ScorpTech x402 API

Farey Child

farey_child

Read-onlyIdempotent

The mediant child of a Farey-neighbor pair. a/b and c/d must satisfy |ad-bc| = 1. A pair that is not adjacent is rejected, as is a non-positive denominator. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/farey-child

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": {
      "a": "<a>",
      "b": "<b>",
      "c": "<c>",
      "d": "<d>"
    },
    "name": "farey_child"
  }
}

Input Schema

Name	Required	Description	Default
`a`	Yes
`b`	Yes
`c`	Yes
`d`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior4/5

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

Annotations cover the safety profile (readOnly, idempotent, non-destructive), and the description adds genuinely useful extra context: invalid pairs are rejected, and every successful call costs $0.001 USDC via x402 with a documented HTTPS fallback endpoint. The one omission is the shape of the returned value, which no output schema supplies either.

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?

Three sentences, front-loaded with the definition, followed by validation rules and then billing/transport details. Every sentence carries information; the HTTPS endpoint line is slightly redundant but legitimately useful for non-MCP callers.

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 4-parameter pure-function tool with no output schema, the definition covers semantics, preconditions and payment. The only real gap is that an agent cannot predict the return payload (e.g., numerator/denominator object vs. string).

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0%, so the description carries the full burden, and it does: a/b and c/d are the two fractions, the |ad-bc| = 1 relation defines the constraint across all four, and the 'non-positive denominator' rejection identifies b and d as denominators. That is more than the bare integer schema conveys.

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 object ('the mediant child of a Farey-neighbor pair') rather than restating the title, and pins it down with the adjacency condition |ad-bc| = 1. It distinguishes itself from siblings like farey_adjacent and farey_count by naming the operation, though it never spells out that the result is (a+c)/(b+d).

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?

Gives preconditions ('must satisfy |ad-bc| = 1', non-positive denominators rejected) which implicitly tell the agent when the call is valid. However, it never routes the agent against alternatives such as farey_adjacent or mediant, so a caller cannot tell which sibling to pick from the description alone.

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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