Nyquist-Shannon Sampling Theorem Applied to LLM Prompts
sinc-LLM treats every prompt as a signal. If you undersample it, the model hallucinates. That is specification aliasing.
The framework decomposes any raw prompt into 6 frequency bands on the specification axis. Each band carries a different type of information the model needs to produce faithful output.
| Band | n | Weight | What It Carries |
|---|---|---|---|
| PERSONA | 0 | 7.0% | Who should answer — the exact expert type |
| CONTEXT | 1 | 6.3% | Background facts, dates, situation |
| DATA | 2 | 3.8% | Specific inputs, metrics, content to process |
| CONSTRAINTS | 3 | 42.7% | Rules — MUST/NEVER/ALWAYS. Longest band. |
| FORMAT | 4 | 26.3% | Exact output structure |
| TASK | 5 | 2.8% | The specific objective |
CONSTRAINTS carries 42.7% of reconstruction quality. When constraints are absent, the model defaults to hedging, over-qualification, and generic patterns — classic aliasing artifacts. Specifying constraints acts as a bandpass filter on the model's output space, narrowing it to the specified behavioral region.
The auto-scatter hook intercepts every raw prompt before the LLM sees it, decomposes it into all 6 bands, and injects the structured result as system context. The model receives both the raw prompt and its sinc decomposition. No prompt is ever blocked. The hook costs $0.002 per call but saves $0.08 per call by eliminating clarification loops — a 38x ROI.
AI Transform is the production feature on sincllm.com that runs the auto-scatter using a locally fine-tuned Qwen2.5-7B model at 290 tokens/second. Zero API cost. The model was distilled from Claude using 113 validated training examples and fine-tuned with Unsloth LoRA in 172 seconds.
| Cost reduction | 97% ($1,500 to $45/month) |
| Token reduction | 95.6% (80,000 to 3,500/session) |
| SNR improvement | 0.003 to 0.855 (285x) |
| Exchange rate | 4.2 to 1.6 responses/prompt |
| Weekly savings | $1,588.56 (measured over 7 days) |
| AI Transform speed | 290 tokens/second |
The framework, auto-scatter hook, training data, and fine-tuning pipeline are open source.
DOI: 10.5281/zenodo.19152668
GitHub: github.com/mdalexandre/sinc-llm
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