L1 ⚛ L1-304 ⊙ Testnet

Semi-Empirical Quantum Chemistry (AM1, PM6, DFTB, xTB)

Computational Chemistry · Parameterized approximate QM

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⬇ L1-304.md

# ⚛ L1 Principle — Semi-Empirical Quantum Chemistry (AM1, PM6, DFTB, xTB) **ID:** `L1-304` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Chemistry — *Parameterized approximate QM* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** semi empirical wavefunction > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554114 --- ## 🧠 1. Introduction **Semi-Empirical Quantum Chemistry (AM1, PM6, DFTB, xTB)** is a **nonlinear inverse problem** whose unknown lives in **semi empirical wavefunction** space, within the **Parameterized approximate QM** sub-domain of **Computational Chemistry**. Measurements consist of electrons collected by an electron detector via a **property benchmark** sensing mechanism. The forward operator applies, in order: E · parameterized fock operator; a fixed-point or gradient iteration on the unknown; O · observables operator. Observations are corrupted by additive Gaussian noise. Well-posed once parameterized; out-of-domain systems fail silently. ## ⚙ 2. Forward Model Physical chain: **x** → E · parameterized fock → O · observables → **y** (detector). ``` y = `O.observables` `E.parameterized_fock` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.parameterized_fock` | E · parameterized fock operator | | `O.observables` | O · observables 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 | Parameterized approximate QM | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | semi_empirical_wavefunction | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed once parameterized; out-of-domain systems fail silently. | Metric | Value | |---|---| | Metric | energy_error_mHa | | Secondary | geometry_RMSD_A | ## 📏 5. Operating Range (Ω) **Center problem class:** `semiempirical_qc` · **Forward operator:** `semiempirical_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Method | — | GFN2-xTB | | N atoms | — | 100 | | N basis | — | 500 | | Dispersion | — | D4 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Method | — | AM1, PM6, PM7, DFTB3, GFN1-xTB, GFN2-xTB | | N atoms | — | 2 – 100000 | | N basis | — | 10 – 500000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** E error <= 3 mHa (~2 kcal/mol) | Metric | Range | |---|---| | Energy error mha | 1.0 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **energy_error_mHa**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7c26b92831516ade7766f5e9090df0136f213203573091666787806fcfea6cc2` - **Chain tx hash:** `0xbe564926d5d03d4f5a7299f3dd8ef5cbda7dbd66be0e2d57d7493b86f5136310` - **Chain block:** `41554114` --- ## File Mapping This bundle consists of: `L1-304.md`, `L1-304.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-304.md` | Source of truth — edit this | Human or LLM | | `L1-304.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 `L1-304`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-304.md).
Regenerate L1-304.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-304-001 Semi-Empirical Quantum Chemistry (AM1, PM6, DFTB, xTB) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554114,
  "chain_hash": "0x7c26b92831516ade7766f5e9090df0136f213203573091666787806fcfea6cc2",
  "chain_tx_hash": "0xbe564926d5d03d4f5a7299f3dd8ef5cbda7dbd66be0e2d57d7493b86f5136310",
  "domain": "Computational Chemistry",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "energy_error_mHa",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "energy_error_mHa",
    "regime": "Well-posed once parameterized; out-of-domain systems fail silently.",
    "secondary": "geometry_RMSD_A"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Computational Chemistry",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "E.parameterized_fock",
      "O.iter",
      "O.observables"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "property_benchmark",
    "solution_space": "semi_empirical_wavefunction",
    "sub_domain": "Parameterized approximate QM",
    "title": "Semi-Empirical Quantum Chemistry (AM1, PM6, DFTB, xTB)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "semiempirical_forward"
    ],
    "allowed_omega_dimensions": [
      "N_atoms",
      "method",
      "N_basis",
      "dispersion"
    ],
    "allowed_problem_classes": [
      "semiempirical_qc"
    ],
    "center_spec": {
      "epsilon_fn_center": "E error \u003c= 3 mHa (~2 kcal/mol)",
      "forward_operator": "semiempirical_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_atoms": 100,
        "N_basis": 500,
        "dispersion": "D4",
        "method": "GFN2-xTB"
      },
      "problem_class": "semiempirical_qc"
    },
    "epsilon_bounds": {
      "energy_error_mHa": [
        1.0,
        50
      ]
    },
    "omega_bounds": {
      "N_atoms": [
        2,
        100000
      ],
      "N_basis": [
        10,
        500000
      ],
      "method": [
        "AM1",
        "PM6",
        "PM7",
        "DFTB3",
        "GFN1-xTB",
        "GFN2-xTB"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Parameterized approximate QM",
  "title": "Semi-Empirical Quantum Chemistry (AM1, PM6, DFTB, xTB)"
}

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