# ⚛  L1 Principle — Classical Molecular Dynamics

**ID:** `L1-299` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Empirical force-field dynamics*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** atomic trajectory
> **📡 Carrier:** none · **🌫 Noise:** thermal langevin
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554113

---

## 🧠 1. Introduction

**Classical Molecular Dynamics** is a **nonlinear inverse problem** whose unknown lives in **atomic trajectory** space, within the **Empirical force-field dynamics** sub-domain of **Computational Chemistry**.

Measurements consist of none via a **md observable** sensing mechanism.

The forward operator applies, in order: E · force field operator; D · time · symplectic operator; O · trajectory operator.

Observations are corrupted by Langevin-type thermal fluctuations. Well-posed forward; force field validity limits accuracy.

## ⚙ 2. Forward Model

Physical chain: **x** → E · force field → D · time · symplectic → O · trajectory → **y** (detector).

```
y = `O.trajectory` `D.time.symplectic` `E.force_field` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.force_field` | E · force field operator |
| `D.time.symplectic` | D · time · symplectic operator |
| `O.trajectory` | O · trajectory operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Empirical force-field dynamics |
| Carrier | none |
| Problem class | nonlinear_inverse |
| Solution space | atomic_trajectory |
| Noise model | thermal_langevin |
| Integration axis | time |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Well-posed forward; force field validity limits accuracy.

| Metric | Value |
|---|---|
| Metric | diffusion_coeff_relative_error |
| Secondary | rdf_L2 |

## 📏 5. Operating Range (Ω)

**Center problem class:** `classical_md` · **Forward operator:** `classical_md_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Ff | — | AMBER |
| T k | — | 300 |
| Dt fs | — | 2 |
| N atoms | — | 1000 |
| N steps | — | 1e+06 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Ff | — | AMBER, CHARMM, OPLS, GROMOS, ReaxFF |
| T k | — | 4 – 5000 |
| Dt fs | — | 0.1 – 10 |
| N atoms | — | 100 – 10000000.0 |
| N steps | — | 1000 – 10000000000.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** D rel error <= 0.04

| Metric | Range |
|---|---|
| Diffusion coeff relative error | 0.01 – 0.4 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **diffusion_coeff_relative_error**, with κ = `200` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x6f7a21f466265980a27ed5c336113f7c954b12f77bc1ec83b1e322cf9cc1cca7`
- **Chain tx hash:** `0xedfe0d821020fa241389cac3b3f6473eb5bdec18d03851ec5e90b623d512f436`
- **Chain block:** `41554113`

---

## File Mapping

This bundle consists of: `L1-299.md`, `L1-299.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-299.md` | Source of truth — edit this | Human or LLM |
| `L1-299.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 `L1-299`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._