ScorpTech x402 API

Centered Polygonal

centered_polygonal

Read-onlyIdempotent

The nth centered s-gonal number, sn(n-1)/2 + 1. Centered triangular 4 is 19, centered square 2 is 5, and centered hexagonal 3 is 19. s runs from 3 to 20 and n 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/centered-polygonal

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": {
      "s": "<s>",
      "n": "<n>"
    },
    "name": "centered_polygonal"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes
`s`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A3.8/5.0

Behavior4/5

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

Annotations already declare read-only, idempotent, non-destructive, open-world behavior. The description adds useful behavioral context beyond annotations: the x402 pricing model ($0.001 USDC per successful call) and an alternate HTTPS endpoint.

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 description is front-loaded with the definition and formula, followed by examples and constraints. The pricing and endpoint sentence is ancillary but useful for this paid API context; overall it is efficient and free of 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 mathematical computation with no output schema, the description provides enough to invoke correctly: formula, examples, ranges, and payment/endpoint details. Explicitly stating the return type would make it complete.

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 parameter meaning. It provides the formula relating s and n, states their valid ranges, and gives worked examples that map s to polygon type and n to the index, compensating well for the missing schema descriptions.

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 clearly identifies the mathematical object computed: the nth centered s-gonal number, with the exact formula. It distinguishes from the ordinary polygonal sibling implicitly through 'centered' and the formula, but does not explicitly name or contrast with the non-centered `polygonal` tool.

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?

Valid input ranges are stated, but there is no explicit guidance on when to use this tool versus the non-centered `polygonal` or related siblings. Usage is implied by the mathematical definition rather than stated.

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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