# ⚛  L1 Principle — Outdoor Noise Propagation — atmospheric refraction + ground effect

**ID:** `L1-271` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Acoustics — *Outdoor sound propagation (ISO 9613 / PE)*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** transmission loss 3D
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554050

---

## 🧠 1. Introduction

**Outdoor Noise Propagation — atmospheric refraction + ground effect** is a **linear inverse problem** whose unknown lives in **transmission loss 3D** space, within the **Outdoor sound propagation (ISO 9613 / PE)** sub-domain of **Acoustics**.

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

The forward operator applies, in order: isotropic point-source emission model; L · atmos absorb operator; L · ground reflect operator; L · diffract · barrier operator; int · range operator.

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

## ⚙ 2. Forward Model

Physical chain: **x** → Source emission → L · atmos absorb → L · ground reflect → L · diffract · barrier → int · range → **y** (detector).

```
y = `int.range` `L.diffract.barrier` `L.ground_reflect` `L.atmos_absorb` δ_source x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.source_emit` | Isotropic point-source emission model |
| `L.atmos_absorb` | L · atmos absorb operator |
| `L.ground_reflect` | L · ground reflect operator |
| `L.diffract.barrier` | L · diffract · barrier operator |
| `int.range` | Int · range operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Acoustics |
| Sub domain | Outdoor sound propagation (ISO 9613 / PE) |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | transmission_loss_3D |
| Noise model | gaussian |
| Integration axis | range |
| Difficulty delta | 5 |
| L dag | 3.7 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | SPL_error_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `outdoor_propagation` · **Forward operator:** `outdoor_propagation_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 20 |
| Freq hz | Hz | 500 |
| R max m | m | 1000 |
| N stations | — | 16 |
| Terrain error | — | 0.1 |
| Temp profile error | — | 0.1 |
| Wind profile error | — | 0.05 |
| Ground impedance error | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | -10 – 40 |
| Freq hz | Hz | 20 – 10000 |
| R max m | m | 50 – 20000 |
| N stations | — | 4 – 128 |
| Terrain error | — | 0.0 – 0.3 |
| Temp profile error | — | 0.0 – 0.3 |
| Wind profile error | — | 0.0 – 0.5 |
| Ground impedance error | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0

| Metric | Range |
|---|---|
| Spl db | 0.5 – 25.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **SPL_error_dB**, with κ = `700` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x952b42579d80049313a9269f6deb0a33ecf06315636e8d82d36c922b145c3d08`
- **Chain tx hash:** `0x5efbba5d82298f33f40d34a5ad0c77740149abe0659b145a66f4fe5c005b9f65`
- **Chain block:** `41554050`

---

## File Mapping

This bundle consists of: `L1-271.md`, `L1-271.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-271.md` | Source of truth — edit this | Human or LLM |
| `L1-271.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 `L1-271`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._