# ⚛  L1 Principle — STEM-EDX — X-ray energy-dispersive elemental mapping

**ID:** `L1-094` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electron Microscopy — *Chemical composition via characteristic X-rays*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** elemental concentration map
> **📡 Carrier:** electron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554185

---

## 🧠 1. Introduction

**STEM-EDX — X-ray energy-dispersive elemental mapping** is a **linear inverse problem** whose unknown lives in **elemental concentration map** space, within the **Chemical composition via characteristic X-rays** sub-domain of **Electron Microscopy**.

Measurements consist of electrons collected by an electron detector via a **edx characteristic xray** sensing mechanism.

The forward operator applies, in order: L · illumination · convergent probe operator; ordered pixel-by-pixel sampling; D · edx detector operator; detector sums all spectral bands.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered elemental concentration map 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 ~= 10); detector_dead_time dominates the stability cliff; peak_overlap 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 · illumination · convergent probe → Raster scan → D · edx detector → Spectral integration → **y** (detector).

```
y = Σ_λ `D.edx_detector` S_raster `L.illumination.convergent_probe` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.illumination.convergent_probe` | L · illumination · convergent probe operator |
| `S.scan.raster` | Ordered pixel-by-pixel sampling |
| `D.edx_detector` | D · edx detector operator |
| `int.spectral` | Detector sums all spectral bands |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electron Microscopy |
| Sub domain | Chemical composition via characteristic X-rays |
| Carrier | electron |
| Problem class | linear_inverse |
| Solution space | elemental_concentration_map |
| Noise model | shot_poisson |
| Integration axis | spectral |
| Difficulty delta | 3 |
| L dag | 3.4 |

## 📡 4. Measurement Model

Existence of the recovered elemental concentration map 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 ~= 10); detector_dead_time dominates the stability cliff; peak_overlap 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:** `stem_edx` · **Forward operator:** `stem_edx_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Kv | — | 200 |
| Dwell ms | ms | 5 |
| N elements | — | 6 |
| Peak overlap | — | 0 |
| Peak electrons | — | 1000 |
| Detector dead time | — | 0.1 |
| Absorption correction | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 2048 |
| W | px | 128 – 2048 |
| Kv | — | 60 – 300 |
| Dwell ms | ms | 0.1 – 1000 |
| N elements | — | 2 – 30 |
| Peak overlap | — | 0.0 – 0.5 |
| Peak electrons | — | 50 – 100000 |
| Detector dead time | — | 0.0 – 0.5 |
| Absorption correction | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0

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

## ⚖ 7. Hardness Function

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

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x9e7ec6f14b81d585009a8ebebd67a34c5ae7609a79cd195746e71996cb81c2c0`
- **Chain tx hash:** `0xff096da21fdb8ac871c47eb8415020407f18667343b8f0c1bde7a89eb2b5cf80`
- **Chain block:** `41554185`

---

## File Mapping

This bundle consists of: `L1-094.md`, `L1-094.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-094.md` | Source of truth — edit this | Human or LLM |
| `L1-094.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 `L1-094`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._