The Six Frequencies Every Prompt Must Carry (Or the AI Fills In the Blanks)
Table of Contents
The Core Thesis
Every prompt you write is a signal. That signal carries information across 6 separate frequency bands. If any band is missing, the LLM fills in the gap from its training data. It produces output that looks like an answer but is made up. This is the same as aliasing in signal processing. When you undersample a waveform, you get phantom frequencies that were never there.
My sinc-prompt specification defines these 6 bands based on my empirical research across 1 million simulations and 275 production observations. These are not random categories. They are the 6 information dimensions an LLM needs to understand your intent without guessing.
The Six Bands Defined
Band 0: PERSONA (Weight: 12.1%)
Who should answer this question? This is not just a job title. It includes the area of expertise, the point of view, the communication style, and how much the reader already knows. When PERSONA is missing, the model defaults to "helpful AI assistant." That is the most generic and least useful voice it has.
Signal example: "You are a principal security engineer at a FAANG company reviewing code for production deployment. You communicate findings as severity-ranked issues with remediation steps. You assume the reader is a senior developer."
Absence cost: The model guesses at expertise level, tone, and reader knowledge. Every guess adds error.
Band 1: CONTEXT (Weight: 9.8%)
What situation are we in? What happened before this prompt? What is the environment and the project? CONTEXT gives the model the background it needs to give a useful, focused response.
Signal example: "We are in sprint 14 of a 16-sprint migration from a monolith to microservices. 8 of 12 services are deployed. The remaining 4 share a database that cannot be split until all are migrated. Production traffic: 2,400 requests per second."
Absence cost: The model invents a context from average training data. Your real situation gets ignored.
Band 2: DATA (Weight: 6.3%)
What exact numbers, facts, and measurements does the model need? DATA is the factual base that stops the model from making up statistics that sound real but are not.
Signal example: "Current database: PostgreSQL 14. Rows: 180M in the largest table. Indexes: 23, of which 7 are unused (verified via pg_stat_user_indexes). Average query time: 340ms. P99: 4.7 seconds."
Absence cost: The model makes up numbers. This is the most obvious form of hallucination. It is also the easiest to prevent.
Band 3: CONSTRAINTS (Weight: 42.7%)
What rules, limits, and requirements apply? CONSTRAINTS is the most important band. Nearly half of output quality depends on it. This is the band most people skip entirely.
Signal example: "Never suggest adding hardware. Budget for tooling changes: $0. Maximum acceptable query time: 500ms for p95. All changes must be reversible within 1 hour. Do not modify any table with active writes during business hours (8am-8pm EST). Do not recommend ORM changes."
Absence cost: The model has no limits. Every approach looks equally fine to it. It picks the statistically average recommendation. That is rarely your best option.
Band 4: FORMAT (Weight: 26.3%)
What shape should the output take? Sections, tables, code blocks, numbered steps, paragraphs, JSON? FORMAT removes a whole dimension of model guessing. It keeps output structure consistent.
Signal example: "Return a numbered list of exactly 5 optimizations. Each item: (1) one-line description, (2) exact SQL or configuration change, (3) expected improvement percentage, (4) risk level (LOW/MEDIUM/HIGH), (5) estimated implementation time."
Absence cost: The model picks a random output shape. Different runs give different formats. Anything that parses that output will break.
Band 5: TASK (Weight: 2.8%)
What is the actual goal? What do you want the model to produce? TASK is the only band most people include. It has the least impact on quality because it only states the destination. It does not say how to get there.
Signal example: "Identify the 5 highest-impact PostgreSQL performance optimizations for our production database and provide implementation-ready fixes."
Absence cost: Small, since most people do state their task. The problem is that they state only the task.
What Happens When Bands Are Missing
The Nyquist-Shannon sampling theorem says that to perfectly reconstruct a signal, you must sample at twice its highest frequency. For a 6-band prompt signal, you need at least 6 samples, one per band.
When you provide only the TASK band (1 of 6), you are sampling at 1/6 the Nyquist rate. The result will alias. This is not a risk. It is a mathematical certainty.
| Bands Provided | Sampling Rate | Reconstruction Quality | Aliasing Level |
|---|---|---|---|
| 1 of 6 | 16.7% Nyquist | Catastrophic | 83% fabrication |
| 2 of 6 | 33.3% Nyquist | Poor | 67% fabrication |
| 3 of 6 | 50% Nyquist | Marginal | 50% fabrication |
| 4 of 6 | 66.7% Nyquist | Acceptable | 33% fabrication |
| 5 of 6 | 83.3% Nyquist | Good | 17% fabrication |
| 6 of 6 | 100% Nyquist | Clean | <5% fabrication |
Aliasing: The Technical Term for Hallucination
In signal processing, aliasing produces phantom frequencies. These are signals that look real but are artifacts of undersampling. In LLM prompting, aliasing produces phantom facts. These are outputs that look authoritative but come from missing specification bands.
The word "hallucination" borrows from human cognition. The correct term is specification aliasing. This distinction changes how you fix the problem. You do not need to fix the model. You need to fix the input by adding the missing bands.
Band Interaction Effects
Bands do not work in isolation. My research found significant interaction effects:
- CONSTRAINTS + FORMAT together contribute more than their individual weights suggest. When both are present, the model's probability space collapses on two dimensions at once. This produces a quality gain that multiplies, not just adds.
- PERSONA + CONSTRAINTS interact to set the expertise level at which the model reads your constraints. A "junior developer" persona with "production-grade" constraints produces very different output than a "senior architect" with the same constraints.
- CONTEXT + DATA together remove the model's need to guess the situation. Without both, the model decides what is relevant. With both, relevance is set in advance.
The Optimal Token Allocation
Given a token budget of 200-230 tokens (the optimal range I identified), spend your tokens in proportion to the quality weights:
| Band | Quality Weight | Token Allocation | Target Tokens |
|---|---|---|---|
| CONSTRAINTS | 42.7% | 42-45% | 85-100 tokens |
| FORMAT | 26.3% | 25-28% | 50-60 tokens |
| PERSONA | 12.1% | 10-12% | 20-25 tokens |
| CONTEXT | 9.8% | 10-12% | 20-25 tokens |
| DATA | 6.3% | 8-10% | 15-20 tokens |
| TASK | 2.8% | 3-5% | 5-10 tokens |
Notice the flip from common practice. People spend 80% of their prompt on TASK and 0% on CONSTRAINTS. The optimal split is 3-5% on TASK and 42-45% on CONSTRAINTS.
Practical Application
I built the sinc-LLM tool at sincllm.com to break any raw prompt into 6 bands automatically. It computes the SNR, spots missing bands, and generates the structured prompt for you. You do not need to memorize these weights or build JSON by hand. Paste your raw prompt and get a 6-band signal back.
The math does not care whether you believe in this framework. A 6-band prompt produces better output than a 1-band prompt because 6 samples reconstruct a signal better than 1 sample. This is the Nyquist theorem. It has been proven correct for 75 years.
Transform any prompt into 6 Nyquist-compliant bands
Try sinc-LLM FreeOr install: pip install sinc-llm
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