ScorpTech x402 API

Sylvester

sylvester

Read-onlyIdempotent

The nth Sylvester number. s(0) is 2, and each later term is s*(s-1)+1. A negative index is rejected. n runs up to 8. Past 15 digits the value is a decimal string. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/sylvester

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": "sylvester"
  }
}

Input Schema

Name	Required	Description	Default
`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 establish that this is a read-only, idempotent, non-destructive operation. The description adds useful behavior beyond annotations: pricing ($0.001 USDC per successful call), x402/Solana payment context, a negative-index rejection rule, and the output changing to a decimal string past 15 digits.

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 description is compact and front-loaded: definition and recurrence first, then validity constraints, output-size behavior, and payment/endpoint details. Every sentence provides information useful for calling or understanding the tool.

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

Completeness5/5

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

For a one-parameter mathematical sequence tool with no output schema, the description covers the computation, index domain, rejection behavior, output representation threshold, and payment model. An agent has enough information to invoke it correctly and understand the expected return shape.

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 parameter meaning. It explains that n is the index, that s(0) is 2, that negative indexes are rejected, and that n runs up to 8, adding substantial semantics beyond the bare integer/maximum 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 identifies a specific mathematical resource, the nth Sylvester number, and defines it via the base case and recurrence. It also states the valid index range, so an agent can distinguish exactly what this tool computes from unrelated sibling arithmetic utilities.

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 name and definition: call it to obtain a Sylvester number for a given index. The description also notes that negative indexes are rejected and n is capped at 8, but it does not explicitly explain when to choose this tool over alternatives or what workflow it fits into.

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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