# ⚛  L1 Principle — Isotope-Ratio Mass Spectrometry (IRMS)

**ID:** `L1-148` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Spectroscopy — *High-precision stable-isotope measurement*
> **🎯 Problem class:** ratio estimation · **🧮 Solution space:** isotope ratio scalar
> **📡 Carrier:** ion · **🌫 Noise:** gaussian plus drift
> **⚖ Difficulty (δ):** 2 · **⛓ Block:** 41554228

---

## 🧠 1. Introduction

**Isotope-Ratio Mass Spectrometry (IRMS)** is a **ratio estimation** whose unknown lives in **isotope ratio scalar** space, within the **High-precision stable-isotope measurement** sub-domain of **Spectroscopy**.

Measurements consist of ions detected after acceleration or extraction via a **magnetic sector ms** sensing mechanism.

The forward operator applies, in order: L · disperse · mass operator; detector accumulates flux over the exposure window.

Observations are corrupted by gaussian plus drift. Ratio-metric measurements are self-correcting for flow/pressure drifts; amplifier nonlinearity and peak tailing are dominant error sources at 0.01-0.1 permil level.

## ⚙ 2. Forward Model

Physical chain: **x** → L · disperse · mass → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.disperse.mass` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.disperse.mass` | L · disperse · mass operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Spectroscopy |
| Sub domain | High-precision stable-isotope measurement |
| Carrier | ion |
| Problem class | ratio_estimation |
| Solution space | isotope_ratio_scalar |
| Noise model | gaussian_plus_drift |
| Integration axis | temporal |
| Difficulty delta | 2 |
| L dag | 2 |

## 📡 4. Measurement Model

Ratio-metric measurements are self-correcting for flow/pressure drifts; amplifier nonlinearity and peak tailing are dominant error sources at 0.01-0.1 permil level.

| Metric | Value |
|---|---|
| Metric | delta_RMSE_permil |
| Secondary | precision_permil |

## 📏 5. Operating Range (Ω)

**Center problem class:** `bulk_irms_delta` · **Forward operator:** `sector_irms_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Mass pair | — | 45 – 44 |
| N replicate | — | 6 |
| Isotope pair | — | 13C12C |
| Peak tailing | — | 0.0001 |
| Memory effect | — | 0.001 |
| Amp nonlinearity | — | 1e-05 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Flow drift | — | 0.0 – 0.05 |
| N replicate | — | 1 – 100 |
| Peak tailing | — | 0.0 – 0.01 |
| Memory effect | — | 0.0 – 0.1 |
| Amp nonlinearity | — | 0.0 – 0.001 |
| Sample size mismatch | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.05 permil RMSE

| Metric | Range |
|---|---|
| Rmse permil | 0.005 – 10 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **delta_RMSE_permil**, with κ = `50` and δ = `2`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x5a451a09d507219dfc23982ffb32a081b7374a92abfa9373c2eebb0826c6c3be`
- **Chain tx hash:** `0xfce7e4d6a071dbda13b030ced6f32481bdf4a87289d7cef70095239c44d48f31`
- **Chain block:** `41554228`

---

## File Mapping

This bundle consists of: `L1-148.md`, `L1-148.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-148.md` | Source of truth — edit this | Human or LLM |
| `L1-148.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 `L1-148`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._