# ⚛  L1 Principle — Free Energy Perturbation (FEP + TI + BAR)

**ID:** `L1-308` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Alchemical free-energy methods*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** DG curve lambda
> **📡 Carrier:** none · **🌫 Noise:** thermal langevin
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554115

---

## 🧠 1. Introduction

**Free Energy Perturbation (FEP + TI + BAR)** is a **nonlinear inverse problem** whose unknown lives in **DG curve lambda** space, within the **Alchemical free-energy methods** sub-domain of **Computational Chemistry**.

Measurements consist of none via a **alchemical free energy** sensing mechanism.

The forward operator applies, in order: E · alchemical hamiltonian operator; S · select operator; adds a prior term that biases the solution toward smoothness/sparsity; O · DG operator.

Observations are corrupted by Langevin-type thermal fluctuations. Well-posed in principle; sampling convergence is practical bottleneck.

## ⚙ 2. Forward Model

Physical chain: **x** → E · alchemical hamiltonian → S · select → O · DG → **y** (detector).

```
y = `O.DG` `S.select` `E.alchemical_hamiltonian` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.alchemical_hamiltonian` | E · alchemical hamiltonian operator |
| `S.select` | S · select operator |
| `O.DG` | O · dg operator |

**🛠 Solver components** _(used inside the solver, not in the forward equation)_:

| Primitive | What it does |
|---|---|
| `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Alchemical free-energy methods |
| Carrier | none |
| Problem class | nonlinear_inverse |
| Solution space | DG_curve_lambda |
| Noise model | thermal_langevin |
| Integration axis | lambda |
| Difficulty delta | 5 |
| L dag | 3.7 |

## 📡 4. Measurement Model

Well-posed in principle; sampling convergence is practical bottleneck.

| Metric | Value |
|---|---|
| Metric | DG_bind_error_kcal_mol |
| Secondary | DG_solv_error_kcal_mol |

## 📏 5. Operating Range (Ω)

**Center problem class:** `free_energy_perturbation` · **Forward operator:** `fep_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T k | — | 298 |
| N lambdas | — | 20 |
| Softcore alpha | — | 0.5 |
| N steps per lambda | — | 1e+06 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 200 – 400 |
| N lambdas | — | 5 – 200 |
| Softcore alpha | — | 0.1 – 1.0 |
| N steps per lambda | — | 10000 – 1000000000.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** DG_bind <= 0.5 kcal/mol

| Metric | Range |
|---|---|
| Dg bind error kcal mol | 0.1 – 10 |

## ⚖ 7. Hardness Function

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

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x890766481cfe6ec2ef45315b1c5583e40a4570af1bd3c633542822fd2de679be`
- **Chain tx hash:** `0x9748073561325005a11c280cc65a1e0ba54fad1abd074d5834e7084c1aacd3e2`
- **Chain block:** `41554115`

---

## File Mapping

This bundle consists of: `L1-308.md`, `L1-308.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-308.md` | Source of truth — edit this | Human or LLM |
| `L1-308.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.
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> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-308`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._