# ⚛  L1 Principle — Vibroacoustics — structure-acoustic coupling

**ID:** `L1-268` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Acoustics — *FEM-BEM coupled vibro-acoustic*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** pressure displacement coupled 2D
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554050

---

## 🧠 1. Introduction

**Vibroacoustics — structure-acoustic coupling** is a **linear inverse problem** whose unknown lives in **pressure displacement coupled 2D** space, within the **FEM-BEM coupled vibro-acoustic** sub-domain of **Acoustics**.

Measurements consist of acoustic pressure waves recorded by transducers via a **pressure accel hybrid** sensing mechanism.

The forward operator applies, in order: L · fem structure operator; L · bem acoustic operator; L · coupling operator; integration over a band of frequencies.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · fem structure → L · bem acoustic → L · coupling → Frequency integration → **y** (detector).

```
y = ∫dω `L.coupling` `L.bem_acoustic` `L.fem_structure` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.fem_structure` | L · fem structure operator |
| `L.bem_acoustic` | L · bem acoustic operator |
| `L.coupling` | L · coupling operator |
| `int.frequency` | Integration over a band of frequencies |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Acoustics |
| Sub domain | FEM-BEM coupled vibro-acoustic |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | pressure_displacement_coupled_2D |
| Noise model | gaussian |
| Integration axis | frequency |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `vibroacoustic_coupled` · **Forward operator:** `vibroacoustic_coupled_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N fluid | — | 10000 |
| N freqs | — | 64 |
| N struct | — | 10000 |
| Mesh error | — | 0 |
| Coupling error | — | 0 |
| Fluid impedance error | — | 0 |
| Structural damping error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N fluid | — | 500 – 500000 |
| N freqs | — | 4 – 512 |
| N struct | — | 500 – 500000 |
| Mesh error | — | 0.0 – 0.1 |
| Coupling error | — | 0.0 – 0.2 |
| Fluid impedance error | — | 0.0 – 0.3 |
| Structural damping error | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x1e015b4aa9470db822fc4e050fbc4b871b6b6e9ce7de33f1ad38584c49a5365c`
- **Chain tx hash:** `0x83ccad2be178f0e9e969b83e4c2e76be2ddc7ba3800f1653804e0d67bcd76d49`
- **Chain block:** `41554050`

---

## File Mapping

This bundle consists of: `L1-268.md`, `L1-268.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-268.md` | Source of truth — edit this | Human or LLM |
| `L1-268.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 `L1-268`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._