# ⚛  L1 Principle — Blind Source Separation (ICA / cocktail-party problem)

**ID:** `L1-388` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Signal Processing — *Statistical independence-based demixing*
> **🎯 Problem class:** bilinear blind factorization · **🧮 Solution space:** independent components
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555197

---

## 🧠 1. Introduction

**Blind Source Separation (ICA / cocktail-party problem)** is a **bilinear blind factorization** whose unknown lives in **independent components** space, within the **Statistical independence-based demixing** sub-domain of **Signal Processing**.

Measurements consist of acoustic pressure waves recorded by transducers via a **linear mixing** sensing mechanism.

The forward operator applies, in order: L · mix · linear operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Identifiable when at most one source is Gaussian (Darmois-Skitovich theorem). Convolutive BSS requires additional constraint (temporal coloration or higher statistics). Underdetermined (N > M) requires sparsity prior.

## ⚙ 2. Forward Model

Physical chain: **x** → L · mix · linear → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.mix.linear` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.mix.linear` | L · mix · linear operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Signal Processing |
| Sub domain | Statistical independence-based demixing |
| Carrier | acoustic |
| Problem class | bilinear_blind_factorization |
| Solution space | independent_components |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 2.2 |

## 📡 4. Measurement Model

Identifiable when at most one source is Gaussian (Darmois-Skitovich theorem). Convolutive BSS requires additional constraint (temporal coloration or higher statistics). Underdetermined (N > M) requires sparsity prior.

| Metric | Value |
|---|---|
| Metric | SIR_dB |
| Secondary | permutation_recovery_rate |

## 📏 5. Operating Range (Ω)

**Center problem class:** `instantaneous_ica` · **Forward operator:** `linear_mixing_determined`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| M | — | 3 |
| N | — | 3 |
| T | — | 10000 |
| Snr db | dB | 30 |
| Kappa a | — | 10 |
| Gaussianity | — | 0 |
| Reverberation ms | ms | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| M | — | 2 – 20 |
| N | — | 2 – 20 |
| T | — | 500 – 200000 |
| Snr db | dB | -10 – 40 |
| Kappa a | — | 1 – 1000 |
| Gaussianity | — | 0.0 – 1.0 |
| Non stationarity | — | 0.0 – 1.0 |
| Reverberation ms | ms | 0 – 500 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0 dB SIR

| Metric | Range |
|---|---|
| Sir db | 0.0 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **SIR_dB**, with κ = `100` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xb87d084c9e96c8c7e8a5b7f3ee8fff943d311de91ac72536f677f6b3a829aff6`
- **Chain tx hash:** `0xdcd8a3c56c9ef2e94ae4e1b2980a0a448b7e516246a119f7b4af40a727cc452b`
- **Chain block:** `41555197`

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## File Mapping

This bundle consists of: `L1-388.md`, `L1-388.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-388.md` | Source of truth — edit this | Human or LLM |
| `L1-388.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-388`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._