ScorpTech x402 Tools

Wythoff

wythoff

Read-onlyIdempotent

The nth lower Wythoff number, floor(n*phi), where phi is (1+sqrt(5))/2. A(1) is 1, A(2) is 3, and A(5) is 8. 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/wythoff

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": "wythoff"
  }
}

Input Schema

Name	Required	Description	Default
`n`	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 readOnlyHint, idempotentHint and destructiveHint=false, so the safety profile is covered. The description adds genuinely new behavioral context: pricing ($0.001 USDC per successful call via x402 on Solana) and an equivalent HTTPS endpoint, which matter for invocation planning. It does not state the return type explicitly, which keeps it below 5.

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?

Four short sentences, front-loaded with the definition and formula, followed by examples, range, then cost/endpoint logistics. Every sentence carries information, though the pricing/URL tail is operational rather than mathematical.

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 single-parameter math tool with no output schema, the description covers the domain definition, input range, sample outputs, and cost. The only gap is that sibling differentiation (wythoff_lower et al.) is absent, which matters in a catalog with seven Wythoff-family tools.

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 the param, and it does: n runs from 1 to 1000000, matching the schema bounds, plus examples anchoring what output corresponds to what input. The type/format (integer) is left to the schema.

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?

It states a specific verb+resource: the nth lower Wythoff number with an explicit formula (floor(n*phi)) and worked examples (A(1)=1, A(2)=3, A(5)=8). The distinction from siblings is only implicit ('lower' vs wythoff_upper), and the description never names wythoff_lower, wythoff_inverse, or wythoff_pair, which it is easily confused with.

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 definition and examples, but there is no statement of when to choose this over wythoff_lower (likely the same sequence), wythoff_upper, wythoff_inverse, or wythoff_pair. The agent must infer routing from the formula alone.

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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