sinc-LLM: Open Source Framework for Nyquist-Compliant Prompts

What Is sinc-LLM?

sinc-LLM is the open-source framework I built. It uses the Nyquist-Shannon sampling theorem to build LLM prompts. Instead of trial and error, it uses math you can check yourself.

I based it on my sinc-LLM paper, where I analyzed 275 production prompt-response pairs across 11 autonomous agents and demonstrated a 97% cost reduction while increasing output quality from SNR 0.003 to 0.92. The math is open and you can check it yourself. The harder question is whether your AI vendor lets you audit their system at all. This article explains the framework. The audit at the end gives you the questions to ask about source-code ownership and platform lock-in.

Core Concepts

I designed sinc-LLM to treat every prompt like a sampled signal. Here are the key ideas:

• 6 Specification Bands, PERSONA, CONTEXT, DATA, CONSTRAINTS, FORMAT, TASK. Every complete prompt must include all 6.
• Nyquist Rate, The lowest rate that still captures the full signal. For prompts, this means all 6 bands must be present.
• Aliasing = Hallucination, When bands are missing, the model makes things up to fill the gaps. This is the same as aliasing in signal processing.
• Band Weighting, CONSTRAINTS (42.7%) and FORMAT (26.3%) matter most for quality. Give them more tokens.

Architecture

The framework has three parts:

1. Auto-Scatter Engine

This tool takes any raw prompt and splits it into 6 bands. It finds missing bands and suggests content to fill them. You can use it from the command line or as an HTTP API.

py -X utf8 auto_scatter.py "your raw prompt" --execute
# or
POST http://localhost:8461/execute

2. sinc JSON Format

A simple format for prompts that meet the Nyquist standard:

{
  "formula": "x(t) = ... sinc((t - nT) / T)",
  "T": "specification-axis",
  "fragments": [
    {"n": 0, "t": "PERSONA", "x": "..."},
    {"n": 1, "t": "CONTEXT", "x": "..."},
    {"n": 2, "t": "DATA", "x": "..."},
    {"n": 3, "t": "CONSTRAINTS", "x": "..."},
    {"n": 4, "t": "FORMAT", "x": "..."},
    {"n": 5, "t": "TASK", "x": "..."}
  ]
}

3. Online Transformer

A free web tool at sincllm.com that turns any raw prompt into sinc JSON format right away.

Getting Started

Clone the repository and start using sinc-LLM in under 5 minutes:

git clone https://github.com/mdalexandre/sinc-llm.git
cd sinc-llm
pip install -r requirements.txt
py -X utf8 auto_scatter.py "Write a blog post about AI" --execute

The auto-scatter engine splits the raw prompt into 6 bands. It finds that CONSTRAINTS, FORMAT, and DATA are missing. Then it suggests content to fill each one.

Community and Contributing

I released sinc-LLM under an open source license on GitHub. You can help in several ways:

• Better band detection
• Support for languages other than English
• Plugins for popular LLM frameworks (LangChain, LlamaIndex)
• Tests with different models
• More studies on band weighting

Read my full paper for the math behind it. Try my online transformer to see it work.

The Bigger Question

The framework is open source for a good reason. The math is the math. The 6 bands are the 6 bands. You can read the code, fork the repo, and suggest better metrics. The argument is yours to check.

Auditing the open framework is the easy part. The hard part is asking your AI vendor if their prompt stack can be audited at all. Do they give you source code in the contract? Can you keep running after termination? Most vendors lock you in.

{
  "formula": "x(t) = Σ x(nT) · sinc((t - nT) / T)",
  "T": "specification-axis",
  "fragments": [
    {
      "n": 0,
      "t": "PERSONA",
      "x": "You are a Open source maintainer and developer advocate. You provide precise, evidence-based analysis with exact numbers and no hedging."
    },
    {
      "n": 1,
      "t": "CONTEXT",
      "x": "This analysis is part of a production system where accuracy determines revenue. The sinc-LLM framework identifies 6 specification bands with measured importance weights."
    },
    {
      "n": 2,
      "t": "DATA",
      "x": "Fragment importance: CONSTRAINTS=42.7%, FORMAT=26.3%, PERSONA=7.0%, CONTEXT=6.3%, DATA=3.8%, TASK=2.8%. SNR formula: 0.588 + 0.267 * G(Z1) * H(Z2) * R(Z3) * G(Z4). Production data: 275 observations, 51 agents."
    },
    {
      "n": 3,
      "t": "CONSTRAINTS",
      "x": "State facts directly. Never hedge with 'I think' or 'probably'. Use exact numbers for every claim. Do not suggest generic solutions. Every recommendation must be specific and verifiable. Include at least 3 MUST/NEVER rules specific to this task."
    },
    {
      "n": 4,
      "t": "FORMAT",
      "x": "Lead with the definitive answer. Use structured headers. Tables for comparisons. Numbered lists for sequences. Code blocks for implementations. No trailing summaries."
    },
    {
      "n": 5,
      "t": "TASK",
      "x": "Write the getting-started tutorial for sinc-llm showing pip install through first SNR computation"
    }
  ]
}