ScorpTech x402 API

Biunitary Sigma

biunitary_sigma

Read-onlyIdempotent

The sum of the bi-unitary divisors of n. For a prime power p^e the exponents run from 0 through e, skipping the middle one when e is even. 6 gives 12, 16 gives 27, 36 gives 50, and 48 gives 108. n runs from 1 to 1000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/biunitary-sigma

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": "biunitary_sigma"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.9/5.0

Behavior4/5

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

Annotations already cover readOnly, idempotent, openWorld, and non-destructive behavior. The description adds useful behavioral context beyond that: cost per successful x402/Solana call and an equivalent HTTPS endpoint, though it does not discuss error behavior or rate limits.

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 definition is front-loaded and the sentences are mostly purposeful. The multiple examples and pricing/endpoint details add density, but they are relevant and not wasted.

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 simple mathematical function with no output schema, the description is largely complete: it defines the computation, gives examples, states the input range, and includes payment/endpoint details. Missing edge-case or error behavior is minor for this tool type.

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

Parameters3/5

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

There is only one parameter, n, and the schema already defines its type and 1..1000000 bounds. The description repeats the range and gives example n values, but with 0% schema description coverage it adds only modest semantic detail beyond the schema.

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 a specific mathematical verb+resource: the sum of the bi-unitary divisors of n. It also clarifies the bi-unitary exponent rule for prime powers and gives concrete outputs, which distinguishes it from related sigma tools even without naming them.

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 mathematical definition, and the examples show expected outputs. However, it does not explicitly say when to choose this over close siblings such as unitary_sigma, infinitary_sigma, or sigma_k, nor does it state exclusions.

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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