# ⚛  L1 Principle — Lucky Imaging Atmospheric Turbulence Recovery

**ID:** `L1-167` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astronomy — *Atmospheric compensation*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554243

---

## 🧠 1. Introduction

**Lucky Imaging Atmospheric Turbulence Recovery** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Atmospheric compensation** sub-domain of **Astronomy**.

Measurements consist of photons collected by an optical detector via a **frame selection deconvolution** sensing mechanism.

The forward operator applies, in order: K · psf · turbulence operator; S · frame · selection operator; O · shift add operator.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D_intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); seeing_variation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → K · psf · turbulence → S · frame · selection → O · shift add → **y** (detector).

```
y = `O.shift_add` `S.frame.selection` `K.psf.turbulence` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `K.psf.turbulence` | K · psf · turbulence operator |
| `S.frame.selection` | S · frame · selection operator |
| `O.shift_add` | O · shift add operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astronomy |
| Sub domain | Atmospheric compensation |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 2D_intensity |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 2.5 |

## 📡 4. Measurement Model

Existence of the recovered 2D_intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); seeing_variation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | Strehl_ratio |
| Secondary | FWHM_lambda_over_D |

## 📏 5. Operating Range (Ω)

**Center problem class:** `linear_inverse` · **Forward operator:** `frame_selection_deconvolution`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| N frames | — | 500 |
| Seeing r0 cm | — | 15 |
| Selection fraction | — | 0.05 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 1024 |
| W | px | 64 – 1024 |
| N frames | — | 100 – 5000 |
| Seeing r0 cm | — | 5.0 – 30.0 |
| Selection fraction | — | 0.001 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.30 Strehl_ratio

| Metric | Range |
|---|---|
| Strehl ratio | 0.05 – 0.8 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **Strehl_ratio**, with κ = `3000` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xf5d129fd0e87d75a8e4f39bc50228553d271dba82358a71a0c1d9308c1d35e8a`
- **Chain tx hash:** `0xe3eba1e4c05b3547a5d45028840008c66af1e0b01c2ce3c6c328a3fa98d877d1`
- **Chain block:** `41554243`

---

## File Mapping

This bundle consists of: `L1-167.md`, `L1-167.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-167.md` | Source of truth — edit this | Human or LLM |
| `L1-167.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 `L1-167`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._