L1 ⚛ L1-344 ⊙ Testnet

Vlasov Equation — collisionless kinetic plasma

Plasma Physics · 6D phase-space Vlasov-Poisson

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⬇ L1-344.md

# ⚛ L1 Principle — Vlasov Equation — collisionless kinetic plasma **ID:** `L1-344` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Plasma Physics — *6D phase-space Vlasov-Poisson* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** distribution function 6D > **📡 Carrier:** plasma · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554095 --- ## 🧠 1. Introduction **Vlasov Equation — collisionless kinetic plasma** is a **linear inverse problem** whose unknown lives in **distribution function 6D** space, within the **6D phase-space Vlasov-Poisson** sub-domain of **Plasma Physics**. Measurements consist of plasma particle and field diagnostics via a **faraday cup lif** sensing mechanism. The forward operator applies, in order: L · distribution f operator; L · advect phase space operator; L · poisson coupling operator; int · phase space operator. Observations are corrupted by additive Gaussian noise. 6D phase space + time = enormous compute requirements; filamentation common. ## ⚙ 2. Forward Model Physical chain: **x** → L · distribution f → L · advect phase space → L · poisson coupling → int · phase space → **y** (detector). ``` y = `int.phase_space` `L.poisson_coupling` `L.advect_phase_space` `L.distribution_f` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.distribution_f` | L · distribution f operator | | `L.advect_phase_space` | L · advect phase space operator | | `L.poisson_coupling` | L · poisson coupling operator | | `int.phase_space` | Int · phase space operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Plasma Physics | | Sub domain | 6D phase-space Vlasov-Poisson | | Carrier | plasma | | Problem class | linear_inverse | | Solution space | distribution_function_6D | | Noise model | gaussian | | Integration axis | phase_space | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model 6D phase space + time = enormous compute requirements; filamentation common. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `vlasov` · **Forward operator:** `vlasov_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N v | — | 64 | | N x | — | 64 | | Snr db | dB | 25 | | N times | — | 500 | | Initial f error | — | 0 | | Electric field error | — | 0 | | Grid phase space error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N v | — | 16 – 2048 | | N x | — | 16 – 2048 | | Snr db | dB | 0 – 40 | | N times | — | 50 – 100000 | | Initial f error | — | 0.0 – 0.3 | | Electric field error | — | 0.0 – 0.2 | | Grid phase space error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 17.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1200` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x30b20f532e5028d4e4138b312a504f25139769f09d61a5e61197cc75b405129b` - **Chain tx hash:** `0x66515ba6cca2e4be7aa6febcf0b17672879f4926b045904711097201019706c4` - **Chain block:** `41554095` --- ## File Mapping This bundle consists of: `L1-344.md`, `L1-344.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-344.md` | Source of truth — edit this | Human or LLM | | `L1-344.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 `L1-344`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-344.md).
Regenerate L1-344.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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📋 JSON metadata

{
  "artifact_id": "L1-344",
  "chain_block": 41554095,
  "chain_hash": "0x30b20f532e5028d4e4138b312a504f25139769f09d61a5e61197cc75b405129b",
  "chain_tx_hash": "0x66515ba6cca2e4be7aa6febcf0b17672879f4926b045904711097201019706c4",
  "domain": "Plasma Physics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 1200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "6D phase space + time = enormous compute requirements; filamentation common.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "plasma",
    "difficulty_delta": 10,
    "domain": "Plasma Physics",
    "integration_axis": "phase_space",
    "noise_model": "gaussian",
    "primitives": [
      "L.distribution_f",
      "L.advect_phase_space",
      "L.poisson_coupling",
      "int.phase_space"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "faraday_cup_lif",
    "solution_space": "distribution_function_6D",
    "sub_domain": "6D phase-space Vlasov-Poisson",
    "title": "Vlasov Equation \u2014 collisionless kinetic plasma"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "vlasov_forward"
    ],
    "allowed_omega_dimensions": [
      "N_x",
      "N_v",
      "N_times",
      "SNR_dB",
      "grid_phase_space_error",
      "electric_field_error",
      "initial_f_error",
      "grid_phase_space_error",
      "electric_field_error",
      "initial_f_error"
    ],
    "allowed_problem_classes": [
      "vlasov"
    ],
    "center_spec": {
      "epsilon_fn_center": "17.0",
      "forward_operator": "vlasov_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_times": 500,
        "N_v": 64,
        "N_x": 64,
        "SNR_dB": 25,
        "electric_field_error": 0.0,
        "grid_phase_space_error": 0.0,
        "initial_f_error": 0.0
      },
      "problem_class": "vlasov"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_times": [
        50,
        100000
      ],
      "N_v": [
        16,
        2048
      ],
      "N_x": [
        16,
        2048
      ],
      "SNR_dB": [
        0,
        40
      ],
      "electric_field_error": [
        0.0,
        0.2
      ],
      "grid_phase_space_error": [
        0.0,
        0.2
      ],
      "initial_f_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "6D phase-space Vlasov-Poisson",
  "title": "Vlasov Equation \u2014 collisionless kinetic plasma"
}

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