# ⚛  L1 Principle — XAS / EXAFS — X-ray Absorption & Extended X-ray Absorption Fine Structure

**ID:** `L1-147` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Spectroscopy — *Inner-shell X-ray absorption + multiple scattering oscillations*
> **🎯 Problem class:** nonlinear inverse structural · **🧮 Solution space:** radial coordination
> **📡 Carrier:** photon · **🌫 Noise:** poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554228

---

## 🧠 1. Introduction

**XAS / EXAFS — X-ray Absorption & Extended X-ray Absorption Fine Structure** is a **nonlinear inverse structural** whose unknown lives in **radial coordination** space, within the **Inner-shell X-ray absorption + multiple scattering oscillations** sub-domain of **Spectroscopy**.

Measurements consist of photons collected by an optical detector via a **xray core absorption** sensing mechanism.

The forward operator applies, in order: L · absorb · photoionization operator; L · scatter · multiple operator; detector sums all spectral bands.

Observations are corrupted by Poisson counting noise. Fourier-transform EXAFS inversion is linear; parameter fitting (R_j, N_j, sigma_j^2) is nonlinear; correlation among N, S_0, sigma is a major ill-conditioning source.

## ⚙ 2. Forward Model

Physical chain: **x** → L · absorb · photoionization → L · scatter · multiple → Spectral integration → **y** (detector).

```
y = Σ_λ `L.scatter.multiple` `L.absorb.photoionization` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.absorb.photoionization` | L · absorb · photoionization operator |
| `L.scatter.multiple` | L · scatter · multiple operator |
| `int.spectral` | Detector sums all spectral bands |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Spectroscopy |
| Sub domain | Inner-shell X-ray absorption + multiple scattering oscillations |
| Carrier | photon |
| Problem class | nonlinear_inverse_structural |
| Solution space | radial_coordination |
| Noise model | poisson |
| Integration axis | spectral |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Fourier-transform EXAFS inversion is linear; parameter fitting (R_j, N_j, sigma_j^2) is nonlinear; correlation among N, S_0, sigma is a major ill-conditioning source.

| Metric | Value |
|---|---|
| Metric | R_j_RMSE_angstrom |
| Secondary | N_j_NMSE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `exafs_radial_fit` · **Forward operator:** `feff_exafs_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N e | — | 400 |
| K max | — | 10 |
| Snr db | dB | 30 |
| K shells | — | 3 |
| S 0 squared | — | 0.85 |
| E0 shift ev | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N e | — | 50 – 2000 |
| K max | — | 4 – 16 |
| Snr db | dB | -5 – 45 |
| K shells | — | 1 – 10 |
| S 0 squared | — | 0.5 – 1.0 |
| E0 shift ev | — | -5 – 5 |
| Detector saturation | — | 0.0 – 0.2 |
| Self absorption correction | — | 0.0 – 0.3 |
| Multiple scattering truncation | — | 1 – 5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.01 A R-RMSE

| Metric | Range |
|---|---|
| Rmse angstrom | 0.001 – 0.2 |

## ⚖ 7. Hardness Function

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

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x6236f942e037e4657879721e22d5d874827bda83260a000ac570672d28dd0418`
- **Chain tx hash:** `0x8d99ca2b6521ca569bb6db1bd5f20f2baadb5662beebbfefdbe56b1493f31a2c`
- **Chain block:** `41554228`

---

## File Mapping

This bundle consists of: `L1-147.md`, `L1-147.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-147.md` | Source of truth — edit this | Human or LLM |
| `L1-147.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 `L1-147`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._