ScorpTech x402 Tools

Cyclotomic Neg

cyclotomic_neg

Read-onlyIdempotent

Phi_n(-1). n=1 gives -2, n=2 gives 0, n=6 gives 3, and n=10 gives 5. 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-neg

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_neg"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.6/5.0

Behavior4/5

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

Annotations already declare read-only, idempotent, non-destructive behavior. The description adds important context beyond annotations: the cost per call, the availability of an HTTPS endpoint, and the valid range for n. It does not contradict annotations.

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 relatively concise and front-loads the core purpose with 'Phi_n(-1)' before examples, constraints, and pricing. It could be slightly better organized, but every sentence 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?

Given the tool's simplicity, the rich annotations, and the lack of an output schema, the description provides sufficient context for an agent to call it correctly: it defines the function, gives examples, states the input range, and discloses cost and alternative access. Minor gaps include error handling, but overall it is complete.

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?

The single parameter n lacks a schema description (0% coverage), but the description compensates by specifying its range (1 to 120) and giving examples of n values with corresponding outputs. This adds substantial meaning beyond the schema's type and bounds.

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 operation: evaluating the n-th cyclotomic polynomial at -1, with concrete examples. It clearly indicates what the tool computes, though it does not explicitly differentiate from sibling tools like 'cyclotomic' which may compute the polynomial itself rather than its value at -1.

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 provides no guidance on when to use this tool versus alternatives. It lacks any mention of prerequisites, typical use cases, or comparison to sibling tools such as 'cyclotomic' or 'cyclotomic_one'.

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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