L1 ⚛ L1-349 ⊙ Testnet

MHD Stability — linear eigenmode growth rates

Plasma Physics · Tokamak/stellarator linear stability

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⬇ L1-349.md

# ⚛ L1 Principle — MHD Stability — linear eigenmode growth rates **ID:** `L1-349` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Plasma Physics — *Tokamak/stellarator linear stability* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** mode growth rates > **📡 Carrier:** plasma · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554096 --- ## 🧠 1. Introduction **MHD Stability — linear eigenmode growth rates** is a **linear inverse problem** whose unknown lives in **mode growth rates** space, within the **Tokamak/stellarator linear stability** sub-domain of **Plasma Physics**. Measurements consist of plasma particle and field diagnostics via a **magnetics fluctuations** sensing mechanism. The forward operator applies, in order: L · linearize mhd operator; L · eigenvalue operator; L · mode classify operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · linearize mhd → L · eigenvalue → L · mode classify → Frequency integration → **y** (detector). ``` y = ∫dω `L.mode_classify` `L.eigenvalue` `L.linearize_mhd` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.linearize_mhd` | L · linearize mhd operator | | `L.eigenvalue` | L · eigenvalue operator | | `L.mode_classify` | L · mode classify operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Plasma Physics | | Sub domain | Tokamak/stellarator linear stability | | Carrier | plasma | | Problem class | linear_inverse | | Solution space | mode_growth_rates | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 5 | | L dag | 3 | ## 📡 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:** `mhd_stability` · **Forward operator:** `mhd_stability_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N modes | — | 20 | | N radial | — | 64 | | Rotation error | — | 0 | | Equilibrium error | — | 0 | | Pressure profile error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N modes | — | 1 – 200 | | N radial | — | 16 – 1024 | | Rotation error | — | 0.0 – 0.3 | | Equilibrium error | — | 0.0 – 0.1 | | Pressure profile error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xdc12de2a17fb3c52f900c1b3dcb95e0478b4e223d0ef25418fbd5b55ed9f43a3` - **Chain tx hash:** `0x648e8509678c982db94b0b419d18ed974feb98f15215bf249230ddfa95acd87b` - **Chain block:** `41554096` --- ## File Mapping This bundle consists of: `L1-349.md`, `L1-349.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-349.md` | Source of truth — edit this | Human or LLM | | `L1-349.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 `L1-349`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-349.md).
Regenerate L1-349.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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L2-349-001 MHD Stability — linear eigenmode growth rates Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-349",
  "chain_block": 41554096,
  "chain_hash": "0xdc12de2a17fb3c52f900c1b3dcb95e0478b4e223d0ef25418fbd5b55ed9f43a3",
  "chain_tx_hash": "0x648e8509678c982db94b0b419d18ed974feb98f15215bf249230ddfa95acd87b",
  "domain": "Plasma Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "plasma",
    "difficulty_delta": 5,
    "domain": "Plasma Physics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.linearize_mhd",
      "L.eigenvalue",
      "L.mode_classify",
      "int.frequency"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "magnetics_fluctuations",
    "solution_space": "mode_growth_rates",
    "sub_domain": "Tokamak/stellarator linear stability",
    "title": "MHD Stability \u2014 linear eigenmode growth rates"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mhd_stability_forward"
    ],
    "allowed_omega_dimensions": [
      "N_modes",
      "N_radial",
      "SNR_dB",
      "equilibrium_error",
      "rotation_error",
      "pressure_profile_error",
      "equilibrium_error",
      "rotation_error",
      "pressure_profile_error"
    ],
    "allowed_problem_classes": [
      "mhd_stability"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "mhd_stability_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_modes": 20,
        "N_radial": 64,
        "SNR_dB": 25,
        "equilibrium_error": 0.0,
        "pressure_profile_error": 0.0,
        "rotation_error": 0.0
      },
      "problem_class": "mhd_stability"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_modes": [
        1,
        200
      ],
      "N_radial": [
        16,
        1024
      ],
      "SNR_dB": [
        0,
        40
      ],
      "equilibrium_error": [
        0.0,
        0.1
      ],
      "pressure_profile_error": [
        0.0,
        0.2
      ],
      "rotation_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Tokamak/stellarator linear stability",
  "title": "MHD Stability \u2014 linear eigenmode growth rates"
}

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