ScorpTech x402 Tools

Ballot

ballot

Read-onlyIdempotent

The ballot number B(n, k) = (n-k+1)/(n+1) * binom(n+k, k), for 0 <= k <= n. B(n, n) is the nth Catalan number. k above n is rejected. Both indexes run up to 2048. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/ballot

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>",
      "k": "<k>"
    },
    "name": "ballot"
  }
}

Input Schema

Name	Required	Description	Default
`k`	Yes
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4.3/5.0

Behavior4/5

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

Annotations already cover read-only, idempotent, non-destructive, and open-world behavior. The description adds useful non-schema context: the x402/Solana pricing model, HTTPS endpoint, and rejection rule for k > n; it does not describe the return format or error shape, but it goes beyond annotations.

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?

The formula is front-loaded, followed by the Catalan relation, domain rule, bounds, and payment details. Every sentence provides operational or mathematical information, with no filler.

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 two-parameter math calculator with no output schema, the description is largely complete: it defines the computation, domain, bounds, and payment model. It could add the return type or precision behavior for very large values, which matters at n,k up to 2048.

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 description coverage is 0%, so the description must carry parameter meaning. It fully defines the roles of n and k in the formula, gives the valid domain 0 <= k <= n, explains that k above n is rejected, and states the 2048 upper bound for both indexes.

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?

The description gives an exact mathematical definition of the ballot number B(n,k), including its formula and the special Catalan case. This lets an agent distinguish it from generic combinatorics siblings even without naming them 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?

It states the core domain constraint (0 <= k <= n) and that k above n is rejected, which implies correct usage. However, it does not explicitly compare with relevant siblings such as catalan, binom, or multichoose, so an agent must infer when to prefer this tool.

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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