# ⚛  L1 Principle — Butler-Volmer Electrochemical Kinetics

**ID:** `L1-311` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Electrode charge-transfer kinetics*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** BV parameter triplet
> **📡 Carrier:** ion · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554127

---

## 🧠 1. Introduction

**Butler-Volmer Electrochemical Kinetics** is a **nonlinear inverse problem** whose unknown lives in **BV parameter triplet** space, within the **Electrode charge-transfer kinetics** sub-domain of **Computational Chemistry**.

Measurements consist of ions detected after acceleration or extraction via a **electrochemical IV** sensing mechanism.

The forward operator applies, in order: E · butler volmer operator; E · mass transport operator; O · i eta operator.

Observations are corrupted by additive Gaussian noise. Well-posed; inversion clean in Tafel regime.

## ⚙ 2. Forward Model

Physical chain: **x** → E · butler volmer → E · mass transport → O · i eta → **y** (detector).

```
y = `O.i_eta` `E.mass_transport` `E.butler_volmer` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.butler_volmer` | E · butler volmer operator |
| `E.mass_transport` | E · mass transport operator |
| `O.i_eta` | O · i eta operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Electrode charge-transfer kinetics |
| Carrier | ion |
| Problem class | nonlinear_inverse |
| Solution space | BV_parameter_triplet |
| Noise model | gaussian |
| Integration axis | potential |
| Difficulty delta | 3 |
| L dag | 2.8 |

## 📡 4. Measurement Model

Well-posed; inversion clean in Tafel regime.

| Metric | Value |
|---|---|
| Metric | log_i_0_error |
| Secondary | alpha_error |

## 📏 5. Operating Range (Ω)

**Center problem class:** `butler_volmer` · **Forward operator:** `butler_volmer_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T k | — | 298 |
| N data | — | 200 |
| Electrolyte | — | aqueous |
| Eta range v | — | -0.5 – 0.5 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 253 – 373 |
| N data | — | 20 – 5000 |
| Electrolyte | — | aqueous, organic, ionic_liquid, molten_salt |
| Eta range v max | — | 0.1 – 2.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** log10(i_0) <= 0.05

| Metric | Range |
|---|---|
| Log i 0 error | 0.02 – 1.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **log_i_0_error**, with κ = `80` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x05a93cd61b3b7411eb038373f40e0b15e4402497833bd478622efd8a427674be`
- **Chain tx hash:** `0x19fecdc76613707cbffc699700c47b8bb02a6e61ea21fba0587cca83a919172c`
- **Chain block:** `41554127`

---

## File Mapping

This bundle consists of: `L1-311.md`, `L1-311.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-311.md` | Source of truth — edit this | Human or LLM |
| `L1-311.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 `L1-311`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._