L1 ⚛ L1-347 ⊙ Testnet

Fokker-Planck — Coulomb-collision kinetic

Plasma Physics · Plasma Coulomb collision operator

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⬇ L1-347.md

# ⚛ L1 Principle — Fokker-Planck — Coulomb-collision kinetic **ID:** `L1-347` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Plasma Physics — *Plasma Coulomb collision operator* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** distribution f with collisions > **📡 Carrier:** plasma · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554095 --- ## 🧠 1. Introduction **Fokker-Planck — Coulomb-collision kinetic** is a **linear inverse problem** whose unknown lives in **distribution f with collisions** space, within the **Plasma Coulomb collision operator** sub-domain of **Plasma Physics**. Measurements consist of plasma particle and field diagnostics via a **thomson scattering fast diagnostics** sensing mechanism. The forward operator applies, in order: L · collision operator operator; L · drift diffusion v operator; L · relaxation operator; int · phase space operator. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · collision operator → L · drift diffusion v → L · relaxation → int · phase space → **y** (detector). ``` y = `int.phase_space` `L.relaxation` `L.drift_diffusion_v` `L.collision_operator` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.collision_operator` | L · collision operator operator | | `L.drift_diffusion_v` | L · drift diffusion v operator | | `L.relaxation` | L · relaxation operator | | `int.phase_space` | Int · phase space operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Plasma Physics | | Sub domain | Plasma Coulomb collision operator | | Carrier | plasma | | Problem class | linear_inverse | | Solution space | distribution_f_with_collisions | | Noise model | gaussian | | Integration axis | phase_space | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 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:** `fokker_planck` · **Forward operator:** `fokker_planck_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N v | — | 128 | | Snr db | dB | 25 | | N times | — | 1000 | | Log lambda error | — | 0 | | Mass ratio error | — | 0 | | Collision freq error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N v | — | 16 – 2048 | | Snr db | dB | 0 – 40 | | N times | — | 50 – 100000 | | Log lambda error | — | 0.0 – 0.1 | | Mass ratio error | — | 0.0 – 0.1 | | Collision freq 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 = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2766624865e2ccec9ad01f38ebf0def6fc2dd97e1b78779a9e4024ba1b1a5b33` - **Chain tx hash:** `0x59d14c6dae81c0f5bb37ea9c0f7813af156903b231b4b87faf613b85d7533627` - **Chain block:** `41554095` --- ## File Mapping This bundle consists of: `L1-347.md`, `L1-347.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-347.md` | Source of truth — edit this | Human or LLM | | `L1-347.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 `L1-347`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-347.md).
Regenerate L1-347.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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L2-347-001 Fokker-Planck — Coulomb-collision kinetic Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-347",
  "chain_block": 41554095,
  "chain_hash": "0x2766624865e2ccec9ad01f38ebf0def6fc2dd97e1b78779a9e4024ba1b1a5b33",
  "chain_tx_hash": "0x59d14c6dae81c0f5bb37ea9c0f7813af156903b231b4b87faf613b85d7533627",
  "domain": "Plasma Physics",
  "hardness_fn": {
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    "kappa": 500,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "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": 3.3,
    "carrier": "plasma",
    "difficulty_delta": 5,
    "domain": "Plasma Physics",
    "integration_axis": "phase_space",
    "noise_model": "gaussian",
    "primitives": [
      "L.collision_operator",
      "L.drift_diffusion_v",
      "L.relaxation",
      "int.phase_space"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "thomson_scattering_fast_diagnostics",
    "solution_space": "distribution_f_with_collisions",
    "sub_domain": "Plasma Coulomb collision operator",
    "title": "Fokker-Planck \u2014 Coulomb-collision kinetic"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fokker_planck_forward"
    ],
    "allowed_omega_dimensions": [
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      "N_times",
      "SNR_dB",
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      "collision_freq_error",
      "log_lambda_error",
      "mass_ratio_error",
      "collision_freq_error"
    ],
    "allowed_problem_classes": [
      "fokker_planck"
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    "center_spec": {
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      "forward_operator": "fokker_planck_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_times": 1000,
        "N_v": 128,
        "SNR_dB": 25,
        "collision_freq_error": 0.0,
        "log_lambda_error": 0.0,
        "mass_ratio_error": 0.0
      },
      "problem_class": "fokker_planck"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_times": [
        50,
        100000
      ],
      "N_v": [
        16,
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      ],
      "SNR_dB": [
        0,
        40
      ],
      "collision_freq_error": [
        0.0,
        0.2
      ],
      "log_lambda_error": [
        0.0,
        0.1
      ],
      "mass_ratio_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Plasma Coulomb collision operator",
  "title": "Fokker-Planck \u2014 Coulomb-collision kinetic"
}

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