# ⚛  L1 Principle — Stellar Atmosphere Spectral Inversion

**ID:** `L1-371` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Stellar spectroscopy*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 1D atmospheric profile
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555177

---

## 🧠 1. Introduction

**Stellar Atmosphere Spectral Inversion** is a **nonlinear inverse problem** whose unknown lives in **1D atmospheric profile** space, within the **Stellar spectroscopy** sub-domain of **Astrophysics**.

Measurements consist of photons collected by an optical detector via a **radiative transfer spectral** sensing mechanism.

The forward operator applies, in order: S · radiative · transfer lte operator; operator inherits structure from a graph (mesh, network); O · chi2 · spectral lines operator.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 1D_atmospheric_profile 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 ~= 500); continuum_normalization_error 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** → S · radiative · transfer lte → Structured graph operator → O · chi2 · spectral lines → **y** (detector).

```
y = `O.chi2.spectral_lines` G `S.radiative.transfer_lte` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.radiative.transfer_lte` | S · radiative · transfer lte operator |
| `G.structured` | Operator inherits structure from a graph (mesh, network) |
| `O.chi2.spectral_lines` | O · chi2 · spectral lines operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Stellar spectroscopy |
| Carrier | photon |
| Problem class | nonlinear_inverse |
| Solution space | 1D_atmospheric_profile |
| Noise model | shot_poisson |
| Integration axis | optical_depth |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Existence of the recovered 1D_atmospheric_profile 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 ~= 500); continuum_normalization_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | spectral_chi2_reduced |
| Secondary | T_eff_RMSE_K |

## 📏 5. Operating Range (Ω)

**Center problem class:** `nonlinear_inverse` · **Forward operator:** `radiative_transfer_spectral`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr | — | 100 |
| T eff k | — | 5500 |
| N lambda | — | 5000 |
| Log g cgs | — | 4 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr | — | 10 – 500 |
| T eff k | — | 3500 – 7500 |
| N lambda | — | 1000 – 50000 |
| Log g cgs | — | 1.0 – 5.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.15 spectral_chi2_reduced

| Metric | Range |
|---|---|
| Spectral chi2 reduced | 0.8 – 5.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **spectral_chi2_reduced**, with κ = `50000.0` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x5fb66349c542ef26e19324c512acc166e8899083bdfe422729638d56682f845c`
- **Chain tx hash:** `0x07de7824abdecdaadb29394b675b2c80f0de7f152526d1cca6f6443dc1f6cb15`
- **Chain block:** `41555177`

---

## File Mapping

This bundle consists of: `L1-371.md`, `L1-371.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-371.md` | Source of truth — edit this | Human or LLM |
| `L1-371.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 `L1-371`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._