# ⚛  L1 Principle — Volume of Fluid (VOF) — multiphase interface tracking

**ID:** `L1-183` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Fluid Dynamics — *Interface-capturing VOF for multiphase*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** interface phase field multiphase
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553967

---

## 🧠 1. Introduction

**Volume of Fluid (VOF) — multiphase interface tracking** is a **nonlinear inverse problem** whose unknown lives in **interface phase field multiphase** space, within the **Interface-capturing VOF for multiphase** sub-domain of **Fluid Dynamics**.

Measurements consist of mechanical vibrations or strain signals via a **high speed camera piv** sensing mechanism.

The forward operator applies, in order: L · vof advect operator; L · interface recon operator; L · surface tension operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · vof advect → L · interface recon → L · surface tension → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.surface_tension` `L.interface_recon` `L.vof_advect` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.vof_advect` | L · vof advect operator |
| `L.interface_recon` | L · interface recon operator |
| `L.surface_tension` | L · surface tension operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Fluid Dynamics |
| Sub domain | Interface-capturing VOF for multiphase |
| Carrier | mechanical |
| Problem class | nonlinear_inverse |
| Solution space | interface_phase_field_multiphase |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `vof` · **Forward operator:** `vof_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Snr db | dB | 30 |
| N times | — | 2000 |
| Coalescence artifact | — | 0 |
| Surface tension error | — | 0 |
| Interface thickness error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 8192 |
| W | px | 32 – 8192 |
| Snr db | dB | 0 – 40 |
| N times | — | 100 – 1000000 |
| Coalescence artifact | — | 0.0 – 0.3 |
| Surface tension error | — | 0.0 – 0.3 |
| Interface thickness error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

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

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x66bf83eb9e0ff26f593944304efb5bcb6f9abff828e9cf4ac0ae2637898db3e4`
- **Chain tx hash:** `0xa2712548089f3def45933aaddedbd99031cacd5d7ce790fd2af7aed1227b1dd0`
- **Chain block:** `41553967`

---

## File Mapping

This bundle consists of: `L1-183.md`, `L1-183.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-183.md` | Source of truth — edit this | Human or LLM |
| `L1-183.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 `L1-183`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._