# ⚛ L1 Principle — Exact Diagonalization of Many-Body Hamiltonians
**ID:** `L1-323` · **Status:** ⊙ Testnet (genesis catalog)
> **🌐 Domain:** Quantum Mechanics — *Full Hilbert space spectra*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** many body eigenstates
> **📡 Carrier:** electron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554081
---
## 🧠 1. Introduction
**Exact Diagonalization of Many-Body Hamiltonians** is a **linear inverse problem** whose unknown lives in **many body eigenstates** space, within the **Full Hilbert space spectra** sub-domain of **Quantum Mechanics**.
Measurements consist of electrons collected by an electron detector via a **energy spectrum benchmark** sensing mechanism.
The forward operator applies, in order: E · Fock basis operator; computes eigen-pairs of a linear operator; O · eigensystem operator.
Observations are corrupted by additive Gaussian noise. Exact to numerical precision; limited by exponential Hilbert space scaling.
## ⚙ 2. Forward Model
Physical chain: **x** → E · Fock basis → O · eigensystem → **y** (detector).
```
y = `O.eigensystem` `E.Fock_basis` x + n, n ~ 𝒩(0, σ²)
```
**Measurement DAG:**
| Primitive | What it does |
|---|---|
| `E.Fock_basis` | E · fock basis operator |
| `O.eigensystem` | O · eigensystem 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 | Quantum Mechanics |
| Sub domain | Full Hilbert space spectra |
| Carrier | electron |
| Problem class | linear_inverse |
| Solution space | many_body_eigenstates |
| Noise model | gaussian |
| Integration axis | energy |
| Difficulty delta | 5 |
| L dag | 3.2 |
## 📡 4. Measurement Model
Exact to numerical precision; limited by exponential Hilbert space scaling.
| Metric | Value |
|---|---|
| Metric | ground_state_E_error_mHa |
| Secondary | first_excited_error |
## 📏 5. Operating Range (Ω)
**Center problem class:** `exact_diagonalization` · **Forward operator:** `exact_diagonalization_forward`
**Center point:**
| Parameter | Unit | Value |
|---|---|---|
| Method | — | Lanczos |
| L sites | — | 16 |
| N states | — | 10 |
| Symmetry | — | U1 |
**Allowed bounds:**
| Parameter | Unit | Range |
|---|---|---|
| L sites | — | 4 – 30 |
| N states | — | 1 – 100 |
| Symmetry | — | none, U1, SU2 |
## 🎯 6. Tolerance (ε)
**Center tolerance:** E error <= 0.01 mHa
| Metric | Range |
|---|---|
| Ground state e error mha | 0.001 – 10 |
## ⚖ 7. Hardness Function
Hardness scales as **`epsilon_fn`** on **ground_state_E_error_mHa**, with κ = `800` and δ = `5`.
## 💾 8. Reference Dataset
- **primary** · weight 1.0 · IPFS _(not pinned yet)_
## 9. On-chain Registration
- **Chain hash:** `0xa73c9ce5fe7e8f728f782cd4082ef7bb7683731ef4ed9829646dcc1aa9a70746`
- **Chain tx hash:** `0xf8c595f54666a3b88fd1f64753914cb7811e2200c9080c28e0fa96e6193ccc21`
- **Chain block:** `41554081`
---
## File Mapping
This bundle consists of: `L1-323.md`, `L1-323.json`.
| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-323.md` | Source of truth — edit this | Human or LLM |
| `L1-323.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 `L1-323`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._