L1 ⚛ L1-107 ⊙ Testnet

Passive Microwave Radiometry

Remote Sensing · Thermal brightness satellite radiometry

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⬇ L1-107.md

# ⚛ L1 Principle — Passive Microwave Radiometry **ID:** `L1-107` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Thermal brightness satellite radiometry* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D brightness temperature > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554198 --- ## 🧠 1. Introduction **Passive Microwave Radiometry** is a **linear inverse problem** whose unknown lives in **2D brightness temperature** space, within the **Thermal brightness satellite radiometry** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **microwave radiometry** sensing mechanism. The forward operator applies, in order: L · radiometer operator; L · antenna pattern operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D brightness temperature is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 7); antenna_sidelobe dominates the stability cliff; land_contamination and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · radiometer → L · antenna pattern → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.antenna_pattern` `L.radiometer` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.radiometer` | L · radiometer operator | | `L.antenna_pattern` | L · antenna pattern operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Thermal brightness satellite radiometry | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | 2D_brightness_temperature | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 2.7 | ## 📡 4. Measurement Model Existence of the recovered 2D brightness temperature is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 7); antenna_sidelobe dominates the stability cliff; land_contamination and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `passive_microwave` · **Forward operator:** `passive_microwave_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1440 | | W | px | 720 | | Rfi | — | 0 | | F ghz | GHz | 19 | | Snr db | dB | 35 | | N channels | — | 12 | | Antenna sidelobe | — | 0.01 | | Land contamination | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 4096 | | W | px | 128 – 4096 | | Rfi | — | 0.0 – 0.5 | | F ghz | GHz | 1 – 300 | | Snr db | dB | 15.0 – 45.0 | | N channels | — | 2 – 30 | | Antenna sidelobe | — | 0.0 – 0.05 | | Land contamination | — | 0.0 – 0.5 | | Surface emissivity uncertainty | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `140` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x04c062d3bb4edd3977b5c7a40ee67915733091a3caf4df796ae1fb37d0a2a3dd` - **Chain tx hash:** `0x3e038aa2c9eb426a13aae60ea001e28fad5a06981010aad9dbfe044d4a283c9c` - **Chain block:** `41554198` --- ## File Mapping This bundle consists of: `L1-107.md`, `L1-107.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-107.md` | Source of truth — edit this | Human or LLM | | `L1-107.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 `L1-107`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-107.md).
Regenerate L1-107.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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L2-107-001 Passive Microwave Radiometry Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Remote Sensing",
  "hardness_fn": {
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    "regime": "Existence of the recovered 2D brightness temperature is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 7); antenna_sidelobe dominates the stability cliff; land_contamination and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
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    "carrier": "radio_wave",
    "difficulty_delta": 3,
    "domain": "Remote Sensing",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
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      "L.antenna_pattern",
      "int.temporal"
    ],
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    "sensing_mechanism": "microwave_radiometry",
    "solution_space": "2D_brightness_temperature",
    "sub_domain": "Thermal brightness satellite radiometry",
    "title": "Passive Microwave Radiometry"
  },
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      "RFI",
      "antenna_sidelobe",
      "land_contamination",
      "RFI",
      "surface_emissivity_uncertainty"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "28.0",
      "forward_operator": "passive_microwave_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_channels": 12,
        "RFI": 0.0,
        "SNR_dB": 35.0,
        "W": 720,
        "antenna_sidelobe": 0.01,
        "f_GHz": 19,
        "land_contamination": 0.0
      },
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        30
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      "RFI": [
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        0.5
      ],
      "SNR_dB": [
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        45.0
      ],
      "W": [
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        4096
      ],
      "antenna_sidelobe": [
        0.0,
        0.05
      ],
      "f_GHz": [
        1,
        300
      ],
      "land_contamination": [
        0.0,
        0.5
      ],
      "surface_emissivity_uncertainty": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Thermal brightness satellite radiometry",
  "title": "Passive Microwave Radiometry"
}

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