ScorpTech x402 API

Cayley Rooted

cayley_rooted

Read-onlyIdempotent

The number of rooted trees on n labeled vertices, n^(n-1). Four vertices give 64. n runs from 1 to 30. 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/cayley-rooted

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": "cayley_rooted"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.8/5.0

Behavior4/5

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

Annotations already declare readOnly/idempotent/non-destructive, so the safety profile is covered. The description adds genuinely useful context beyond annotations: the numeric overflow behavior (decimal string past 15 digits) and the $0.001 USDC x402 pricing per successful call, which is important pre-call information.

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?

Front-loads the definition, formula, and example, then domain, output format, and pricing in quick succession. Slightly dense but each sentence carries distinct information with no true waste.

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 correctly explains the return value (integer normally, decimal string past 15 digits) and the input bound. Complete enough for an agent to call correctly; only missing explicit sibling differentiation.

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 coverage is 0%, so the description must carry parameter meaning. It does: 'n runs from 1 to 30' clarifies the single parameter's semantic domain and meaning (count of labeled vertices), compensating for the undocumented schema.

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?

States a specific mathematical function with verb-like framing, gives the exact formula n^(n-1), a concrete example (4 vertices -> 64), and defines the domain. This distinguishes it implicitly from the 'cayley' sibling (which uses n^(n-2)) via the formula, though it never names that sibling explicitly.

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?

Provides the valid input range (n from 1 to 30) and output format behavior, which guides correct invocation. However, it never says when to use this versus the 'cayley' sibling or other tree-counting tools, leaving the alternative selection to inference from the formula.

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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