ScorpTech x402 API

Dedekind Psi

dedekind_psi

Read-onlyIdempotent

Dedekind's psi function, n times the product of (1+1/p) over the distinct prime factors of n. psi(1) is 1, psi(2) is 3, and psi(6) is 12. n runs from 1 to 1000000000000. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/dedekind-psi

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": "dedekind_psi"
  }
}

Input Schema

Name	Required	Description	Default
`n`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 23, 2026

TDQS

A4/5.0

Behavior4/5

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

Annotations already establish read-only, idempotent, non-destructive behavior. The description adds important non-annotation context: cost per successful call, x402/Solana payment, and an 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.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the definition; examples, range, price, and endpoint each add useful information without filler. No sentence is 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 one-parameter math tool with annotations, the description covers domain, examples, cost, and access route. It omits an explicit statement of return type or error behavior, though the examples make the return value inferable.

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?

With zero schema description coverage, the description compensates by defining n as the input to psi and giving bounds plus examples. It does not add format details beyond integer, but that is sufficient for this one-parameter tool.

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?

States the exact mathematical function, formula, and sample values, uniquely identifying dedekind_psi among the many math siblings. An agent can determine what it computes without opening the schema.

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?

Gives the input domain but no guidance on when to choose this over sibling functions or when not to use it. Usage is implied by the function definition rather than explicitly routed.

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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