L1 ⚛ L1-106 ⊙ Testnet

Very Long Baseline Interferometry (VLBI)

Remote Sensing · Radio-astronomy aperture synthesis

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Markdown — human-readable source of truth

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⬇ L1-106.md

# ⚛ L1 Principle — Very Long Baseline Interferometry (VLBI) **ID:** `L1-106` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Radio-astronomy aperture synthesis* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D brightness temperature > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554198 --- ## 🧠 1. Introduction **Very Long Baseline Interferometry (VLBI)** is a **linear inverse problem** whose unknown lives in **2D brightness temperature** space, within the **Radio-astronomy aperture synthesis** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **radio interferometry** sensing mechanism. The forward operator applies, in order: L · radio antenna array operator; L · cross correlation operator; L · fourier synthesis operator; pixel-level spatial averaging on the detector. 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 moderately conditioned (kappa_eff ~= 30); ionospheric_delay dominates the stability cliff; atomic_clock_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → L · radio antenna array → L · cross correlation → L · fourier synthesis → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.fourier_synthesis` `L.cross_correlation` `L.radio_antenna_array` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.radio_antenna_array` | L · radio antenna array operator | | `L.cross_correlation` | L · cross correlation operator | | `L.fourier_synthesis` | L · fourier synthesis operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Radio-astronomy aperture synthesis | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | 2D_brightness_temperature | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 10 | | L dag | 4.5 | ## 📡 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 moderately conditioned (kappa_eff ~= 30); ionospheric_delay dominates the stability cliff; atomic_clock_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `vlbi_synthesis` · **Forward operator:** `vlbi_synthesis_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N time | — | 360 | | Snr db | dB | 15 | | Lambda cm | — | 1.3 | | N antennas | — | 10 | | N baselines | — | 45 | | Ionospheric delay | — | 0 | | Atomic clock drift | — | 0 | | Uv coverage fraction | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Rfi | — | 0.0 – 0.5 | | N time | — | 60 – 3600 | | Snr db | dB | 0.0 – 30.0 | | Lambda cm | — | 0.01 – 500 | | N antennas | — | 4 – 100 | | N baselines | — | 6 – 4950 | | Ionospheric delay | — | 0.0 – 1.0 | | Atomic clock drift | — | 0.0 – 0.01 | | Uv coverage fraction | — | 0.005 – 0.5 | | Station position error | — | 0.0 – 10.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 16.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa51dd80c6821bfd1279298e61363c430f23166022cc2823dec91fd70e2a2144d` - **Chain tx hash:** `0x6a377ce2880888bdb45d08e790a9cf4b2a41387e4d06cdc2b37cb91f3ce65deb` - **Chain block:** `41554198` --- ## File Mapping This bundle consists of: `L1-106.md`, `L1-106.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-106.md` | Source of truth — edit this | Human or LLM | | `L1-106.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 `L1-106`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-106.md).
Regenerate L1-106.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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L2-106-001 Very Long Baseline Interferometry (VLBI) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-106",
  "chain_block": 41554198,
  "chain_hash": "0xa51dd80c6821bfd1279298e61363c430f23166022cc2823dec91fd70e2a2144d",
  "chain_tx_hash": "0x6a377ce2880888bdb45d08e790a9cf4b2a41387e4d06cdc2b37cb91f3ce65deb",
  "domain": "Remote Sensing",
  "hardness_fn": {
    "delta": 10,
    "kappa": 600,
    "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": "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 moderately conditioned (kappa_eff ~= 30); ionospheric_delay dominates the stability cliff; atomic_clock_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.5,
    "carrier": "radio_wave",
    "difficulty_delta": 10,
    "domain": "Remote Sensing",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.radio_antenna_array",
      "L.cross_correlation",
      "L.fourier_synthesis",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "radio_interferometry",
    "solution_space": "2D_brightness_temperature",
    "sub_domain": "Radio-astronomy aperture synthesis",
    "title": "Very Long Baseline Interferometry (VLBI)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "vlbi_synthesis_forward"
    ],
    "allowed_omega_dimensions": [
      "N_antennas",
      "N_baselines",
      "N_time",
      "lambda_cm",
      "UV_coverage_fraction",
      "SNR_dB",
      "ionospheric_delay",
      "atomic_clock_drift",
      "ionospheric_delay",
      "atomic_clock_drift",
      "station_position_error",
      "RFI"
    ],
    "allowed_problem_classes": [
      "vlbi_synthesis"
    ],
    "center_spec": {
      "epsilon_fn_center": "16.0",
      "forward_operator": "vlbi_synthesis_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_antennas": 10,
        "N_baselines": 45,
        "N_time": 360,
        "SNR_dB": 15.0,
        "UV_coverage_fraction": 0.1,
        "atomic_clock_drift": 0.0,
        "ionospheric_delay": 0.0,
        "lambda_cm": 1.3
      },
      "problem_class": "vlbi_synthesis"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "N_antennas": [
        4,
        100
      ],
      "N_baselines": [
        6,
        4950
      ],
      "N_time": [
        60,
        3600
      ],
      "RFI": [
        0.0,
        0.5
      ],
      "SNR_dB": [
        0.0,
        30.0
      ],
      "UV_coverage_fraction": [
        0.005,
        0.5
      ],
      "atomic_clock_drift": [
        0.0,
        0.01
      ],
      "ionospheric_delay": [
        0.0,
        1.0
      ],
      "lambda_cm": [
        0.01,
        500
      ],
      "station_position_error": [
        0.0,
        10.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Radio-astronomy aperture synthesis",
  "title": "Very Long Baseline Interferometry (VLBI)"
}

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