6-Band Prompt Decomposition: The Complete Technical Guide

What Is 6-Band Decomposition?

Most prompts fail because they undersample the specification. They name a task without naming the constraints, or they describe a persona without setting the format, or they give context but skip the data. The output is then a guess across the missing dimensions, which is what hallucination actually is at the signal level.

I built the sinc-LLM framework on a Nyquist-Shannon argument applied to prompts: every effective specification samples exactly six bands, identified empirically from 275 production prompt-response pairs across 11 autonomous agents. This article maps each band, its measured weight in output quality, and the diagnostic question you can ask any AI vendor about how they handle it.

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. In my production systems, 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. I found this consistent across all 11 agents I 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 I observed 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.

The Bigger Question

Six bands. Three weight tiers. Two ratios that beat surface metrics. Use the framework on every prompt before you ship it to production.

Decomposing your own prompts is the easy part. The hard part is asking your AI vendor whether their CONSTRAINTS band is 40+% of tokens, whether they monitor band-coverage drift, whether they can show you the prompt template currently running your workload. Most can't answer in plain English. Their inability is the answer.

{
  "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"
    }
  ]
}