# ⚛  L1 Principle — Boundary Layer — Prandtl / Blasius near-wall flow

**ID:** `L1-174` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Fluid Dynamics — *Laminar and turbulent boundary layers*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** velocity profile near wall
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553965

---

## 🧠 1. Introduction

**Boundary Layer — Prandtl / Blasius near-wall flow** is a **nonlinear inverse problem** whose unknown lives in **velocity profile near wall** space, within the **Laminar and turbulent boundary layers** sub-domain of **Fluid Dynamics**.

Measurements consist of mechanical vibrations or strain signals via a **hot wire piv** sensing mechanism.

The forward operator applies, in order: L · prandtl bl operator; L · similarity operator; L · transition operator; pixel-level spatial averaging on the detector.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · prandtl bl → L · similarity → L · transition → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.transition` `L.similarity` `L.prandtl_bl` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.prandtl_bl` | L · prandtl bl operator |
| `L.similarity` | L · similarity operator |
| `L.transition` | L · transition operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Fluid Dynamics |
| Sub domain | Laminar and turbulent boundary layers |
| Carrier | mechanical |
| Problem class | nonlinear_inverse |
| Solution space | velocity_profile_near_wall |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 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:** `boundary_layer` · **Forward operator:** `boundary_layer_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N y | — | 200 |
| Re x | — | 1e+06 |
| Snr db | dB | 30 |
| Re x error | — | 0 |
| Roughness error | — | 0 |
| Pressure gradient error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N y | — | 32 – 10000 |
| Re x | — | 100.0 – 10000000000.0 |
| Snr db | dB | 0 – 40 |
| Re x error | — | 0.0 – 0.1 |
| Roughness error | — | 0.0 – 0.3 |
| Pressure gradient error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 24.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xc86fdd1107c12722f81c4dfed9f473281486663a91a1ed9c2eeec4bd6b6ecae6`
- **Chain tx hash:** `0xeed16d987b690f4f718857ade27f039ed01e7d3a6aaedc1be4f7b610057a94f0`
- **Chain block:** `41553965`

---

## File Mapping

This bundle consists of: `L1-174.md`, `L1-174.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-174.md` | Source of truth — edit this | Human or LLM |
| `L1-174.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 `L1-174`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._