# ⚛  L1 Principle — Protein Folding Energy Landscape Inversion

**ID:** `L1-412` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Biology — *Structural biology*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D protein structure
> **📡 Carrier:** N/A · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 50 · **⛓ Block:** 41555219

---

## 🧠 1. Introduction

**Protein Folding Energy Landscape Inversion** is a **nonlinear inverse problem** whose unknown lives in **3D protein structure** space, within the **Structural biology** sub-domain of **Computational Biology**.

Measurements consist of N/A via a **cryo em nmr structure determination** sensing mechanism.

The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · md · molecular dynamics operator; O · rmsd · structure comparison operator.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D_protein_structure 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 ~= 10000000.0); conformational_heterogeneity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → Pointwise nonlinearity → S · md · molecular dynamics → O · rmsd · structure comparison → **y** (detector).

```
y = `O.rmsd.structure_comparison` `S.md.molecular_dynamics` f(·) x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `N.pointwise` | Applies a smooth nonlinear function element-wise |
| `S.md.molecular_dynamics` | S · md · molecular dynamics operator |
| `O.rmsd.structure_comparison` | O · rmsd · structure comparison operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Biology |
| Sub domain | Structural biology |
| Carrier | N/A |
| Problem class | nonlinear_inverse |
| Solution space | 3D_protein_structure |
| Noise model | shot_poisson |
| Integration axis | conformation_space |
| Difficulty delta | 50 |
| L dag | 6.5 |

## 📡 4. Measurement Model

Existence of the recovered 3D_protein_structure 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 ~= 10000000.0); conformational_heterogeneity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | TM_score |
| Secondary | RMSD_Angstrom |

## 📏 5. Operating Range (Ω)

**Center problem class:** `nonlinear_inverse` · **Forward operator:** `cryo_em_nmr_structure_determination`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N residues | — | 200 |
| Map snr db | dB | 10 |
| N conformations | — | 1 |
| Resolution angstrom | — | 3 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N residues | — | 10 – 10000 |
| Map snr db | dB | 5 – 30 |
| N conformations | — | 1 – 100 |
| Resolution angstrom | — | 1.5 – 10.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.70 TM_score

| Metric | Range |
|---|---|
| Tm score | 0.1 – 1.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **TM_score**, with κ = `10000000000.0` and δ = `50`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x8d1ac8ba34fb77a3f6168e7a8f27664ced1e4082d8d748c18eb95cf2f7b5e847`
- **Chain tx hash:** `0xbd019dc9b103ba59d579a469649c3cf3bd2a5873356fed950380c083728ccc27`
- **Chain block:** `41555219`

---

## File Mapping

This bundle consists of: `L1-412.md`, `L1-412.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-412.md` | Source of truth — edit this | Human or LLM |
| `L1-412.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 `L1-412`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._