6-Band Prompt Decomposition: The Complete Technical Guide

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

What Is 6-Band Decomposition?

6-band prompt decomposition is the core technique of the sinc-LLM framework. It treats every LLM prompt as a specification signal composed of 6 frequency bands that must all be sampled to avoid aliasing (hallucination).

x(t) = Σ x(nT) · sinc((t - nT) / T)

The 6 bands were identified empirically from 275 production prompt-response pairs across 11 autonomous agents performing diverse tasks. Every effective prompt, regardless of domain, samples exactly these 6 specification dimensions.

Band 0: PERSONA, Who Answers

Quality weight: ~5%Recommended allocation: 1-2 sentences*Role:* Sets the expertise context and reasoning framework

PERSONA defines the role, expertise, and perspective the model should adopt. It is the lowest-weight band because LLMs can produce competent output with a generic persona, but specific personas improve domain accuracy.

Effective: "You are a senior distributed systems engineer with 10 years of experience in event-driven architectures."

Ineffective: "You are a helpful AI assistant." (This adds no specification information.)

Band 1-2: CONTEXT and DATA, The Facts

CONTEXT quality weight: ~12% | DATA quality weight: ~8%Combined allocation: ~40% of non-CONSTRAINTS tokens

CONTEXT provides situational background: what project, what environment, what has been tried, what constraints exist in the world (not in the output). CONTEXT answers "What is the situation?"

DATA provides specific inputs: code to review, numbers to analyze, documents to summarize, examples to follow. DATA answers "What are the inputs?"

The distinction matters because CONTEXT is reusable across related prompts (same project, same environment) while DATA changes per request. This enables efficient caching of CONTEXT bands.

Band 3: CONSTRAINTS, The Dominant Band (42.7%)

Quality weight: 42.7%Recommended allocation: 40-50% of total prompt tokens*Role:* Narrows the output space to match your specification

CONSTRAINTS is the single most important band. It carries nearly half the output quality weight. This finding was consistent across all 11 agents studied, from code execution to content evaluation to memory management.

Why is CONSTRAINTS dominant? Because LLMs are generative models, they produce the most likely completion given the context. Without constraints, "most likely" means "most generic." Constraints shift the distribution from generic to specific, from the model's default to your actual requirement.

Types of effective constraints:

• Negative constraints: "Do not include X" (most informative per token)

• Quantitative limits: "Maximum N words/items/steps"

• Conditional rules: "If X then Y, else Z"

• Quality gates: "Only include if confidence > threshold"

• Scope boundaries: "Only address X, do not discuss Y or Z"

Band 4-5: FORMAT and TASK

FORMAT quality weight: 26.3% | TASK quality weight: ~6%

FORMAT specifies the exact structure of the output: JSON schema, markdown headers, table format, code style, section order. FORMAT is the second most important band because it directly determines whether the output is usable without post-processing.

TASK is the actual instruction. It carries only ~6% quality weight because by the time bands 0-4 are well-specified, the task is heavily constrained. "Analyze the data" becomes unambiguous when the persona, context, data, constraints, and format are all explicit.

The convergent allocation across all 11 agents:

• CONSTRAINTS + FORMAT: ~50% of tokens (69% of quality weight)

• CONTEXT + DATA: ~40% of tokens

• PERSONA + TASK: ~10% of tokens

Use the sinc-LLM transformer to auto-decompose prompts. Source on GitHub. Full paper at DOI: 10.5281/zenodo.19152668.

Transform any prompt into 6 Nyquist-compliant bands

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Related Articles

• The Prompt Engineering Framework for 2026: Signal-Theoretic Decomposition

• AI Prompt Constraints: The Most Important Part of Any Prompt

• The Nyquist-Shannon Theorem Applied to AI Prompts

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 Signal processing engineer applying DSP to NLP. 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": "Decompose the raw prompt 'Help me plan a marketing campaign' into all 6 specification bands with importance weighting"
}
]
}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