# ⚛  L1 Principle — Solar EUV/X-ray Image Reconstruction

**ID:** `L1-169` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astronomy — *Solar physics*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D emission measure
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554244

---

## 🧠 1. Introduction

**Solar EUV/X-ray Image Reconstruction** is a **linear inverse problem** whose unknown lives in **2D emission measure** space, within the **Solar physics** sub-domain of **Astronomy**.

Measurements consist of photons collected by an optical detector via a **coded aperture euv** sensing mechanism.

The forward operator applies, in order: K · psf · coded aperture operator; detector sums all spectral bands; S · dem · inversion operator.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D_emission_measure 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 ~= 80); calibration_uncertainty_percent 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 · coded aperture → Spectral integration → S · dem · inversion → **y** (detector).

```
y = `S.dem.inversion` Σ_λ `K.psf.coded_aperture` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `K.psf.coded_aperture` | K · psf · coded aperture operator |
| `int.spectral` | Detector sums all spectral bands |
| `S.dem.inversion` | S · dem · inversion operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astronomy |
| Sub domain | Solar physics |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 2D_emission_measure |
| Noise model | shot_poisson |
| Integration axis | spectral_line_of_sight |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered 2D_emission_measure 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 ~= 80); calibration_uncertainty_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | DEM_reconstruction_chi2 |
| Secondary | temperature_peak_error_K |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| N t bins | — | 20 |
| N channels | — | 6 |
| Noise sigma percent | — | 5 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 4096 |
| W | px | 128 – 4096 |
| N t bins | — | 10 – 50 |
| N channels | — | 3 – 12 |
| Noise sigma percent | — | 1.0 – 20.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.3 DEM_reconstruction_chi2

| Metric | Range |
|---|---|
| Dem reconstruction chi2 | 0.5 – 5.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **DEM_reconstruction_chi2**, with κ = `2000` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x54d4eb44d5d77a2a317aa9432ca35d4269f074f7ca5df07c2f1f251a479c0b7d`
- **Chain tx hash:** `0x3edc2adb7e4fc53309d4bca81fc5308fb1a80d587bf350ef821358b046a9bf02`
- **Chain block:** `41554244`

---

## File Mapping

This bundle consists of: `L1-169.md`, `L1-169.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-169.md` | Source of truth — edit this | Human or LLM |
| `L1-169.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 `L1-169`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._