# ⚛  L1 Principle — Electron Energy Loss Spectroscopy (EELS)

**ID:** `L1-090` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electron Microscopy — *Inelastic-electron chemical spectroscopy*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D eels hyperspectral
> **📡 Carrier:** electron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554184

---

## 🧠 1. Introduction

**Electron Energy Loss Spectroscopy (EELS)** is a **linear inverse problem** whose unknown lives in **3D eels hyperspectral** space, within the **Inelastic-electron chemical spectroscopy** sub-domain of **Electron Microscopy**.

Measurements consist of electrons collected by an electron detector via a **inelastic electron spectrum** sensing mechanism.

The forward operator applies, in order: L · transmit sample operator; L · energy dispersion operator; D · eels spectrum operator; detector sums all spectral bands.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D eels hyperspectral is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 14); zero_loss_drift dominates the stability cliff; plural_scattering and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

## ⚙ 2. Forward Model

Physical chain: **x** → L · transmit sample → L · energy dispersion → D · eels spectrum → Spectral integration → **y** (detector).

```
y = Σ_λ `D.eels_spectrum` `L.energy_dispersion` `L.transmit_sample` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.transmit_sample` | L · transmit sample operator |
| `L.energy_dispersion` | L · energy dispersion operator |
| `D.eels_spectrum` | D · eels spectrum operator |
| `int.spectral` | Detector sums all spectral bands |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electron Microscopy |
| Sub domain | Inelastic-electron chemical spectroscopy |
| Carrier | electron |
| Problem class | linear_inverse |
| Solution space | 3D_eels_hyperspectral |
| Noise model | shot_poisson |
| Integration axis | spectral |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Existence of the recovered 3D eels hyperspectral is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 14); zero_loss_drift dominates the stability cliff; plural_scattering and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `eels_hyperspectral` · **Forward operator:** `eels_hyperspectral_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| W | px | 256 |
| Kv | — | 200 |
| N e | — | 2048 |
| Pixel nm | nm | 1 |
| E range ev | — | 0 – 2000 |
| Peak electrons | — | 500 |
| Zero loss drift | — | 0 |
| Plural scattering | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 2048 |
| W | px | 64 – 2048 |
| Kv | — | 80 – 300 |
| N e | — | 256 – 8192 |
| Pixel nm | nm | 0.1 – 10 |
| Edge overlap | — | 0.0 – 0.3 |
| Peak electrons | — | 10 – 5000 |
| Zero loss drift | — | 0.0 – 5.0 |
| Plural scattering | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `280` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x890ccef37ca5d79dedbed7809b3866929b4909f52cab29ebe4c0933ba1c06bc1`
- **Chain tx hash:** `0xb70f5d2dbe19a6b193e9178b78756c1490bba760fd7aa3e0bcb9bf5c46a1d723`
- **Chain block:** `41554184`

---

## File Mapping

This bundle consists of: `L1-090.md`, `L1-090.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-090.md` | Source of truth — edit this | Human or LLM |
| `L1-090.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 `L1-090`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._