L1 ⚛ L1-350 ⊙ Testnet

Plasma Sheath — Debye-scale boundary layer

Plasma Physics · Plasma-wall sheath region

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Markdown — human-readable source of truth

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⬇ L1-350.md

# ⚛ L1 Principle — Plasma Sheath — Debye-scale boundary layer **ID:** `L1-350` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Plasma Physics — *Plasma-wall sheath region* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** potential density sheath > **📡 Carrier:** plasma · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554096 --- ## 🧠 1. Introduction **Plasma Sheath — Debye-scale boundary layer** is a **linear inverse problem** whose unknown lives in **potential density sheath** space, within the **Plasma-wall sheath region** sub-domain of **Plasma Physics**. Measurements consist of plasma particle and field diagnostics via a **langmuir probe** sensing mechanism. The forward operator applies, in order: L · poisson operator; L · fluid ion operator; L · boltzmann electron 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 · poisson → L · fluid ion → L · boltzmann electron → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.boltzmann_electron` `L.fluid_ion` `L.poisson` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.poisson` | L · poisson operator | | `L.fluid_ion` | L · fluid ion operator | | `L.boltzmann_electron` | L · boltzmann electron operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Plasma Physics | | Sub domain | Plasma-wall sheath region | | Carrier | plasma | | Problem class | linear_inverse | | Solution space | potential_density_sheath | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | 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:** `sheath` · **Forward operator:** `sheath_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N z | — | 128 | | Snr db | dB | 30 | | Boundary error | — | 0 | | Electron temp error | — | 0 | | Bohm criterion error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N z | — | 32 – 4096 | | Snr db | dB | 0 – 40 | | Boundary error | — | 0.0 – 0.2 | | Electron temp error | — | 0.0 – 0.1 | | Bohm criterion 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 = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7862b542e53c593030b5c781933863bbaff726966854a3914de1be8a0cc85c4a` - **Chain tx hash:** `0x63de17a4d2f14d406ff36a593472e98ff744ed300600bfc476602987e7e6061e` - **Chain block:** `41554096` --- ## File Mapping This bundle consists of: `L1-350.md`, `L1-350.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-350.md` | Source of truth — edit this | Human or LLM | | `L1-350.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 `L1-350`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-350.md).
Regenerate L1-350.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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L2-350-001 Plasma Sheath — Debye-scale boundary layer Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-350",
  "chain_block": 41554096,
  "chain_hash": "0x7862b542e53c593030b5c781933863bbaff726966854a3914de1be8a0cc85c4a",
  "chain_tx_hash": "0x63de17a4d2f14d406ff36a593472e98ff744ed300600bfc476602987e7e6061e",
  "domain": "Plasma Physics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "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": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "plasma",
    "difficulty_delta": 3,
    "domain": "Plasma Physics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.poisson",
      "L.fluid_ion",
      "L.boltzmann_electron",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "langmuir_probe",
    "solution_space": "potential_density_sheath",
    "sub_domain": "Plasma-wall sheath region",
    "title": "Plasma Sheath \u2014 Debye-scale boundary layer"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "sheath_forward"
    ],
    "allowed_omega_dimensions": [
      "N_z",
      "SNR_dB",
      "boundary_error",
      "electron_temp_error",
      "bohm_criterion_error",
      "boundary_error",
      "electron_temp_error",
      "bohm_criterion_error"
    ],
    "allowed_problem_classes": [
      "sheath"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "sheath_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_z": 128,
        "SNR_dB": 30,
        "bohm_criterion_error": 0.0,
        "boundary_error": 0.0,
        "electron_temp_error": 0.0
      },
      "problem_class": "sheath"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_z": [
        32,
        4096
      ],
      "SNR_dB": [
        0,
        40
      ],
      "bohm_criterion_error": [
        0.0,
        0.2
      ],
      "boundary_error": [
        0.0,
        0.2
      ],
      "electron_temp_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Plasma-wall sheath region",
  "title": "Plasma Sheath \u2014 Debye-scale boundary layer"
}

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