# ⚛  L1 Principle — DLVO Colloidal Force Theory

**ID:** `L1-478` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Polymer Physics — *Colloidal stability*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** pair potential V of h
> **📡 Carrier:** ion · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555300

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## 🧠 1. Introduction

**DLVO Colloidal Force Theory** is a **nonlinear inverse problem** whose unknown lives in **pair potential V of h** space, within the **Colloidal stability** sub-domain of **Polymer Physics**.

Measurements consist of ions detected after acceleration or extraction via a **colloidal probe AFM** sensing mechanism.

The forward operator applies, in order: E · vdW operator; E · double layer operator; an unspecified linear measurement operator; O · force distance operator.

Observations are corrupted by additive Gaussian noise. Well-posed when both V_vdW and V_EDL contribute; ill-conditioned when one dominates (high ionic strength → secondary minimum masking).

## ⚙ 2. Forward Model

Physical chain: **x** → E · vdW → E · double layer → Generic linear operator → O · force distance → **y** (detector).

```
y = `O.force_distance` A `E.double_layer` `E.vdW` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.vdW` | E · vdw operator |
| `E.double_layer` | E · double layer operator |
| `L.linear_op` | An unspecified linear measurement operator |
| `O.force_distance` | O · force distance operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Polymer Physics |
| Sub domain | Colloidal stability |
| Carrier | ion |
| Problem class | nonlinear_inverse |
| Solution space | pair_potential_V_of_h |
| Noise model | gaussian |
| Integration axis | separation |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Well-posed when both V_vdW and V_EDL contribute; ill-conditioned when one dominates (high ionic strength → secondary minimum masking).

| Metric | Value |
|---|---|
| Metric | V_of_h_RMSE_kT |
| Secondary | aggregation_rate_error |

## 📏 5. Operating Range (Ω)

**Center problem class:** `dlvo_parameter_inversion` · **Forward operator:** `dlvo_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T k | — | 298 |
| I mm | mm | 10 |
| R nm | nm | 100 |
| Psi 0 mv | — | -40 |
| A hamaker zj | — | 5 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 273 – 373 |
| I mm | mm | 0.1 – 1000 |
| R nm | nm | 10 – 5000 |
| Psi 0 mv | — | -120 – 120 |
| A hamaker zj | — | 0.5 – 20.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** V(h) RMSE <= 0.3 k_B T

| Metric | Range |
|---|---|
| V of h rmse kt | 0.1 – 5.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **V_of_h_RMSE_kT**, with κ = `80` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x4d8f1be2284ec379bed19e7de846fd5c81093b9a0a820df4419f275cf9741e79`
- **Chain tx hash:** `0xda5dbcb7cfcce87f8e60452909f0e3f7b5d2726cddea09e46655d45ee656dc3d`
- **Chain block:** `41555300`

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## File Mapping

This bundle consists of: `L1-478.md`, `L1-478.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-478.md` | Source of truth — edit this | Human or LLM |
| `L1-478.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 `L1-478`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._