L1 ⚛ L1-344 ⊙ Testnet

Vlasov Equation — collisionless kinetic plasma

Plasma Physics · 6D phase-space Vlasov-Poisson

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⬇ principle.md ⬇ principle.json

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⬇ L1-344.md ⬇ L1-344.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-344 (Vlasov Equation — collisionless kinetic plasma) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-344.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-344.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 = `int.phase_space` `L.poisson_coupling` `L.advect_phase_space` `L.distribution_f` x + n,    n ~ 𝒩(0, σ²)

world state x (distribution function 6D)

→

L · distribution f `L.distribution_f`

→

L · advect phase space `L.advect_phase_space`

→

L · poisson coupling `L.poisson_coupling`

→

int · phase space `int.phase_space`

→

observation y (plasma detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ 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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📋 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"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "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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