L1 ⚛ L1-200 ⊙ Testnet

Participating Media — RTE with gas/soot emission-absorption

Heat Transfer · Line-by-line gas spectroscopy + soot radiation

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⬇ L1-200.md

# ⚛ L1 Principle — Participating Media — RTE with gas/soot emission-absorption **ID:** `L1-200` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *Line-by-line gas spectroscopy + soot radiation* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D soot concentration and temp > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034 --- ## 🧠 1. Introduction **Participating Media — RTE with gas/soot emission-absorption** is a **nonlinear inverse problem** whose unknown lives in **3D soot concentration and temp** space, within the **Line-by-line gas spectroscopy + soot radiation** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **multispectral pyrometer** sensing mechanism. The forward operator applies, in order: L · gas absorb operator; L · soot emit operator; L · line by line operator; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · gas absorb → L · soot emit → L · line by line → Spectral integration → **y** (detector). ``` y = Σ_λ `L.line_by_line` `L.soot_emit` `L.gas_absorb` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.gas_absorb` | L · gas absorb operator | | `L.soot_emit` | L · soot emit operator | | `L.line_by_line` | L · line by line operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | Line-by-line gas spectroscopy + soot radiation | | Carrier | thermal | | Problem class | nonlinear_inverse | | Solution space | 3D_soot_concentration_and_temp | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 5 | | L dag | 3.7 | ## 📡 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:** `participating_media` · **Forward operator:** `participating_media_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 | | Snr db | dB | 30 | | N freqs | — | 32 | | N species | — | 4 | | Gas conc error | — | 0 | | T nonuniformity | — | 0 | | Band model error | — | 0 | | Soot index error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 8 – 256 | | Snr db | dB | 0 – 40 | | N freqs | — | 4 – 1024 | | N species | — | 1 – 20 | | Gas conc error | — | 0.0 – 0.2 | | T nonuniformity | — | 0.0 – 0.3 | | Band model error | — | 0.0 – 0.2 | | Soot index error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | 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:** `0x05baf99467fc03a6446d5b0f15ddcb519c4f23c94754a4d2d78ced4c41f7a9ce` - **Chain tx hash:** `0xd41fabba8faaa5072f72587e28bc8c12d851c9770b915b04eed21833f66d16e2` - **Chain block:** `41554034` --- ## File Mapping This bundle consists of: `L1-200.md`, `L1-200.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-200.md` | Source of truth — edit this | Human or LLM | | `L1-200.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 `L1-200`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-200.md).
Regenerate L1-200.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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L2-200-001 Participating Media — RTE with gas/soot emission-absorption Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-200",
  "chain_block": 41554034,
  "chain_hash": "0x05baf99467fc03a6446d5b0f15ddcb519c4f23c94754a4d2d78ced4c41f7a9ce",
  "chain_tx_hash": "0xd41fabba8faaa5072f72587e28bc8c12d851c9770b915b04eed21833f66d16e2",
  "domain": "Heat Transfer",
  "hardness_fn": {
    "delta": 5,
    "kappa": 700,
    "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": 3.7,
    "carrier": "thermal",
    "difficulty_delta": 5,
    "domain": "Heat Transfer",
    "integration_axis": "spectral",
    "noise_model": "gaussian",
    "primitives": [
      "L.gas_absorb",
      "L.soot_emit",
      "L.line_by_line",
      "int.spectral"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "multispectral_pyrometer",
    "solution_space": "3D_soot_concentration_and_temp",
    "sub_domain": "Line-by-line gas spectroscopy + soot radiation",
    "title": "Participating Media \u2014 RTE with gas/soot emission-absorption"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "participating_media_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_species",
      "N_freqs",
      "SNR_dB",
      "gas_conc_error",
      "T_nonuniformity",
      "soot_index_error",
      "band_model_error",
      "gas_conc_error",
      "T_nonuniformity",
      "soot_index_error",
      "band_model_error"
    ],
    "allowed_problem_classes": [
      "participating_media"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "participating_media_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_freqs": 32,
        "N_species": 4,
        "SNR_dB": 30,
        "T_nonuniformity": 0.0,
        "W": 128,
        "Z": 32,
        "band_model_error": 0.0,
        "gas_conc_error": 0.0,
        "soot_index_error": 0.0
      },
      "problem_class": "participating_media"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "N_freqs": [
        4,
        1024
      ],
      "N_species": [
        1,
        20
      ],
      "SNR_dB": [
        0,
        40
      ],
      "T_nonuniformity": [
        0.0,
        0.3
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        8,
        256
      ],
      "band_model_error": [
        0.0,
        0.2
      ],
      "gas_conc_error": [
        0.0,
        0.2
      ],
      "soot_index_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Line-by-line gas spectroscopy + soot radiation",
  "title": "Participating Media \u2014 RTE with gas/soot emission-absorption"
}

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