# ⚛  L1 Principle — Aeroacoustics — Lighthill analogy (jet/airframe noise)

**ID:** `L1-270` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Acoustics — *Lighthill source-term aeroacoustic prediction*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** far field spl spectrum
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554050

---

## 🧠 1. Introduction

**Aeroacoustics — Lighthill analogy (jet/airframe noise)** is a **nonlinear inverse problem** whose unknown lives in **far field spl spectrum** space, within the **Lighthill source-term aeroacoustic prediction** 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: L · les source operator; L · lighthill integral operator; L · green function 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 · les source → L · lighthill integral → L · green function → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.green_function` `L.lighthill_integral` `L.les_source` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.les_source` | L · les source operator |
| `L.lighthill_integral` | L · lighthill integral operator |
| `L.green_function` | L · green function operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Acoustics |
| Sub domain | Lighthill source-term aeroacoustic prediction |
| Carrier | acoustic |
| Problem class | nonlinear_inverse |
| Solution space | far_field_spl_spectrum |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 10 |
| L dag | 3.8 |

## 📡 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:** `lighthill_aeroacoustic` · **Forward operator:** `lighthill_aeroacoustic_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| M jet | — | 0.8 |
| N les | — | 10000000 |
| N mic | — | 32 |
| Snr db | dB | 30 |
| Freq hz max | — | 10000 |
| Refraction error | — | 0 |
| Observer pos error | — | 0 |
| Les resolution error | — | 0.05 |
| Source region trunc error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| M jet | — | 0.1 – 2.0 |
| N les | — | 1000000 – 10000000000 |
| N mic | — | 4 – 256 |
| Snr db | dB | 0 – 40 |
| Freq hz max | — | 100 – 50000 |
| Refraction error | — | 0.0 – 0.2 |
| Observer pos error | — | 0.0 – 0.05 |
| Les resolution error | — | 0.01 – 0.3 |
| Source region trunc error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0

| Metric | Range |
|---|---|
| Spl db | 0.5 – 30.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **SPL_error_dB**, with κ = `1600` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x060827f466c50a201e63d9cf576060fd9014fa2a3358e697ca798d0b1b8cee3b`
- **Chain tx hash:** `0x72caca7d75d010cdefd81e08ba9bafa5b26890eed4ffcf0fbf99ae2fd356f80a`
- **Chain block:** `41554050`

---

## File Mapping

This bundle consists of: `L1-270.md`, `L1-270.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-270.md` | Source of truth — edit this | Human or LLM |
| `L1-270.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 `L1-270`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._