L1 ⚛ L1-342 ⊙ Testnet

Ideal MHD — magnetohydrodynamics infinite-conductivity limit

Plasma Physics · Ideal MHD plasma simulation

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⬇ L1-342.md

# ⚛ L1 Principle — Ideal MHD — magnetohydrodynamics infinite-conductivity limit **ID:** `L1-342` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Plasma Physics — *Ideal MHD plasma simulation* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** plasma B u rho T spacetime > **📡 Carrier:** plasma · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554081 --- ## 🧠 1. Introduction **Ideal MHD — magnetohydrodynamics infinite-conductivity limit** is a **linear inverse problem** whose unknown lives in **plasma B u rho T spacetime** space, within the **Ideal MHD plasma simulation** sub-domain of **Plasma Physics**. Measurements consist of plasma particle and field diagnostics via a **langmuir probe bdotfield** sensing mechanism. The forward operator applies, in order: mass-balance: ∂_t ρ + ∇·(ρv) = 0; L · momentum lorentz operator; L · induction operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → Continuity equation → L · momentum lorentz → L · induction → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.induction` `L.momentum_lorentz` ∂_t ρ + ∇·(ρv) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.continuity` | Mass-balance: ∂_t ρ + ∇·(ρv) = 0 | | `L.momentum_lorentz` | L · momentum lorentz operator | | `L.induction` | L · induction operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Plasma Physics | | Sub domain | Ideal MHD plasma simulation | | Carrier | plasma | | Problem class | linear_inverse | | Solution space | plasma_B_u_rho_T_spacetime | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `ideal_mhd` · **Forward operator:** `ideal_mhd_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 25 | | N times | — | 500 | | Bc error | — | 0 | | Rho error | — | 0 | | B field error | — | 0 | | Temperature error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Z | — | 16 – 1024 | | Snr db | dB | 0 – 40 | | N times | — | 50 – 100000 | | Bc error | — | 0.0 – 0.2 | | Rho error | — | 0.0 – 0.2 | | B field error | — | 0.0 – 0.1 | | Temperature error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `700` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x094b240ce49152ed372797943e5a6ff1c785b8bd9e7acc12253e7c2cd57c0749` - **Chain tx hash:** `0x22ee0542582470af5b01ab08c9fa548c2204ad518e0bca8010ed0efabd9a8616` - **Chain block:** `41554081` --- ## File Mapping This bundle consists of: `L1-342.md`, `L1-342.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-342.md` | Source of truth — edit this | Human or LLM | | `L1-342.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 `L1-342`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-342.md).
Regenerate L1-342.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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L2-342-001 Ideal MHD — magnetohydrodynamics infinite-conductivity limit Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554081,
  "chain_hash": "0x094b240ce49152ed372797943e5a6ff1c785b8bd9e7acc12253e7c2cd57c0749",
  "chain_tx_hash": "0x22ee0542582470af5b01ab08c9fa548c2204ad518e0bca8010ed0efabd9a8616",
  "domain": "Plasma Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 700,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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  "observable_profile": {
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    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "plasma",
    "difficulty_delta": 5,
    "domain": "Plasma Physics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.continuity",
      "L.momentum_lorentz",
      "L.induction",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "langmuir_probe_bdotfield",
    "solution_space": "plasma_B_u_rho_T_spacetime",
    "sub_domain": "Ideal MHD plasma simulation",
    "title": "Ideal MHD \u2014 magnetohydrodynamics infinite-conductivity limit"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "W",
      "Z",
      "N_times",
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      "bc_error",
      "B_field_error",
      "rho_error",
      "temperature_error",
      "bc_error"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "ideal_mhd_forward",
      "input_format": "measurement_only",
      "omega": {
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        "H": 256,
        "N_times": 500,
        "SNR_dB": 25,
        "W": 256,
        "Z": 128,
        "bc_error": 0.0,
        "rho_error": 0.0,
        "temperature_error": 0.0
      },
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    "epsilon_bounds": {
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      "B_field_error": [
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        0.1
      ],
      "H": [
        32,
        2048
      ],
      "N_times": [
        50,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "Z": [
        16,
        1024
      ],
      "bc_error": [
        0.0,
        0.2
      ],
      "rho_error": [
        0.0,
        0.2
      ],
      "temperature_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Ideal MHD plasma simulation",
  "title": "Ideal MHD \u2014 magnetohydrodynamics infinite-conductivity limit"
}

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