# ⚛  L1 Principle — Duct Acoustics — wave propagation in ducts / silencers

**ID:** `L1-269` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Acoustics — *Modal transmission in non-uniform ducts*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** modal amplitudes 1D
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554050

---

## 🧠 1. Introduction

**Duct Acoustics — wave propagation in ducts / silencers** is a **linear inverse problem** whose unknown lives in **modal amplitudes 1D** space, within the **Modal transmission in non-uniform ducts** sub-domain of **Acoustics**.

Measurements consist of acoustic pressure waves recorded by transducers via a **pressure in duct** sensing mechanism.

The forward operator applies, in order: L · modal decomp operator; L · transfer matrix operator; L · impedance BC 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 · modal decomp → L · transfer matrix → L · impedance BC → Frequency integration → **y** (detector).

```
y = ∫dω `L.impedance_BC` `L.transfer_matrix` `L.modal_decomp` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.modal_decomp` | L · modal decomp operator |
| `L.transfer_matrix` | L · transfer matrix operator |
| `L.impedance_BC` | L · impedance bc operator |
| `int.frequency` | Integration over a band of frequencies |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Acoustics |
| Sub domain | Modal transmission in non-uniform ducts |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | modal_amplitudes_1D |
| Noise model | gaussian |
| Integration axis | frequency |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 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:** `duct_transfer_matrix` · **Forward operator:** `duct_transfer_matrix_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| L m | m | 1 |
| M mach | — | 0.1 |
| Snr db | dB | 30 |
| N modes | — | 8 |
| Freq hz | Hz | 1000 |
| N probes | — | 8 |
| Flow mach error | — | 0 |
| Duct geometry error | — | 0 |
| Liner impedance error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| L m | m | 0.1 – 20 |
| M mach | — | 0.0 – 0.8 |
| Snr db | dB | 0 – 40 |
| N modes | — | 1 – 32 |
| Freq hz | Hz | 50 – 10000 |
| N probes | — | 2 – 64 |
| Flow mach error | — | 0.0 – 0.1 |
| Duct geometry error | — | 0.0 – 0.05 |
| Liner impedance error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 23.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xac80efe9fe6428c69aa301b45fa50b19aef2242caa1d0655455a91c5cb479297`
- **Chain tx hash:** `0x540ead0642df71e750eebe3333794c903f5a4175ab7040f8c9df01397b6805ef`
- **Chain block:** `41554050`

---

## File Mapping

This bundle consists of: `L1-269.md`, `L1-269.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-269.md` | Source of truth — edit this | Human or LLM |
| `L1-269.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 `L1-269`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._