# ⚛  L1 Principle — Stellar Structure Inverse Problem

**ID:** `L1-370` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Stellar physics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 1D stellar profile
> **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555177

---

## 🧠 1. Introduction

**Stellar Structure Inverse Problem** is a **parameter-estimation problem** whose unknown lives in **1D stellar profile** space, within the **Stellar physics** sub-domain of **Astrophysics**.

Measurements consist of N/A via a **stellar oscillation inversion** sensing mechanism.

The forward operator applies, in order: S · helioseismic · kernel operator; O · rnla · inversion operator; time evolution of the state.

Observations are corrupted by observation gaussian. Existence of the recovered 1D_stellar_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 ~= 50); surface_term_offset dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → S · helioseismic · kernel → O · rnla · inversion → Time derivative → **y** (detector).

```
y = ∂_t `O.rnla.inversion` `S.helioseismic.kernel` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.helioseismic.kernel` | S · helioseismic · kernel operator |
| `O.rnla.inversion` | O · rnla · inversion operator |
| `D.time` | Time evolution of the state |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Stellar physics |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | 1D_stellar_profile |
| Noise model | observation_gaussian |
| Integration axis | radial |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered 1D_stellar_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 ~= 50); surface_term_offset dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | sound_speed_inversion_chi2 |
| Secondary | density_profile_RMSE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `stellar_oscillation_inversion`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N modes | — | 200 |
| Mass msun | — | 1 |
| Metallicity z | — | 0.02 |
| Noise sigma microhz | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N modes | — | 20 – 1000 |
| Mass msun | — | 0.5 – 2.0 |
| Metallicity z | — | 0.001 – 0.05 |
| Noise sigma microhz | — | 0.01 – 1.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.2 sound_speed_inversion_chi2

| Metric | Range |
|---|---|
| Sound speed inversion chi2 | 0.8 – 3.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **sound_speed_inversion_chi2**, with κ = `1000.0` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xffd57bfc88bee31c965a9647a73d78e9ebbf054029f9b88c52055e1e9d941207`
- **Chain tx hash:** `0xe71800b693887c668fa41382d57492941a4b92db66fefb2c231e6145aab73f9d`
- **Chain block:** `41555177`

---

## File Mapping

This bundle consists of: `L1-370.md`, `L1-370.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-370.md` | Source of truth — edit this | Human or LLM |
| `L1-370.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 `L1-370`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._