You Have Been Using AI Wrong. Here Is the Proof.
By Mario Alexandre
March 22, 2026
Prompt EngineeringAI Tips
The Uncomfortable Truth
Every prompt you have ever written to ChatGPT, Claude, Gemini, or any other LLM is broken. Not slightly suboptimal. Not "could be better." Broken. I can prove it with a number: your prompts have a signal-to-noise ratio of 0.003. That means for every 1 token of useful specification, there are 333 tokens of ambiguity the model must fill in by guessing.
You write "Summarize this document" and then complain that the summary is too long, too generic, misses the key points, or includes irrelevant details. You write "Write me a blog post" and get a hedging, disclaimer-filled, mediocre wall of text. You write "Analyze this data" and receive a superficial overview instead of the deep technical breakdown you wanted. Then you blame the model.
The model is not the problem. Your prompt is the problem.
One Sample of a Six-Band Signal
I am Mario Alexandre. I am an electrical engineer, not a prompt engineer. When I looked at how people communicate with LLMs, I did not see a writing problem. I saw a signal processing problem. And signal processing has a theorem for exactly this situation.
x(t) = ฮฃ x(nT) ยท sinc((t - nT) / T)
The Nyquist-Shannon sampling theorem, published in 1949, states: to perfectly reconstruct a signal containing N frequency bands, you need at least N samples. Below that, you get aliasing, phantom signals that look real but do not exist in the original.
Your intent when prompting an AI has 6 specification bands:
PERSONA, who should answer (expert type, voice, perspective)
CONTEXT, the situation, facts, prior state
DATA, specific inputs, numbers, references
CONSTRAINTS, rules, boundaries, what NOT to do
FORMAT, output structure, length, style
TASK, the actual objective
When you write "Summarize this document," you are providing 1 band (TASK) out of 6. That is a 6:1 undersampling ratio. The model MUST fill in the other 5 bands to produce any output at all. Every band it fills in from its training distribution instead of your specification is a potential hallucination, a hedge, a generic default, or an irrelevant tangent.
You are not prompting the model. You are undersampling your own intent and blaming the model for the aliasing artifacts.
The 42.7% You Are Missing
Across 275 production prompt-response pairs, I measured the contribution of each specification band to output quality. The results demolish everything the prompt engineering industry has taught you:
| Band | Contribution to Output Quality | What Most Prompts Include |
|---|---|---|
| CONSTRAINTS | 42.7% | Nothing (0 tokens) |
| FORMAT | 26.3% | Nothing (0 tokens) |
| PERSONA | 12.1% | Sometimes ("Act as...") |
| CONTEXT | 9.8% | Partial |
| DATA | 6.3% | Sometimes |
| TASK | 2.8% | Always (this IS the prompt for most people) |
Read that table again. The TASK, the thing you think is the prompt, accounts for 2.8% of output quality. CONSTRAINTS, the band that almost nobody includes, accounts for 42.7%. You are obsessing over 2.8% of the signal while ignoring 42.7%.
This is why "prompt engineering" feels like voodoo. People tweak their task description endlessly, trying different phrasings, different orderings, different magic words. They are optimizing 2.8% of the signal. The remaining 97.2% is either missing or uncontrolled. No amount of task-phrasing wizardry compensates for missing CONSTRAINTS and FORMAT.
What the Model Does with Your Broken Prompt
When you omit CONSTRAINTS, the model uses defaults from its training distribution:
Hedging language ("It is important to note that...", "While there are many perspectives...")
Disclaimers ("I am an AI and cannot...", "Results may vary...")
Generic structure (introduction, body, conclusion, regardless of whether that is what you needed)
Medium length (not short enough to seem lazy, not long enough to seem excessive)
Professional-but-bland tone (the statistical mean of all tones in training data)
Every one of those defaults is the model filling a CONSTRAINTS gap. You did not say "no hedging," so it hedges. You did not say "no disclaimers," so it disclaims. You did not say "short and direct," so it produces medium-length professional prose. The model is doing exactly what you asked, which is almost nothing.
When you omit FORMAT, the model picks whatever structure appeared most frequently in its training data for similar tasks. That is why every ChatGPT response looks the same: numbered lists, bold headers, and exactly 5 bullet points. That is not ChatGPT's style. That is the absence of your style, filled in with the training distribution's mode.
The Proof: 275 Observations, 97% Cost Reduction
The numbers from the sinc-LLM research are not theoretical projections. They are measurements from production systems running real workloads:
| Metric | Before (Raw Prompts) | After (6-Band sinc) |
|---|---|---|
| Signal-to-Noise Ratio | 0.003 | 0.92 |
| Monthly Token Usage | 80,000 | 2,500 |
| Monthly API Cost | $1,500 | $45 |
| Hallucination Rate | High (uncontrolled) | Near-zero |
| Output Usability | Requires editing | Use as-is |
97% cost reduction. 97% fewer tokens. SNR improvement from 0.003 to 0.92. These are not cherry-picked results from one agent on one task. These are aggregate measurements across 11 agents performing diverse real-world tasks over 275 observations.
The 6-Band Decomposition
Here is the fix. Take any prompt you would normally send and decompose it into 6 bands before sending. The sinc-LLM framework does this automatically, but you can do it manually in 60 seconds:
PERSONA (12.1%): Define the expert who should answer. Not "Act as an expert." Specify: "You are a B2B SaaS copywriter who writes high-converting cold emails in short sentences."
CONTEXT (9.8%): State the situation. Company name, industry, stage, relevant facts. Everything the model needs to situate itself.
DATA (6.3%): Specific inputs. Numbers, references, data points. If you are asking for analysis, provide what to analyze.
CONSTRAINTS (42.7%): This is the big one. What must the output NOT do? Word limits. Forbidden phrases. Required inclusions. Tone rules. Compliance requirements. Format restrictions. Every constraint you add replaces a default the model would have invented.
FORMAT (26.3%): Exact output structure. "Return: subject line, 3 paragraphs, CTA text." Not "write it nicely", specify the skeleton.
TASK (2.8%): The objective. Keep it short. The other 5 bands carry the specification.
A Real Example: Before and After
Here is what a properly decomposed prompt looks like in the sinc JSON format:
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.
{Install:
"formula": "x(t) = Sigma x(nT) * sinc((t - nT) / T)",
"T": "specification-axis",
"fragments": [
{
"n": 0,
"t": "PERSONA",
"x": "You are a direct-response copywriter who writes high-converting cold emails for B2B SaaS companies. You write in short sentences. You never hedge. Every line earns the next line."
},
{
"n": 1,
"t": "CONTEXT",
"x": "DLux Digital is launching a new API product called PayFlow for fintech CFOs. Series A company, 50 employees. The product reduces payment reconciliation time from 4 hours to 12 minutes. Price: $99/month. Competitor Stripe Reconcile charges $299/month."
},
{
"n": 2,
"t": "DATA",
"x": "Product: PayFlow API. Price: $99/mo. Target: CFOs at fintech companies, 50-200 employees. Key metric: 4 hours to 12 minutes reconciliation. Competitor: Stripe Reconcile at $299/mo. Launch date: April 1, 2026."
},
{
"n": 3,
"t": "CONSTRAINTS",
"x": "Maximum 150 words. No jargon. No buzzwords. No 'revolutionary' or 'cutting-edge' or 'leverage'. One CTA only. Do not mention AI or machine learning. Do not use exclamation marks. Subject line must be under 8 words. First sentence must reference a specific pain point the CFO has. Compliance: CAN-SPAM compliant, include unsubscribe mention."
},
{
"n": 4,
"t": "FORMAT",
"x": "Return exactly: (1) Subject line (under 8 words). (2) Email body: 3 short paragraphs. (3) CTA button text (under 5 words). (4) Unsubscribe line. No headers, no formatting, just the raw email text ready to paste into an email tool."
},
{
"n": 5,
"t": "TASK",
"x": "Write a cold outreach email for the PayFlow API launch targeting fintech CFOs."
}
]
}pip install sinc-llm | GitHub | Paper
Compare that to the raw version most people would send: "Write a cold email for my new API product PayFlow targeting fintech CFOs." That raw version forces the model to guess the price, the competitor, the word limit, the tone, the structure, the CAN-SPAM requirements, and the ban on buzzwords. Every guess is a place where the output diverges from what you actually wanted.
Stop Blaming the Model
The models are not broken. GPT-4, Claude, Gemini, they are extraordinarily capable systems that respond precisely to the specifications they receive. The problem is that "Write me a marketing email" is not a specification. It is a wish. And models fulfill wishes the way a genie does: technically correct, but not what you meant, because you did not say what you meant.
Say what you mean. Decompose your intent into 6 bands. Spend most of your effort on CONSTRAINTS (42.7% of quality) and FORMAT (26.3% of quality). The TASK is the easy part, it is the 2.8% you were already getting right.
Try sinc-LLM free to auto-decompose any prompt. Read the token optimization guide to understand the cost implications. Explore the open source framework on GitHub. Or read the full paper with all 275 observations. If you are running production LLM systems and want to implement this at scale, I can help.
The era of raw prompting is over. The signal processing era of AI has begun.
Your prompt is the problem. Fix it in 60 seconds.
Related Articles
How to Reduce LLM API Costs by 97% with Structured Prompting
AI Prompt Constraints: The Most Important Part of Any Prompt
Reasoning Models Burn Tokens Filling Gaps You Left in Your Prompt
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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