# ⚛  L1 Principle — Additive Manufacturing (Selective Laser Melting) Thermal Model

**ID:** `L1-341` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Materials Science — *Laser-powder-bed melt pool thermodynamics*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** melt pool thermal velocity
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554130

---

## 🧠 1. Introduction

**Additive Manufacturing (Selective Laser Melting) Thermal Model** is a **nonlinear inverse problem** whose unknown lives in **melt pool thermal velocity** space, within the **Laser-powder-bed melt pool thermodynamics** sub-domain of **Materials Science**.

Measurements consist of photons collected by an optical detector via a **laser powder bed thermal** sensing mechanism.

The forward operator applies, in order: E · thermal operator; E · fluid operator; E · phase change operator; a fixed-point or gradient iteration on the unknown; O · melt pool operator.

Observations are corrupted by additive Gaussian noise. Highly non-linear multiphysics; well-posed locally; inversion of (alpha, k_T) from thermal video is moderately ill-conditioned.

## ⚙ 2. Forward Model

Physical chain: **x** → E · thermal → E · fluid → E · phase change → O · melt pool → **y** (detector).

```
y = `O.melt_pool` `E.phase_change` `E.fluid` `E.thermal` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.thermal` | E · thermal operator |
| `E.fluid` | E · fluid operator |
| `E.phase_change` | E · phase change operator |
| `O.melt_pool` | O · melt pool operator |

**🛠 Solver components** _(used inside the solver, not in the forward equation)_:

| Primitive | What it does |
|---|---|
| `O.iter` | A fixed-point or gradient iteration on the unknown |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Materials Science |
| Sub domain | Laser-powder-bed melt pool thermodynamics |
| Carrier | photon |
| Problem class | nonlinear_inverse |
| Solution space | melt_pool_thermal_velocity |
| Noise model | gaussian |
| Integration axis | time_space |
| Difficulty delta | 5 |
| L dag | 3.9 |

## 📡 4. Measurement Model

Highly non-linear multiphysics; well-posed locally; inversion of (alpha, k_T) from thermal video is moderately ill-conditioned.

| Metric | Value |
|---|---|
| Metric | melt_pool_depth_relative_error |
| Secondary | peak_T_error_K |

## 📏 5. Operating Range (Ω)

**Center problem class:** `additive_manufacturing` · **Forward operator:** `AM_thermal_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| P w | — | 200 |
| V mm s | s | 800 |
| Hatch um | µm | 100 |
| Layer um | µm | 30 |
| Material | — | Ti6Al4V |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| P w | — | 50 – 2000 |
| V mm s | s | 50 – 5000 |
| Hatch um | µm | 30 – 300 |
| Layer um | µm | 10 – 100 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** melt-pool depth rel error <= 0.06

| Metric | Range |
|---|---|
| Melt pool depth relative error | 0.02 – 0.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **melt_pool_depth_relative_error**, with κ = `900` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x8d070d81fee915beb20cd54ccc595e5001048ff10e1949cfea72d30e6a9d69d5`
- **Chain tx hash:** `0x1e0cedbc313ead1259c262b3755778a5aeabdee043dbd863676b1af3efc15458`
- **Chain block:** `41554130`

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## File Mapping

This bundle consists of: `L1-341.md`, `L1-341.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-341.md` | Source of truth — edit this | Human or LLM |
| `L1-341.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 `L1-341`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._