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Mario Alexandre
Mario Alexandre

Posted on • Originally published at tokencalc.pro

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

#llm #python #ai #opensource

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

By Mario Alexandre
March 21, 2026
sinc-LLM
Prompt Engineering

What Is sinc-LLM?

sinc-LLM is an open source framework that applies the Nyquist-Shannon sampling theorem to Large Language Model prompts. It provides a mathematical foundation for prompt engineering, replacing trial-and-error with formal specification theory.

x(t) = Σ x(nT) · sinc((t - nT) / T)

The framework is based on the sinc-LLM paper by Mario Alexandre, which 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.

Core Concepts

sinc-LLM treats every prompt as a sampled version of a continuous specification signal. The key concepts:

  • 6 Specification Bands, PERSONA, CONTEXT, DATA, CONSTRAINTS, FORMAT, TASK. Every complete prompt must sample all 6.

  • Nyquist Rate, The minimum sampling rate for faithful reconstruction. For prompts, this means all 6 bands must be present.

  • Aliasing = Hallucination, When bands are missing, the model fills them with phantom specifications. This is mathematically equivalent to aliasing in signal processing.

  • Band Weighting, CONSTRAINTS (42.7%) and FORMAT (26.3%) carry the most quality weight. Token allocation should reflect this.

Architecture

The framework provides three components:

1. Auto-Scatter Engine

Takes any raw prompt and decomposes it into 6 specification bands. Identifies missing bands and suggests content. Available as CLI tool and HTTP API.

py -X utf8 auto_scatter.py "your raw prompt" --execute

or

POST http://localhost:8461/execute

2. sinc JSON Format

A structured format for Nyquist-compliant prompts:

{
"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 tokencalc.pro that converts raw prompts into sinc JSON format in real time.

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 will decompose the raw prompt into 6 bands, identify that CONSTRAINTS, FORMAT, and DATA are missing, and suggest content for each missing band.

Community and Contributing

sinc-LLM is released under an open source license on GitHub. Contributions are welcome in several areas:

  • Band detection accuracy improvements

  • Language support beyond English

  • Integration plugins for popular LLM frameworks (LangChain, LlamaIndex)

  • Empirical validation studies with different models

  • Additional ablation studies on band weighting

Read the full paper for the theoretical foundation. Try the online transformer to see it in action.

Transform any prompt into 6 Nyquist-compliant bands

Try sinc-LLM Free

Related Articles

Real sinc-LLM Prompt Example

This is the exact JSON format that sinc-LLM uses. Paste any raw prompt at tokencalc.pro to generate one automatically.

{
"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"
}
]
}Install: pip install sinc-llm | GitHub | Paper

Originally published at tokencalc.pro

sinc-LLM applies the Nyquist-Shannon sampling theorem to LLM prompts. Read the spec | pip install sinc-prompt | npm install sinc-prompt

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