# ⚛  L1 Principle — 21cm Cosmology Reionization Signal

**ID:** `L1-378` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Epoch of reionization*
> **🎯 Problem class:** statistical inverse · **🧮 Solution space:** 3D 21cm brightness temperature
> **📡 Carrier:** radio_wave · **🌫 Noise:** thermal gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41555178

---

## 🧠 1. Introduction

**21cm Cosmology Reionization Signal** is a **statistical inverse problem** whose unknown lives in **3D 21cm brightness temperature** space, within the **Epoch of reionization** sub-domain of **Astrophysics**.

Measurements consist of radio-frequency electromagnetic waves via a **radio interferometry 21cm** sensing mechanism.

The forward operator applies, in order: F · fourier · power spectrum 3d operator; S · foreground · removal wedge operator; O · chi2 · 21cm ps operator.

Observations are corrupted by thermally-driven Gaussian fluctuations. Existence of the recovered 3D_21cm_brightness_temperature 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 ~= 5000); calibration_errors_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → F · fourier · power spectrum 3d → S · foreground · removal wedge → O · chi2 · 21cm ps → **y** (detector).

```
y = `O.chi2.21cm_ps` `S.foreground.removal_wedge` `F.fourier.power_spectrum_3d` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `F.fourier.power_spectrum_3d` | F · fourier · power spectrum 3d operator |
| `S.foreground.removal_wedge` | S · foreground · removal wedge operator |
| `O.chi2.21cm_ps` | O · chi2 · 21cm ps operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Epoch of reionization |
| Carrier | radio_wave |
| Problem class | statistical_inverse |
| Solution space | 3D_21cm_brightness_temperature |
| Noise model | thermal_gaussian |
| Integration axis | frequency_redshift |
| Difficulty delta | 10 |
| L dag | 4.5 |

## 📡 4. Measurement Model

Existence of the recovered 3D_21cm_brightness_temperature 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 ~= 5000); calibration_errors_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | power_spectrum_detection_SNR |
| Secondary | chi2_reduced_power_spectrum |

## 📏 5. Operating Range (Ω)

**Center problem class:** `statistical_inverse` · **Forward operator:** `radio_interferometry_21cm`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Noise k | — | 0.05 |
| N antennas | — | 350 |
| Integration hours | — | 1000 |
| Foreground level k | — | 200 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Noise k | — | 0.01 – 0.5 |
| N antennas | — | 20 – 1000 |
| Integration hours | — | 100 – 10000 |
| Foreground level k | — | 50 – 1000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 2.0 power_spectrum_detection_SNR

| Metric | Range |
|---|---|
| Power spectrum detection snr | 1.0 – 10.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **power_spectrum_detection_SNR**, with κ = `10000000.0` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xace44b37cbf5ce999782c567d6623aed4f2d57d3054e38e173cb44c41f5e6481`
- **Chain tx hash:** `0x14f260752a75cf485240378901e1554d023c3b948368ca982f3dcc9eec53d047`
- **Chain block:** `41555178`

---

## File Mapping

This bundle consists of: `L1-378.md`, `L1-378.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-378.md` | Source of truth — edit this | Human or LLM |
| `L1-378.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 `L1-378`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._