L1 ⚛ L1-105 ⊙ Testnet

Doppler Weather Radar

Remote Sensing · Atmospheric Doppler reflectivity + velocity

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Markdown — human-readable source of truth

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⬇ L1-105.md

# ⚛ L1 Principle — Doppler Weather Radar **ID:** `L1-105` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Atmospheric Doppler reflectivity + velocity* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D reflectivity velocity > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554198 --- ## 🧠 1. Introduction **Doppler Weather Radar** is a **linear inverse problem** whose unknown lives in **3D reflectivity velocity** space, within the **Atmospheric Doppler reflectivity + velocity** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **doppler radar** sensing mechanism. The forward operator applies, in order: L · emit · pulse operator; L · volume scatter operator; L · doppler frequency shift operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D reflectivity velocity 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 ~= 9); beam_blockage dominates the stability cliff; AP_propagation 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 · emit · pulse → L · volume scatter → L · doppler frequency shift → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.doppler_frequency_shift` `L.volume_scatter` `L.emit.pulse` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.pulse` | L · emit · pulse operator | | `L.volume_scatter` | L · volume scatter operator | | `L.doppler_frequency_shift` | L · doppler frequency shift operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Atmospheric Doppler reflectivity + velocity | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | 3D_reflectivity_velocity | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Existence of the recovered 3D reflectivity velocity 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 ~= 9); beam_blockage dominates the stability cliff; AP_propagation 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:** `doppler_weather_radar` · **Forward operator:** `doppler_weather_radar_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N az | — | 720 | | N el | — | 12 | | Prf hz | Hz | 1000 | | Snr db | dB | 25 | | N range | — | 500 | | Lambda cm | — | 10 | | Beam blockage | — | 0 | | Ap propagation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N az | — | 180 – 1440 | | N el | — | 1 – 25 | | Prf hz | Hz | 200 – 5000 | | Snr db | dB | 5.0 – 40.0 | | N range | — | 100 – 2000 | | Clutter | — | 0.0 – 0.5 | | Aliasing | — | 0.0 – 0.5 | | Lambda cm | — | 0.5 – 30 | | Beam blockage | — | 0.0 – 0.3 | | Ap propagation | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `180` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x55a2425a8f8239e71d1a32aad88a7cb9bafe351bbf7937a6b5a2416e27c5925e` - **Chain tx hash:** `0xce7dd03592c22bcccad295eb0f83db4f0e3bfb0032e289e0a1b23484382a3f4e` - **Chain block:** `41554198` --- ## File Mapping This bundle consists of: `L1-105.md`, `L1-105.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-105.md` | Source of truth — edit this | Human or LLM | | `L1-105.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 `L1-105`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-105.md).
Regenerate L1-105.json so every field matches the Markdown.
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L2-105-001 Doppler Weather Radar Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-105",
  "chain_block": 41554198,
  "chain_hash": "0x55a2425a8f8239e71d1a32aad88a7cb9bafe351bbf7937a6b5a2416e27c5925e",
  "chain_tx_hash": "0xce7dd03592c22bcccad295eb0f83db4f0e3bfb0032e289e0a1b23484382a3f4e",
  "domain": "Remote Sensing",
  "hardness_fn": {
    "delta": 3,
    "kappa": 180,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 3D reflectivity velocity 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 ~= 9); beam_blockage dominates the stability cliff; AP_propagation 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"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "radio_wave",
    "difficulty_delta": 3,
    "domain": "Remote Sensing",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.emit.pulse",
      "L.volume_scatter",
      "L.doppler_frequency_shift",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "doppler_radar",
    "solution_space": "3D_reflectivity_velocity",
    "sub_domain": "Atmospheric Doppler reflectivity + velocity",
    "title": "Doppler Weather Radar"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "doppler_weather_radar_forward"
    ],
    "allowed_omega_dimensions": [
      "N_range",
      "N_az",
      "N_el",
      "lambda_cm",
      "PRF_Hz",
      "SNR_dB",
      "beam_blockage",
      "AP_propagation",
      "beam_blockage",
      "AP_propagation",
      "aliasing",
      "clutter"
    ],
    "allowed_problem_classes": [
      "doppler_weather_radar"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "doppler_weather_radar_forward",
      "input_format": "measurement_only",
      "omega": {
        "AP_propagation": 0.0,
        "N_az": 720,
        "N_el": 12,
        "N_range": 500,
        "PRF_Hz": 1000,
        "SNR_dB": 25.0,
        "beam_blockage": 0.0,
        "lambda_cm": 10
      },
      "problem_class": "doppler_weather_radar"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "AP_propagation": [
        0.0,
        0.3
      ],
      "N_az": [
        180,
        1440
      ],
      "N_el": [
        1,
        25
      ],
      "N_range": [
        100,
        2000
      ],
      "PRF_Hz": [
        200,
        5000
      ],
      "SNR_dB": [
        5.0,
        40.0
      ],
      "aliasing": [
        0.0,
        0.5
      ],
      "beam_blockage": [
        0.0,
        0.3
      ],
      "clutter": [
        0.0,
        0.5
      ],
      "lambda_cm": [
        0.5,
        30
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Atmospheric Doppler reflectivity + velocity",
  "title": "Doppler Weather Radar"
}

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