L1 ⚛ L1-298 ⊙ Testnet

Ab Initio Molecular Dynamics (Car-Parrinello / BOMD)

Computational Chemistry · On-the-fly DFT forces in MD

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⬇ L1-298.md

# ⚛ L1 Principle — Ab Initio Molecular Dynamics (Car-Parrinello / BOMD) **ID:** `L1-298` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Chemistry — *On-the-fly DFT forces in MD* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** atomic trajectory plus orbitals > **📡 Carrier:** electron · **🌫 Noise:** thermal langevin > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554113 --- ## 🧠 1. Introduction **Ab Initio Molecular Dynamics (Car-Parrinello / BOMD)** is a **nonlinear inverse problem** whose unknown lives in **atomic trajectory plus orbitals** space, within the **On-the-fly DFT forces in MD** sub-domain of **Computational Chemistry**. Measurements consist of electrons collected by an electron detector via a **trajectory observable** sensing mechanism. The forward operator applies, in order: E · dft forces operator; D · time · symplectic operator; O · trajectory operator. Observations are corrupted by Langevin-type thermal fluctuations. Well-posed locally; ergodic sampling requires long trajectories; DFT error propagates. ## ⚙ 2. Forward Model Physical chain: **x** → E · dft forces → D · time · symplectic → O · trajectory → **y** (detector). ``` y = `O.trajectory` `D.time.symplectic` `E.dft_forces` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.dft_forces` | E · dft forces operator | | `D.time.symplectic` | D · time · symplectic operator | | `O.trajectory` | O · trajectory operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Chemistry | | Sub domain | On-the-fly DFT forces in MD | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | atomic_trajectory_plus_orbitals | | Noise model | thermal_langevin | | Integration axis | time | | Difficulty delta | 10 | | L dag | 3.7 | ## 📡 4. Measurement Model Well-posed locally; ergodic sampling requires long trajectories; DFT error propagates. | Metric | Value | |---|---| | Metric | diffusion_coeff_relative_error | | Secondary | rdf_L2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `ab_initio_md` · **Forward operator:** `aimd_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Xc | — | PBE | | T k | — | 300 | | Dt fs | — | 0.5 | | N atoms | — | 64 | | N steps | — | 10000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Xc | — | LDA, PBE, B3LYP | | T k | — | 4 – 5000 | | Dt fs | — | 0.01 – 5 | | N atoms | — | 8 – 10000 | | N steps | — | 1000 – 10000000.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** D rel error <= 0.05 | Metric | Range | |---|---| | Diffusion coeff relative error | 0.02 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **diffusion_coeff_relative_error**, with κ = `1500` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x098f7fc316e02a630384a7ffa9fa8d90623f88dc6586d2192161c9b6feb66ef1` - **Chain tx hash:** `0xddbabc4b25ae2e56bc698b5abe8d705a56abbc12116c8a3f3bcf976f53e2be0d` - **Chain block:** `41554113` --- ## File Mapping This bundle consists of: `L1-298.md`, `L1-298.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-298.md` | Source of truth — edit this | Human or LLM | | `L1-298.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 `L1-298`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-298.md).
Regenerate L1-298.json so every field matches the Markdown.
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L2-298-001 Ab Initio Molecular Dynamics (Car-Parrinello / BOMD) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-298",
  "chain_block": 41554113,
  "chain_hash": "0x098f7fc316e02a630384a7ffa9fa8d90623f88dc6586d2192161c9b6feb66ef1",
  "chain_tx_hash": "0xddbabc4b25ae2e56bc698b5abe8d705a56abbc12116c8a3f3bcf976f53e2be0d",
  "domain": "Computational Chemistry",
  "hardness_fn": {
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    "kappa": 1500,
    "metric": "diffusion_coeff_relative_error",
    "type": "epsilon_fn"
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "diffusion_coeff_relative_error",
    "regime": "Well-posed locally; ergodic sampling requires long trajectories; DFT error propagates.",
    "secondary": "rdf_L2"
  },
  "physics_fingerprint": {
    "L_DAG": 3.7,
    "carrier": "electron",
    "difficulty_delta": 10,
    "domain": "Computational Chemistry",
    "integration_axis": "time",
    "noise_model": "thermal_langevin",
    "primitives": [
      "E.dft_forces",
      "D.time.symplectic",
      "O.trajectory"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "trajectory_observable",
    "solution_space": "atomic_trajectory_plus_orbitals",
    "sub_domain": "On-the-fly DFT forces in MD",
    "title": "Ab Initio Molecular Dynamics (Car-Parrinello / BOMD)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "aimd_forward"
    ],
    "allowed_omega_dimensions": [
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      "T_K",
      "N_steps",
      "dt_fs",
      "xc"
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    "allowed_problem_classes": [
      "ab_initio_md"
    ],
    "center_spec": {
      "epsilon_fn_center": "D rel error \u003c= 0.05",
      "forward_operator": "aimd_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_steps": 10000,
        "T_K": 300,
        "dt_fs": 0.5,
        "xc": "PBE"
      },
      "problem_class": "ab_initio_md"
    },
    "epsilon_bounds": {
      "diffusion_coeff_relative_error": [
        0.02,
        0.5
      ]
    },
    "omega_bounds": {
      "N_atoms": [
        8,
        10000
      ],
      "N_steps": [
        1000,
        10000000.0
      ],
      "T_K": [
        4,
        5000
      ],
      "dt_fs": [
        0.01,
        5
      ],
      "xc": [
        "LDA",
        "PBE",
        "B3LYP"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "On-the-fly DFT forces in MD",
  "title": "Ab Initio Molecular Dynamics (Car-Parrinello / BOMD)"
}

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