# ⚛  L1 Principle — Cryo-EM Single-Particle Analysis (SPA)

**ID:** `L1-129` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Scientific Instrumentation — *Near-atomic 3D reconstruction of frozen-hydrated biomolecules*
> **🎯 Problem class:** tomographic inverse with pose · **🧮 Solution space:** 3d coulomb potential
> **📡 Carrier:** electron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554213

---

## 🧠 1. Introduction

**Cryo-EM Single-Particle Analysis (SPA)** is a **tomographic inverse with pose** whose unknown lives in **3d coulomb potential** space, within the **Near-atomic 3D reconstruction of frozen-hydrated biomolecules** sub-domain of **Scientific Instrumentation**.

Measurements consist of electrons collected by an electron detector via a **weak phase transmission** sensing mechanism.

The forward operator applies, in order: L · project · euler operator; L · modulate · ctf operator; pixel-level spatial averaging on the detector.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Signal-to-noise per image ~0.01-0.1; collective averaging boosts SNR as sqrt(N). Mismatch: pose-estimation error, CTF miscalibration, conformational heterogeneity (multi-class), preferential orientation.

## ⚙ 2. Forward Model

Physical chain: **x** → L · project · euler → L · modulate · ctf → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.modulate.ctf` `L.project.euler` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.project.euler` | L · project · euler operator |
| `L.modulate.ctf` | L · modulate · ctf operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Scientific Instrumentation |
| Sub domain | Near-atomic 3D reconstruction of frozen-hydrated biomolecules |
| Carrier | electron |
| Problem class | tomographic_inverse_with_pose |
| Solution space | 3d_coulomb_potential |
| Noise model | shot_poisson |
| Integration axis | projection |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Signal-to-noise per image ~0.01-0.1; collective averaging boosts SNR as sqrt(N). Mismatch: pose-estimation error, CTF miscalibration, conformational heterogeneity (multi-class), preferential orientation.

| Metric | Value |
|---|---|
| Metric | resolution_angstrom |
| Secondary | FSC_0.143 |

## 📏 5. Operating Range (Ω)

**Center problem class:** `spa_homogeneous` · **Forward operator:** `spa_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Dose | — | 30 |
| N particle | — | 100000 |
| Defocus um | µm | 1.5 |
| Pixel angstrom | — | 1 |
| Pose estimate error | — | 0 |
| Conformational heterogeneity | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Dose | — | 10 – 100 |
| N particle | — | 1000 – 10000000 |
| Defocus um | µm | 0.3 – 5.0 |
| Pixel angstrom | — | 0.5 – 3.0 |
| Ctf miscalibration | — | 0.0 – 500 |
| Per particle motion | — | 0.0 – 5 |
| Pose estimate error | — | 0.0 – 10 |
| Preferential orientation | — | 0.0 – 0.8 |
| Conformational heterogeneity | — | 0.0 – 1.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.5 Å resolution

| Metric | Range |
|---|---|
| Resolution angstrom | 1.5 – 15 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **resolution_angstrom**, with κ = `1000` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xaaa726f4455d5c140143ffbd8c7321773279c57efdff74c29eff1d2d2cd948d3`
- **Chain tx hash:** `0x22ccda357f539047c2daa1d41b4447ee79e3bf5561621d4bd8ee90249bdb7c10`
- **Chain block:** `41554213`

---

## File Mapping

This bundle consists of: `L1-129.md`, `L1-129.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-129.md` | Source of truth — edit this | Human or LLM |
| `L1-129.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 `L1-129`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._