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Involution Mod

involution_mod
Read-onlyIdempotent

I(n) mod m, the involution number reduced by a positive modulus. Zero is rejected. n runs from 0 to 100. The residue is smaller than the modulus. Price: $0.001 USDC per successful call (x402, Solana). Same tool over HTTPS: POST https://scorptech.it.com/api/x402/v1/involution-mod

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>",
      "mod": "<mod>"
    },
    "name": "involution_mod"
  }
}

Input Schema

NameRequiredDescriptionDefault
nYes
modYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. Added

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, open-world, non-destructive. The description adds genuinely useful context beyond that: a $0.001 USDC per-successful-call cost model with x402/Solana, a rejection rule for zero, and an output bound (residue < modulus). These are real behavioral traits not in the structured fields.

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 core definition, then constraints, cost, and endpoint. Each sentence carries operational information; nothing is redundant padding.

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?

With no output schema, the description supplies the return property (residue smaller than modulus) and covers input constraints, error condition, pricing, and an HTTP fallback. Adequate for a two-parameter read-only math tool, though the string-encoded modulus is under-explained.

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 coverage is 0%, so the description must carry semantics. It clarifies mod as a positive modulus with zero rejected and restates the n range, which helps. But it does not explain why mod is a digit-string up to 600 chars (big-integer representation), leaving a notable gap in the highest-risk parameter.

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?

States a specific operation: the involution number I(n) reduced modulo m, giving verb-like compute semantics and resource. It is clearly the modular variant of the involution family, though it doesn't explicitly name involution/involution_sum as siblings to disambiguate.

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?

'Zero is rejected' and 'n runs from 0 to 100' provide constraint-level guidance that prevents invalid calls. However, there is no explicit when-to-use-vs-alternatives routing (e.g., versus involution or involution_sum), so usage is only implied.

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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