# ⚛  L1 Principle — Room Acoustics — image-source method (shoebox rooms)

**ID:** `L1-260` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Acoustics — *Image-source mirror-reflection model*
> **🎯 Problem class:** forward · **🧮 Solution space:** room impulse response 1D
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554036

---

## 🧠 1. Introduction

**Room Acoustics — image-source method (shoebox rooms)** is a **forward-model simulation** whose unknown lives in **room impulse response 1D** space, within the **Image-source mirror-reflection model** sub-domain of **Acoustics**.

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

The forward operator applies, in order: L · mirror · images operator; L · delay sum operator; L · absorb operator; detector accumulates flux over the exposure window.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · mirror · images → L · delay sum → L · absorb → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.absorb` `L.delay_sum` `L.mirror.images` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.mirror.images` | L · mirror · images operator |
| `L.delay_sum` | L · delay sum operator |
| `L.absorb` | L · absorb operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Acoustics |
| Sub domain | Image-source mirror-reflection model |
| Carrier | acoustic |
| Problem class | forward |
| Solution space | room_impulse_response_1D |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 2.8 |

## 📡 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:** `image_source` · **Forward operator:** `image_source_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H m | m | 3 |
| L m | m | 6 |
| W m | m | 8 |
| Fs khz | kHz | 48 |
| Max order | — | 20 |
| Geometry error | — | 0 |
| Src rec pos error | — | 0 |
| Reflection coeff error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H m | m | 2 – 15 |
| L m | m | 2 – 30 |
| W m | m | 2 – 30 |
| Fs khz | kHz | 8 – 96 |
| Max order | — | 1 – 80 |
| Geometry error | — | 0.0 – 0.02 |
| Src rec pos error | — | 0.0 – 0.1 |
| Reflection coeff error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x92baec9e350ee978330a22258a0d887b082d6e2e8cac88eeb9a7d1a538763155`
- **Chain tx hash:** `0x1c72ee217e0dbd26fb1313a70396e766d262abbd5f98563becec5699705d1954`
- **Chain block:** `41554036`

---

## File Mapping

This bundle consists of: `L1-260.md`, `L1-260.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-260.md` | Source of truth — edit this | Human or LLM |
| `L1-260.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 `L1-260`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._