# ⚛  L1 Principle — Cosmological N-body (Large-Scale Structure)

**ID:** `L1-365` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Cosmological simulation*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 3D dark matter density
> **📡 Carrier:** N/A · **🌫 Noise:** cosmic variance
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555176

---

## 🧠 1. Introduction

**Cosmological N-body (Large-Scale Structure)** is a **parameter-estimation problem** whose unknown lives in **3D dark matter density** space, within the **Cosmological simulation** sub-domain of **Astrophysics**.

Measurements consist of N/A via a **pm tree gravity** sensing mechanism.

The forward operator applies, in order: F · fourier · pm gravity operator; S · tree · force softening operator; O · leapfrog · comoving operator.

Observations are corrupted by cosmic variance. Existence of the recovered 3D_dark_matter_density 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 ~= 10000.0); cosmological_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → F · fourier · pm gravity → S · tree · force softening → O · leapfrog · comoving → **y** (detector).

```
y = `O.leapfrog.comoving` `S.tree.force_softening` `F.fourier.pm_gravity` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `F.fourier.pm_gravity` | F · fourier · pm gravity operator |
| `S.tree.force_softening` | S · tree · force softening operator |
| `O.leapfrog.comoving` | O · leapfrog · comoving operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Cosmological simulation |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | 3D_dark_matter_density |
| Noise model | cosmic_variance |
| Integration axis | comoving_time |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Existence of the recovered 3D_dark_matter_density 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 ~= 10000.0); cosmological_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | matter_power_spectrum_P_k_chi2 |
| Secondary | halo_mass_function_error |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Omega m | m | 0.3 |
| Sigma 8 | — | 0.8 |
| N particles | — | 134217728 |
| Box size mpc h | — | 250 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Omega m | m | 0.2 – 0.5 |
| Sigma 8 | — | 0.6 – 1.0 |
| N particles | — | 262144 – 8589934592 |
| Box size mpc h | — | 50 – 2000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1.02 matter_power_spectrum_P_k_chi2

| Metric | Range |
|---|---|
| Matter power spectrum p k chi2 | 0.9 – 1.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **matter_power_spectrum_P_k_chi2**, with κ = `100000000.0` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x5eaf872422d70c8c95f19857af65a6a30c2ca15580c7ffbe8f8e2fd5740a8e78`
- **Chain tx hash:** `0x287c23d7c0934b4ae7f925e4e0ad660ae6ca5ba15542041f1afd30a62d551832`
- **Chain block:** `41555176`

---

## File Mapping

This bundle consists of: `L1-365.md`, `L1-365.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-365.md` | Source of truth — edit this | Human or LLM |
| `L1-365.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 `L1-365`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._