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Thue Cube

thue_cube
Read-onlyIdempotent

Find a cube in a 0/1 string, a block xxx. 000 is a cube at index 0 of length 1. A Thue-Morse prefix has no cube. An empty string or a character other than 0 or 1 is rejected. The string stops at 512 characters. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/thue-cube

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": {
      "bits": "<bits>"
    },
    "name": "thue_cube"
  }
}

Input Schema

NameRequiredDescriptionDefault
bitsYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A3.7/5.0
Behavior5/5

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

Annotations already declare this is a read-only, idempotent, non-destructive operation. The description adds substantial behavioral context beyond that: rejection rules (empty string or non-0/1 characters), a maximum length of 512 characters, a per-call price of $0.001 USDC on Solana via x402, and an alternative HTTPS endpoint. These details are critical for an agent to invoke the tool correctly.

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 appropriately sized and front-loaded, starting with the core operation and an example. Subsequent sentences add essential constraints, pricing, and endpoint information. Minor redundancy exists between the rejection and length sentences, but overall every sentence earns its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's simplicity, the description covers input validation, cost, and access well. However, it does not specify what the tool returns: whether it returns the index and length of the first cube, all cubes, or null if none exists. The example implies output structure but leaves the return behavior ambiguous, which is a gap since there is no output schema.

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 description coverage is 0%, so the description must carry the full burden for the single 'bits' parameter. It does so effectively: it specifies the input must be a 0/1 string, cannot be empty or contain other characters, and is limited to 512 characters. The example '000 is a cube at index 0 of length 1' reinforces the parameter's role as a binary string to search, though it does not explicitly name the parameter.

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 verb ('Find') and resource ('a cube in a 0/1 string'), defines a cube as 'a block xxx', and gives a concrete example ('000 is a cube at index 0 of length 1'). However, it does not explicitly differentiate this tool from sibling tools like thue_morse or thue_prefix, leaving the agent to infer the distinction from the name and description.

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 explicit guidance on when to use this tool versus alternatives. It mentions a mathematical property ('A Thue-Morse prefix has no cube') and input constraints, but these are not framed as usage conditions or comparisons to sibling tools.

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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