L1 ⚛ L1-322 ⊙ Testnet

Density Matrix Renormalization Group (DMRG)

Quantum Mechanics · Matrix-product-state ground states

⬇ Download bundle 🚀 Submit to mainnet — earn 5% royalty

🎁 Contribute & earn PWM

Improve L1-322 — submit with or without uploading. Accepted submissions earn the 1/16 modify share of A(t).

✨ Submit without uploading free check · 1×

One click — no files, no typing. We submit a check of L1-322 for you; it goes through review and earns the 1/16 share once. One free no-upload Principle per account.

You'll be asked to log in first — then it's one click, no files.

⬆ Or submit by uploading your files

Upload your .md + .json as a modification of L1-322. Unlimited.

🛠 Helper: build your files in ChatGPT / Gemini / Claude

Layer template

⬇ principle.md ⬇ principle.json

Fork L1-322

⬇ L1-322.md ⬇ L1-322.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-322 (Density Matrix Renormalization Group (DMRG)) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-322.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-322.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = `O.gs_energy` `E.MPO_hamiltonian` x + n,    n ~ 𝒩(0, σ²)

world state x (matrix product state)

→

E · MPO hamiltonian `E.MPO_hamiltonian`

→

O · gs energy `O.gs_energy`

→

observation y (electron detector)

Noise: additive Gaussian noise

Solver / auxiliary components (1)

O.regularize — adds a prior term that biases the solution toward smoothness/sparsity

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-322.md

# ⚛ L1 Principle — Density Matrix Renormalization Group (DMRG) **ID:** `L1-322` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Matrix-product-state ground states* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** matrix product state > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554081 --- ## 🧠 1. Introduction **Density Matrix Renormalization Group (DMRG)** is a **nonlinear inverse problem** whose unknown lives in **matrix product state** space, within the **Matrix-product-state ground states** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **energy correlation benchmark** sensing mechanism. The forward operator applies, in order: E · MPO hamiltonian operator; adds a prior term that biases the solution toward smoothness/sparsity; O · gs energy operator. Observations are corrupted by additive Gaussian noise. Exponential precision with bond dimension M in 1D; 2D DMRG limited by transverse correlation length. ## ⚙ 2. Forward Model Physical chain: **x** → E · MPO hamiltonian → O · gs energy → **y** (detector). ``` y = `O.gs_energy` `E.MPO_hamiltonian` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.MPO_hamiltonian` | E · mpo hamiltonian operator | | `O.gs_energy` | O · gs energy operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | Matrix-product-state ground states | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | matrix_product_state | | Noise model | gaussian | | Integration axis | site_index | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model Exponential precision with bond dimension M in 1D; 2D DMRG limited by transverse correlation length. | Metric | Value | |---|---| | Metric | gs_energy_error_mHa_per_site | | Secondary | entanglement_entropy_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `dmrg` · **Forward operator:** `dmrg_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Model | — | Heisenberg_spin_half | | L sites | — | 100 | | N sweeps | — | 20 | | Bond dim m | m | 200 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | L sites | — | 10 – 10000 | | N sweeps | — | 5 – 200 | | Bond dim m | m | 20 – 10000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** E/site error <= 0.1 mHa | Metric | Range | |---|---| | Gs energy error mha per site | 0.01 – 10 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **gs_energy_error_mHa_per_site**, with κ = `2000` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xbc5d5c6cd3a3ecd4c21449e1696807dbe2d7d4a9eb7dfdc3cecb2049cc1f0131` - **Chain tx hash:** `0x8bdc1ba462a809c8da5d0beb1dc469cb04ac5311b487f0907277292e32cfa2fc` - **Chain block:** `41554081` --- ## File Mapping This bundle consists of: `L1-322.md`, `L1-322.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-322.md` | Source of truth — edit this | Human or LLM | | `L1-322.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 `L1-322`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

💬

Ask the PWM AI agent AI

Ask about this Density Matrix Renormalization Group (DMRG) — or how to improve it & earn PWM

Free to search; log in to chat with the agent & earn PWM. How it works ↗

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Digital Twin 1 child ▾

L2-322-001 Density Matrix Renormalization Group (DMRG) Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-322",
  "chain_block": 41554081,
  "chain_hash": "0xbc5d5c6cd3a3ecd4c21449e1696807dbe2d7d4a9eb7dfdc3cecb2049cc1f0131",
  "chain_tx_hash": "0x8bdc1ba462a809c8da5d0beb1dc469cb04ac5311b487f0907277292e32cfa2fc",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 2000,
    "metric": "gs_energy_error_mHa_per_site",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "gs_energy_error_mHa_per_site",
    "regime": "Exponential precision with bond dimension M in 1D; 2D DMRG limited by transverse correlation length.",
    "secondary": "entanglement_entropy_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "electron",
    "difficulty_delta": 10,
    "domain": "Quantum Mechanics",
    "integration_axis": "site_index",
    "noise_model": "gaussian",
    "primitives": [
      "E.MPO_hamiltonian",
      "O.regularize",
      "O.gs_energy"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "energy_correlation_benchmark",
    "solution_space": "matrix_product_state",
    "sub_domain": "Matrix-product-state ground states",
    "title": "Density Matrix Renormalization Group (DMRG)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "dmrg_forward"
    ],
    "allowed_omega_dimensions": [
      "L_sites",
      "bond_dim_M",
      "N_sweeps",
      "model"
    ],
    "allowed_problem_classes": [
      "dmrg"
    ],
    "center_spec": {
      "epsilon_fn_center": "E/site error \u003c= 0.1 mHa",
      "forward_operator": "dmrg_forward",
      "input_format": "measurement_only",
      "omega": {
        "L_sites": 100,
        "N_sweeps": 20,
        "bond_dim_M": 200,
        "model": "Heisenberg_spin_half"
      },
      "problem_class": "dmrg"
    },
    "epsilon_bounds": {
      "gs_energy_error_mHa_per_site": [
        0.01,
        10
      ]
    },
    "omega_bounds": {
      "L_sites": [
        10,
        10000
      ],
      "N_sweeps": [
        5,
        200
      ],
      "bond_dim_M": [
        20,
        10000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Matrix-product-state ground states",
  "title": "Density Matrix Renormalization Group (DMRG)"
}

🎁

Earn PWM by promoting this to mainnet

• PWM emission on accept — your share of A(t) (1/16 modify · 3/16 new)
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Go to submit ↑

How: use the “Contribute & earn PWM” panel at the top — either Submit without uploading (one click) or upload your files. Then the review runs and, on accept, it’s promoted to mainnet.