# ⚛  L1 Principle — Eyring Transition State Theory

**ID:** `L1-303` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Reaction rate prediction from QM*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** TS barrier frequency
> **📡 Carrier:** none · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554114

---

## 🧠 1. Introduction

**Eyring Transition State Theory** is a **nonlinear inverse problem** whose unknown lives in **TS barrier frequency** space, within the **Reaction rate prediction from QM** sub-domain of **Computational Chemistry**.

Measurements consist of none via a **rate vs T measurement** sensing mechanism.

The forward operator applies, in order: E · quantum chemistry operator; E · TS structure operator; computes eigen-pairs of a linear operator; O · rate k T operator.

Observations are corrupted by additive Gaussian noise. Well-posed from QM; inversion for barrier + frequencies requires wide T-range.

## ⚙ 2. Forward Model

Physical chain: **x** → E · quantum chemistry → E · TS structure → O · rate k T → **y** (detector).

```
y = `O.rate_k_T` `E.TS_structure` `E.quantum_chemistry` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.quantum_chemistry` | E · quantum chemistry operator |
| `E.TS_structure` | E · ts structure operator |
| `O.rate_k_T` | O · rate k t operator |

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

| Primitive | What it does |
|---|---|
| `E.eigensolve` | Computes eigen-pairs of a linear operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Reaction rate prediction from QM |
| Carrier | none |
| Problem class | nonlinear_inverse |
| Solution space | TS_barrier_frequency |
| Noise model | gaussian |
| Integration axis | temperature |
| Difficulty delta | 5 |
| L dag | 3.4 |

## 📡 4. Measurement Model

Well-posed from QM; inversion for barrier + frequencies requires wide T-range.

| Metric | Value |
|---|---|
| Metric | log_k_error |
| Secondary | Ea_error_kcal_mol |

## 📏 5. Operating Range (Ω)

**Center problem class:** `transition_state_theory` · **Forward operator:** `tst_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N atoms | — | 10 |
| T k range | — | 200 – 500 |
| Tunneling | — | SCT |
| N temperatures | — | 15 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N atoms | — | 3 – 1000 |
| Tunneling | — | none, Wigner, Eckart, SCT |
| T k range max | — | 500 – 3000 |
| N temperatures | — | 3 – 200 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** log10(k) <= 0.1

| Metric | Range |
|---|---|
| Log k error | 0.05 – 2.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **log_k_error**, with κ = `300` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x6a06873a0fc9356d7b210f03fedf74cb20434eb31c8ecc1f4433622ce797e545`
- **Chain tx hash:** `0xafab6944916d097c500bbd23356047a99f3f29db5d380c7ed800103d8cd5169b`
- **Chain block:** `41554114`

---

## File Mapping

This bundle consists of: `L1-303.md`, `L1-303.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-303.md` | Source of truth — edit this | Human or LLM |
| `L1-303.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 `L1-303`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._