# ⚛ L1 Principle — Hartree-Fock Self-Consistent Field
**ID:** `L1-295` · **Status:** ⊙ Testnet (genesis catalog)
> **🌐 Domain:** Computational Chemistry — *Mean-field electron correlation baseline*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** hf mo coefficients
> **📡 Carrier:** electron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554113
---
## 🧠 1. Introduction
**Hartree-Fock Self-Consistent Field** is a **nonlinear inverse problem** whose unknown lives in **hf mo coefficients** space, within the **Mean-field electron correlation baseline** sub-domain of **Computational Chemistry**.
Measurements consist of electrons collected by an electron detector via a **molecular benchmark** sensing mechanism.
The forward operator applies, in order: E · fock operator operator; a fixed-point or gradient iteration on the unknown; O · hf wavefunction operator.
Observations are corrupted by additive Gaussian noise. Well-posed; no correlation; missing ~1% of total energy.
## ⚙ 2. Forward Model
Physical chain: **x** → E · fock operator → O · hf wavefunction → **y** (detector).
```
y = `O.hf_wavefunction` `E.fock_operator` x + n, n ~ 𝒩(0, σ²)
```
**Measurement DAG:**
| Primitive | What it does |
|---|---|
| `E.fock_operator` | E · fock operator operator |
| `O.hf_wavefunction` | O · hf wavefunction 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 | Computational Chemistry |
| Sub domain | Mean-field electron correlation baseline |
| Carrier | electron |
| Problem class | nonlinear_inverse |
| Solution space | hf_mo_coefficients |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 3.1 |
## 📡 4. Measurement Model
Well-posed; no correlation; missing ~1% of total energy.
| Metric | Value |
|---|---|
| Metric | HF_energy_error_mHa |
| Secondary | orbital_energy_error_eV |
## 📏 5. Operating Range (Ω)
**Center problem class:** `hartree_fock` · **Forward operator:** `hf_forward`
**Center point:**
| Parameter | Unit | Value |
|---|---|---|
| Basis | — | cc-pVDZ |
| N basis | — | 100 |
| Symmetry | — | C1 |
| N electrons | — | 10 |
**Allowed bounds:**
| Parameter | Unit | Range |
|---|---|---|
| Basis | — | STO-3G, cc-pVDZ, cc-pVTZ, aug-cc-pVQZ |
| N basis | — | 20 – 10000 |
| N electrons | — | 2 – 1000 |
## 🎯 6. Tolerance (ε)
**Center tolerance:** HF E error <= 0.3 mHa
| Metric | Range |
|---|---|
| Hf energy error mha | 0.1 – 10 |
## ⚖ 7. Hardness Function
Hardness scales as **`epsilon_fn`** on **HF_energy_error_mHa**, with κ = `300` and δ = `3`.
## 💾 8. Reference Dataset
- **primary** · weight 1.0 · IPFS _(not pinned yet)_
## 9. On-chain Registration
- **Chain hash:** `0x6b76b255439952725b7127122cd263f86ba1343fc5feb9342f168125e4462c9b`
- **Chain tx hash:** `0xe7eeceefb7c0249c3a79431159bcfebefd1d4329444246973527ddb479465da9`
- **Chain block:** `41554113`
---
## File Mapping
This bundle consists of: `L1-295.md`, `L1-295.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-295.md` | Source of truth — edit this | Human or LLM |
| `L1-295.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 `L1-295`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._