L1 ⚛ L1-348 ⊙ Testnet

Grad-Shafranov — tokamak equilibrium

Plasma Physics · Tokamak 2D magnetostatic equilibrium

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⬇ L1-348.md

# ⚛ L1 Principle — Grad-Shafranov — tokamak equilibrium **ID:** `L1-348` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Plasma Physics — *Tokamak 2D magnetostatic equilibrium* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** poloidal flux function > **📡 Carrier:** plasma · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554095 --- ## 🧠 1. Introduction **Grad-Shafranov — tokamak equilibrium** is a **nonlinear inverse problem** whose unknown lives in **poloidal flux function** space, within the **Tokamak 2D magnetostatic equilibrium** sub-domain of **Plasma Physics**. Measurements consist of plasma particle and field diagnostics via a **magnetics mse thomson** sensing mechanism. The forward operator applies, in order: L · gs elliptic operator; L · pressure profile operator; L · current profile operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · gs elliptic → L · pressure profile → L · current profile → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.current_profile` `L.pressure_profile` `L.gs_elliptic` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.gs_elliptic` | L · gs elliptic operator | | `L.pressure_profile` | L · pressure profile operator | | `L.current_profile` | L · current profile operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Plasma Physics | | Sub domain | Tokamak 2D magnetostatic equilibrium | | Carrier | plasma | | Problem class | nonlinear_inverse | | Solution space | poloidal_flux_function | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 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:** `grad_shafranov` · **Forward operator:** `grad_shafranov_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N r | — | 128 | | N z | — | 128 | | Snr db | dB | 25 | | N magnetics | — | 64 | | Boundary error | — | 0 | | Current prior error | — | 0 | | Pressure prior error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N r | — | 32 – 1024 | | N z | — | 32 – 1024 | | Snr db | dB | 0 – 40 | | N magnetics | — | 8 – 1024 | | Boundary error | — | 0.0 – 0.2 | | Current prior error | — | 0.0 – 0.2 | | Pressure prior error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `440` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4b67628fe974a57d2a607e54abb90c58cdcb89859ff82ae8554fe3ab6268c74a` - **Chain tx hash:** `0x17aa90ca770cfafbf348db74a6c88e3034ab3cbd32f7e202d8cac6068b1c74dd` - **Chain block:** `41554095` --- ## File Mapping This bundle consists of: `L1-348.md`, `L1-348.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-348.md` | Source of truth — edit this | Human or LLM | | `L1-348.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 `L1-348`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-348.md).
Regenerate L1-348.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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L2-348-001 Grad-Shafranov — tokamak equilibrium Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-348",
  "chain_block": 41554095,
  "chain_hash": "0x4b67628fe974a57d2a607e54abb90c58cdcb89859ff82ae8554fe3ab6268c74a",
  "chain_tx_hash": "0x17aa90ca770cfafbf348db74a6c88e3034ab3cbd32f7e202d8cac6068b1c74dd",
  "domain": "Plasma Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 440,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
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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": 3.2,
    "carrier": "plasma",
    "difficulty_delta": 5,
    "domain": "Plasma Physics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.gs_elliptic",
      "L.pressure_profile",
      "L.current_profile",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "magnetics_mse_thomson",
    "solution_space": "poloidal_flux_function",
    "sub_domain": "Tokamak 2D magnetostatic equilibrium",
    "title": "Grad-Shafranov \u2014 tokamak equilibrium"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "grad_shafranov_forward"
    ],
    "allowed_omega_dimensions": [
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      "N_Z",
      "N_magnetics",
      "SNR_dB",
      "pressure_prior_error",
      "current_prior_error",
      "boundary_error",
      "pressure_prior_error",
      "current_prior_error",
      "boundary_error"
    ],
    "allowed_problem_classes": [
      "grad_shafranov"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "grad_shafranov_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_R": 128,
        "N_Z": 128,
        "N_magnetics": 64,
        "SNR_dB": 25,
        "boundary_error": 0.0,
        "current_prior_error": 0.0,
        "pressure_prior_error": 0.0
      },
      "problem_class": "grad_shafranov"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_R": [
        32,
        1024
      ],
      "N_Z": [
        32,
        1024
      ],
      "N_magnetics": [
        8,
        1024
      ],
      "SNR_dB": [
        0,
        40
      ],
      "boundary_error": [
        0.0,
        0.2
      ],
      "current_prior_error": [
        0.0,
        0.2
      ],
      "pressure_prior_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Tokamak 2D magnetostatic equilibrium",
  "title": "Grad-Shafranov \u2014 tokamak equilibrium"
}

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