# ⚛  L1 Principle — N-body Gravitational Simulation

**ID:** `L1-364` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Astrophysics — *Orbital dynamics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 6N phase space
> **📡 Carrier:** N/A · **🌫 Noise:** observation gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555176

---

## 🧠 1. Introduction

**N-body Gravitational Simulation** is a **parameter-estimation problem** whose unknown lives in **6N phase space** space, within the **Orbital dynamics** sub-domain of **Astrophysics**.

Measurements consist of N/A via a **gravitational force summation** sensing mechanism.

The forward operator applies, in order: F · gravity · nbody operator; S · tree · barnes hut operator; O · leapfrog · integrator operator.

Observations are corrupted by observation gaussian. Existence of the recovered 6N_phase_space 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 ~= 500); initial_condition_uncertainty 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** → F · gravity · nbody → S · tree · barnes hut → O · leapfrog · integrator → **y** (detector).

```
y = `O.leapfrog.integrator` `S.tree.barnes_hut` `F.gravity.nbody` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `F.gravity.nbody` | F · gravity · nbody operator |
| `S.tree.barnes_hut` | S · tree · barnes hut operator |
| `O.leapfrog.integrator` | O · leapfrog · integrator operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Astrophysics |
| Sub domain | Orbital dynamics |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | 6N_phase_space |
| Noise model | observation_gaussian |
| Integration axis | time |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered 6N_phase_space 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 ~= 500); initial_condition_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | orbital_energy_conservation_relative |
| Secondary | position_RMSE_AU |

## 📏 5. Operating Range (Ω)

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

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Dt yr | — | 0.01 |
| N bodies | — | 100 |
| T end yr | — | 100 |
| Softening au | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Dt yr | — | 0.001 – 0.1 |
| N bodies | — | 10 – 10000 |
| T end yr | — | 10 – 10000 |
| Softening au | — | 0.01 – 1.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 1e-6 orbital_energy_conservation_relative

| Metric | Range |
|---|---|
| Orbital energy conservation relative | 1e-10 – 0.001 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **orbital_energy_conservation_relative**, with κ = `100000.0` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x63131da3973889de4d4c05e7deab5eac1b2dad7dcb58980a385f24ff7b1e1bd5`
- **Chain tx hash:** `0x7da15624c8618e308950b5083db53d3625dac3b115d254c571f4138589bd2402`
- **Chain block:** `41555176`

---

## File Mapping

This bundle consists of: `L1-364.md`, `L1-364.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-364.md` | Source of truth — edit this | Human or LLM |
| `L1-364.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 `L1-364`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._