# ⚛  L1 Principle — Baryon Acoustic Oscillation (BAO) Fitting

**ID:** `L1-379` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Large-scale structure*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** cosmological distance ratios
> **📡 Carrier:** N/A · **🌫 Noise:** cosmic variance gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555179

---

## 🧠 1. Introduction

**Baryon Acoustic Oscillation (BAO) Fitting** is a **parameter-estimation problem** whose unknown lives in **cosmological distance ratios** space, within the **Large-scale structure** sub-domain of **Astrophysics**.

Measurements consist of N/A via a **two point correlation function** sensing mechanism.

The forward operator applies, in order: F · fourier · power spectrum operator; S · bao · peak fitting operator; O · chi2 · dv rd operator.

Observations are corrupted by cosmic variance gaussian. Existence of the recovered cosmological_distance_ratios 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 ~= 30); galaxy_bias_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → F · fourier · power spectrum → S · bao · peak fitting → O · chi2 · dv rd → **y** (detector).

```
y = `O.chi2.dv_rd` `S.bao.peak_fitting` `F.fourier.power_spectrum` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `F.fourier.power_spectrum` | F · fourier · power spectrum operator |
| `S.bao.peak_fitting` | S · bao · peak fitting operator |
| `O.chi2.dv_rd` | O · chi2 · dv rd operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Large-scale structure |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | cosmological_distance_ratios |
| Noise model | cosmic_variance_gaussian |
| Integration axis | comoving_separation |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered cosmological_distance_ratios 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 ~= 30); galaxy_bias_nonlinearity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | D_V_rd_sigma_percent |
| Secondary | chi2_reduced_BAO |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Z eff | — | 0.5 |
| N gal million | — | 1 |
| Sigma v fog kms | — | 400 |
| Survey volume gpc3 h | — | 5 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Z eff | — | 0.1 – 2.0 |
| N gal million | — | 0.1 – 50.0 |
| Sigma v fog kms | — | 100 – 1000 |
| Survey volume gpc3 h | — | 0.5 – 50.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.0 D_V_rd_sigma_percent

| Metric | Range |
|---|---|
| D v rd sigma percent | 0.2 – 5.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **D_V_rd_sigma_percent**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x54d5c4986c82178bde140866b70cf9a8a814f8ea0c8401ad1090574d1a23355d`
- **Chain tx hash:** `0x5de8e7f922b44181ffe3356362a7da94c0b9bf6e21e4f9ce3a53469432f9618f`
- **Chain block:** `41555179`

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## File Mapping

This bundle consists of: `L1-379.md`, `L1-379.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-379.md` | Source of truth — edit this | Human or LLM |
| `L1-379.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 `L1-379`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._