
}

Input Schema

Name	Required	Description	Default
`a`	Yes
`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 readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false. The description adds useful non-annotation context: output changes to a decimal string past 15 digits, pricing is $0.001 USDC per successful x402 call on Solana, and an HTTPS endpoint is available.

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 description is front-loaded with the definition and examples, then adds constraints, output format, and payment details. It is appropriately sized, though the phrase 'integer a at least 2' is slightly redundant with the later 'a from 2 to 20' range.

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 two-parameter math tool with rich annotations and no output schema, the description is nearly complete: it explains the computation, input bounds, output type past 15 digits, and pricing/access. The main remaining gap is explicit differentiation from the cyclotomic sibling tools.

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 defines Phi_n(a), gives examples, and states that n runs 1 to 40 and a from 2 to 20, but it largely repeats the schema min/max bounds and does not fully describe each parameter beyond mathematical 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 states a specific mathematical computation, Phi_n(a), with concrete examples and clear input ranges. It does not explicitly distinguish this tool from siblings such as cyclotomic_coeff, cyclotomic_height, cyclotomic_neg, or cyclotomic_one, so sibling differentiation is left to name inference.

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 parameter ranges but does not say when to use this tool versus alternatives like cyclotomic_coeff or cyclotomic_height. No exclusions, prerequisites, or selection guidance are provided.

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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