# ⚛  L1 Principle — Chemical Kinetics via Stiff ODEs

**ID:** `L1-300` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Reaction network dynamics*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** concentration time series
> **📡 Carrier:** none · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554114

---

## 🧠 1. Introduction

**Chemical Kinetics via Stiff ODEs** is a **nonlinear inverse problem** whose unknown lives in **concentration time series** space, within the **Reaction network dynamics** sub-domain of **Computational Chemistry**.

Measurements consist of none via a **species concentration** sensing mechanism.

The forward operator applies, in order: E · mass action operator; D · time · implicit operator; O · concentration profile operator.

Observations are corrupted by additive Gaussian noise. Well-posed; inverse (rate constant fit) requires data across T for identifiability.

## ⚙ 2. Forward Model

Physical chain: **x** → E · mass action → D · time · implicit → O · concentration profile → **y** (detector).

```
y = `O.concentration_profile` `D.time.implicit` `E.mass_action` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.mass_action` | E · mass action operator |
| `D.time.implicit` | D · time · implicit operator |
| `O.concentration_profile` | O · concentration profile operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Reaction network dynamics |
| Carrier | none |
| Problem class | nonlinear_inverse |
| Solution space | concentration_time_series |
| Noise model | gaussian |
| Integration axis | time |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Well-posed; inverse (rate constant fit) requires data across T for identifiability.

| Metric | Value |
|---|---|
| Metric | concentration_L2_error |
| Secondary | rate_constant_relative_error |

## 📏 5. Operating Range (Ω)

**Center problem class:** `chemical_kinetics_ode` · **Forward operator:** `kinetics_ode_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T k | — | 298 |
| T end s | s | 100 |
| N species | — | 10 |
| N reactions | — | 20 |
| Log k range | — | -4 – 4 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 273 – 2000 |
| T end s | s | 0.001 – 1000000.0 |
| N species | — | 2 – 1000 |
| N reactions | — | 1 – 10000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** c L2 <= 0.01 M

| Metric | Range |
|---|---|
| Concentration l2 error | 0.005 – 0.3 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **concentration_L2_error**, with κ = `150` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x57f9b0b587ffecd8fbc97e817a3f48b9a3740a90cfe224c223eb4518ca7c24c3`
- **Chain tx hash:** `0x69b90bf91345d1560aa3bc161fca1f2a2cbc92e1e254767fde84b4d6507e96dd`
- **Chain block:** `41554114`

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## File Mapping

This bundle consists of: `L1-300.md`, `L1-300.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-300.md` | Source of truth — edit this | Human or LLM |
| `L1-300.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 `L1-300`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._