L1 ⚛ L1-199 ⊙ Testnet

Radiative Transfer Equation — radiative heat exchange

Heat Transfer · RTE inversion for surface emissivity / participating media

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⬇ L1-199.md

# ⚛ L1 Principle — Radiative Transfer Equation — radiative heat exchange **ID:** `L1-199` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Heat Transfer — *RTE inversion for surface emissivity / participating media* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D radiance field spectral > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554034 --- ## 🧠 1. Introduction **Radiative Transfer Equation — radiative heat exchange** is a **linear inverse problem** whose unknown lives in **3D radiance field spectral** space, within the **RTE inversion for surface emissivity / participating media** sub-domain of **Heat Transfer**. Measurements consist of thermal radiation / temperature measurements via a **ir spectroradiometer** sensing mechanism. The forward operator applies, in order: isotropic point-source emission model; L · absorb scatter operator; L · surface reflect operator; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Volume RTE becomes ill-posed for optically thick media; well-posed for optically thin. ## ⚙ 2. Forward Model Physical chain: **x** → Source emission → L · absorb scatter → L · surface reflect → Spectral integration → **y** (detector). ``` y = Σ_λ `L.surface_reflect` `L.absorb_scatter` δ_source x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.source_emit` | Isotropic point-source emission model | | `L.absorb_scatter` | L · absorb scatter operator | | `L.surface_reflect` | L · surface reflect operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Heat Transfer | | Sub domain | RTE inversion for surface emissivity / participating media | | Carrier | thermal | | Problem class | linear_inverse | | Solution space | 3D_radiance_field_spectral | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Volume RTE becomes ill-posed for optically thick media; well-posed for optically thin. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `rte` · **Forward operator:** `rte_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 | | N dirs | — | 16 | | Snr db | dB | 30 | | N freqs | — | 16 | | Kappa error | — | 0 | | Emissivity error | — | 0 | | Phase function error | — | 0 | | Scatter albedo error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 8 – 256 | | N dirs | — | 1 – 256 | | Snr db | dB | 0 – 40 | | N freqs | — | 1 – 256 | | Kappa error | — | 0.0 – 0.1 | | Emissivity error | — | 0.0 – 0.3 | | Phase function error | — | 0.0 – 0.3 | | Scatter albedo error | — | 0.0 – 0.3 | ## 🎯 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 = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x697e60188454474c9e570631c22778318398976c10ae7b6215f774f82aff924b` - **Chain tx hash:** `0x37198c0141c7f2396c52d44dd987daee9f5874d68798ade54dadc3828a2683bf` - **Chain block:** `41554034` --- ## File Mapping This bundle consists of: `L1-199.md`, `L1-199.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-199.md` | Source of truth — edit this | Human or LLM | | `L1-199.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 `L1-199`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-199.md).
Regenerate L1-199.json so every field matches the Markdown.
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L2-199-001 Radiative Transfer Equation — radiative heat exchange Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-199",
  "chain_block": 41554034,
  "chain_hash": "0x697e60188454474c9e570631c22778318398976c10ae7b6215f774f82aff924b",
  "chain_tx_hash": "0x37198c0141c7f2396c52d44dd987daee9f5874d68798ade54dadc3828a2683bf",
  "domain": "Heat Transfer",
  "hardness_fn": {
    "delta": 5,
    "kappa": 600,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Volume RTE becomes ill-posed for optically thick media; well-posed for optically thin.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "thermal",
    "difficulty_delta": 5,
    "domain": "Heat Transfer",
    "integration_axis": "spectral",
    "noise_model": "gaussian",
    "primitives": [
      "L.source_emit",
      "L.absorb_scatter",
      "L.surface_reflect",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "ir_spectroradiometer",
    "solution_space": "3D_radiance_field_spectral",
    "sub_domain": "RTE inversion for surface emissivity / participating media",
    "title": "Radiative Transfer Equation \u2014 radiative heat exchange"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "W",
      "Z",
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      "N_dirs",
      "SNR_dB",
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      "emissivity_error",
      "phase_function_error",
      "kappa_error",
      "scatter_albedo_error",
      "emissivity_error",
      "phase_function_error"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
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      "forward_operator": "rte_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_dirs": 16,
        "N_freqs": 16,
        "SNR_dB": 30,
        "W": 128,
        "Z": 32,
        "emissivity_error": 0.0,
        "kappa_error": 0.0,
        "phase_function_error": 0.0,
        "scatter_albedo_error": 0.0
      },
      "problem_class": "rte"
    },
    "epsilon_bounds": {
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        45.0
      ]
    },
    "omega_bounds": {
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        1024
      ],
      "N_dirs": [
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        256
      ],
      "N_freqs": [
        1,
        256
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        8,
        256
      ],
      "emissivity_error": [
        0.0,
        0.3
      ],
      "kappa_error": [
        0.0,
        0.1
      ],
      "phase_function_error": [
        0.0,
        0.3
      ],
      "scatter_albedo_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "RTE inversion for surface emissivity / participating media",
  "title": "Radiative Transfer Equation \u2014 radiative heat exchange"
}

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