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Cube Ways

cube_ways
Read-onlyIdempotent

How many ways n is a sum of positive cubes, ignoring order and allowing repeats. 0 has 1 empty sum, 2 has 1, 8 has 2, and 16 has 3. n runs from 0 to 2000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/cube-ways

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": "cube_ways"
  }
}

Input Schema

NameRequiredDescriptionDefault
nYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

TDQS

A4.2/5.0
Behavior4/5

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

Annotations already declare readOnly, idempotent, non-destructive, and open-world behavior, so the bar is lower. The description still adds real context: the input domain cap of 2000, the $0.001 USDC per-successful-call price on x402/Solana, and an alternative HTTPS endpoint — all things the agent cannot learn from annotations or schema.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Three short sentences: definition and examples first, valid domain second, commercial/transport details last. Every clause carries information — no filler, no restatement of the title.

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 one-parameter deterministic math tool with no output schema, the definition plus examples are sufficient to predict the result. The only gap is that it never explicitly says the return value is a single integer count, though 'how many ways' strongly implies it.

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 the parameter meaning, and it does: it defines n as the number being decomposed into cubes and gives the 0–2000 range plus four concrete input/output examples that make the mapping unambiguous. It does not restate type constraints, but the schema already handles those.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a precise mathematical function (count of unordered, repeat-allowing representations of n as a sum of positive cubes) with worked examples (0→1, 2→1, 8→2, 16→3) that pin down the exact semantics. This clearly separates it from neighbors like cube_sum, cube_min, coin_ways, and partition, whose meanings would otherwise be confusable in a catalog of thousands of math tools.

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?

Usage is implied by the single-purpose nature of the computation and the stated domain (n from 0 to 2000), but there is no explicit guidance on when to prefer this over related siblings such as coin_ways or partition, and no stated error behavior for out-of-range n.

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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