# ⚛  L1 Principle — Exoplanet Transit Photometry Inversion

**ID:** `L1-380` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Exoplanet characterization*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** transit parameter vector
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555179

---

## 🧠 1. Introduction

**Exoplanet Transit Photometry Inversion** is a **parameter-estimation problem** whose unknown lives in **transit parameter vector** space, within the **Exoplanet characterization** sub-domain of **Astrophysics**.

Measurements consist of photons collected by an optical detector via a **transit photometry** sensing mechanism.

The forward operator applies, in order: time evolution of the state; O · chi2 · lightcurve transit operator; S · limb · darkening operator.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered transit_parameter_vector 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 ~= 40); stellar_activity_spots 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** → Time derivative → O · chi2 · lightcurve transit → S · limb · darkening → **y** (detector).

```
y = `S.limb.darkening` `O.chi2.lightcurve_transit` ∂_t x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `D.time` | Time evolution of the state |
| `O.chi2.lightcurve_transit` | O · chi2 · lightcurve transit operator |
| `S.limb.darkening` | S · limb · darkening operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Exoplanet characterization |
| Carrier | photon |
| Problem class | parameter_estimation |
| Solution space | transit_parameter_vector |
| Noise model | shot_poisson |
| Integration axis | temporal_photometric |
| Difficulty delta | 3 |
| L dag | 2.5 |

## 📡 4. Measurement Model

Existence of the recovered transit_parameter_vector 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 ~= 40); stellar_activity_spots dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | R_p_R_star_sigma_ppm |
| Secondary | chi2_reduced |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Cadence min | — | 2 |
| N transit points | — | 500 |
| Snr per point ppm | — | 100 |
| R p r star percent | — | 1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Cadence min | — | 0.5 – 30.0 |
| N transit points | — | 50 – 10000 |
| Snr per point ppm | — | 10 – 1000 |
| R p r star percent | — | 0.1 – 20.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 50 R_p_R_star_sigma_ppm

| Metric | Range |
|---|---|
| R p r star sigma ppm | 10 – 500 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **R_p_R_star_sigma_ppm**, with κ = `1000` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x959e27141050f07714e8d1f80502bd53320ebb5437732b10064ba7ee787f25c8`
- **Chain tx hash:** `0xaa5746f60df91d0b2c21563071688afd202c4282c23a072c7be7e7ad939a7b4d`
- **Chain block:** `41555179`

---

## File Mapping

This bundle consists of: `L1-380.md`, `L1-380.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-380.md` | Source of truth — edit this | Human or LLM |
| `L1-380.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 `L1-380`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._