ScorpTech x402 API

Neg Pell Count

neg_pell_count

Read-onlyIdempotent

How many nonsquares from 1 through n have an odd continued-fraction period, so the negative Pell equation is solvable. Through 2 there is 1, through 10 there are 3, and through 13 there are 4. n runs from 1 to 500. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/neg-pell-count

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": "neg_pell_count"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.5/5.0

Behavior4/5

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

Annotations already establish that this is a read-only, idempotent, non-destructive operation. The description usefully adds the paid-call price, the x402/Solana payment context, and an HTTPS endpoint, which are relevant behavioral details beyond the annotations.

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 examples, range, and payment details are compact. There is little waste, though the payment/endpoint sentence is operationally separate from the core mathematical definition.

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 counting tool with no output schema, the description gives enough context: what is counted, the input range, illustrative outputs, and cost/access details. It does not define the underlying terms in depth, but that is a minor gap for this audience.

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?

Schema description coverage is 0%, so the description must carry the burden. It clarifies that n is an upper bound from 1 to 500 and provides sample mappings such as n=10 returning 3, but it does not add syntax or further parameter detail beyond that.

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 mathematical count: nonsquares from 1 through n with an odd continued-fraction period. It is clear what is being counted, but it does not explicitly distinguish this from sibling tools such as neg_pell or pell_equation.

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?

It gives the valid domain of n and illustrative examples, but it provides no guidance on when to use this tool instead of related siblings like neg_pell or pell_equation. There are no exclusions or alternative-selection cues.

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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