By Mario Alexandre · March 27, 2026 · 12 min read
I have spent two years building prompt engineering tools. I ran 275 experiments on prompt structure. I measured the difference between raw and structured prompts on every major LLM. This guide shares what I learned about talking to AI models in 2026. It is not the surface tips you see everywhere. It is the math framework that explains why some prompts work and most do not.
When you send a prompt to an LLM, you are sending a specification. The model tries to rebuild your intent from that specification. The problem is that most prompts are very underspecified. They contain only a fraction of the information the model needs to give you exactly what you want.
I call this specification aliasing. The term comes from signal processing theory. When you sample a signal below the Nyquist rate, the result contains false frequencies. These are artifacts that were never in the original signal. In LLM terms, those artifacts are hallucinations, irrelevant tangents, wrong formats, and misunderstood requirements.
This is the Nyquist-Shannon sampling theorem. It is the math foundation of sinc-LLM. Your intent is the continuous signal x(t). The prompt is the set of discrete samples x(nT). The LLM output is the reconstruction. If you sample at the Nyquist rate, which is 6 bands, the reconstruction is perfect. Below that rate, you get aliasing.
After many experiments, I found exactly 6 independent specification dimensions. Together they capture the full bandwidth of LLM task specification:
Six is not arbitrary. I tested decompositions from 3 bands to 12 bands across 275 experiments. Below 6 bands, output quality drops. Missing dimensions cause hallucinations. Above 6 bands, the extra dimensions are redundant. They can be expressed as combinations of the core 6. Six is the Nyquist rate: the minimum sampling rate that captures the full specification bandwidth without aliasing.
The CONSTRAINTS band (n=3) is the most important by far. Removing any other single band lowers output quality by 8-15%. Removing CONSTRAINTS lowers it by 42.7%. This makes sense. Constraints set the boundary conditions for acceptable output. Without them, the model explores regions you never intended.
sinc-LLM outputs structured prompts in sinc JSON format. This is a standard representation that works with every major LLM:
{
"formula": "x(t) = \u03a3 x(nT) \u00b7 sinc((t - nT) / T)",
"T": "specification-axis",
"fragments": [
{"n": 0, "t": "PERSONA", "x": "Expert data scientist with 10 years ML experience"},
{"n": 1, "t": "CONTEXT", "x": "Building a recommendation engine for an e-commerce platform"},
{"n": 2, "t": "DATA", "x": "Dataset: 2M user interactions, 50K products, sparse matrix"},
{"n": 3, "t": "CONSTRAINTS", "x": "Must use collaborative filtering. Latency under 100ms. No PII in logs. Python 3.11+. Must handle cold-start users with content-based fallback"},
{"n": 4, "t": "FORMAT", "x": "Python module with type hints, docstrings, and pytest tests"},
{"n": 5, "t": "TASK", "x": "Implement the recommendation engine with train/predict/evaluate methods"}
]
}
This format is not just for readability. The JSON structure ensures every band is present. It documents the formula. It also lets you parse the prompt with code for automated pipelines.
Before writing a prompt, ask yourself: "What would I specify in each of the 6 bands?" If you cannot fill a band, that is a gap. The LLM will fill that gap with guesses. The technique is simple. Think in bands, not in prose. Read more in our 7 techniques article.
Make the CONSTRAINTS band the longest band in every prompt. Include what to do and what not to do. Add boundary conditions, quality requirements, technical specs, and guardrails against hallucinations. See best practices for detailed examples.
Treat the FORMAT band as a contract, not a suggestion. Instead of "provide a summary," specify "JSON object with keys: title (string, max 60 chars), summary (string, 2-3 sentences), key_points (array of 3-5 strings), confidence (float 0-1)."
Put real data in the DATA band. Use real examples, real numbers, real code. The model uses your data as anchor points. If you provide accurate data, the output stays close to reality. If you provide no data, the model generates plausible-sounding fiction. Learn more about preventing hallucinations.
Generic personas produce generic output. "You are a helpful assistant" is the worst persona you can write. It gives the model no domain expertise to draw on. Instead, name the exact expert you would hire for this task: "Senior tax attorney specializing in multi-state S-corp taxation with 20 years of practice."
The 6-band structure works with any model. Still, each model has traits worth knowing:
The fastest way to start with 6-band decomposition is to use sinc-LLM. Paste any raw prompt and it breaks it into all 6 bands. It fills in content for any missing dimensions. No theory needed. Just paste and get a structured prompt that works.
If you are just starting out, read our beginner's guide. For more advanced work, explore few-shot prompting, zero-shot prompting, and chain-of-thought prompting.
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