L1 ⚛ L1-168 ⊙ Testnet

Event Horizon Telescope (VLBI) Imaging

Astronomy · Radio interferometry

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⬇ L1-168.md

# ⚛ L1 Principle — Event Horizon Telescope (VLBI) Imaging **ID:** `L1-168` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astronomy — *Radio interferometry* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D brightness temperature > **📡 Carrier:** radio_wave · **🌫 Noise:** thermal gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554244 --- ## 🧠 1. Introduction **Event Horizon Telescope (VLBI) Imaging** is a **nonlinear inverse problem** whose unknown lives in **2D brightness temperature** space, within the **Radio interferometry** sub-domain of **Astronomy**. Measurements consist of radio-frequency electromagnetic waves via a **vlbi sparse aperture** sensing mechanism. The forward operator applies, in order: F · fourier · nufft operator; S · closure · phase operator; adds a prior term that biases the solution toward smoothness/sparsity; O · chi2 · visibility operator. Observations are corrupted by thermally-driven Gaussian fluctuations. 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 declared priors. Stability is conditionally stable (kappa_eff ~= 1000); station_gain_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → F · fourier · nufft → S · closure · phase → O · chi2 · visibility → **y** (detector). ``` y = `O.chi2.visibility` `S.closure.phase` `F.fourier.nufft` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `F.fourier.nufft` | F · fourier · nufft operator | | `S.closure.phase` | S · closure · phase operator | | `O.chi2.visibility` | O · chi2 · visibility operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astronomy | | Sub domain | Radio interferometry | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_brightness_temperature | | Noise model | thermal_gaussian | | Integration axis | uv_plane | | Difficulty delta | 5 | | 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 declared priors. Stability is conditionally stable (kappa_eff ~= 1000); station_gain_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | chi2_reduced | | Secondary | image_fidelity_score | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `vlbi_sparse_aperture` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 64 | | W | px | 64 | | N baselines | — | 15 | | Uv fraction | — | 0.001 | | Noise sigma jy | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 512 | | W | px | 32 – 512 | | N baselines | — | 6 – 50 | | Uv fraction | — | 0.0001 – 0.01 | | Noise sigma jy | — | 0.01 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.2 chi2_reduced | Metric | Range | |---|---| | Chi2 reduced | 0.8 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **chi2_reduced**, with κ = `1000000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc117659285882e17ebe99e1e597e0872c212d4fd5da6b7b9bde35261efd32c2b` - **Chain tx hash:** `0x6ce6ec74df271331b2949e1d1555e365520aa5620795915d1b2370904d5daa35` - **Chain block:** `41554244` --- ## File Mapping This bundle consists of: `L1-168.md`, `L1-168.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-168.md` | Source of truth — edit this | Human or LLM | | `L1-168.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 `L1-168`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-168.md).
Regenerate L1-168.json so every field matches the Markdown.
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L2-168-001 Event Horizon Telescope (VLBI) Imaging — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41554244,
  "chain_hash": "0xc117659285882e17ebe99e1e597e0872c212d4fd5da6b7b9bde35261efd32c2b",
  "chain_tx_hash": "0x6ce6ec74df271331b2949e1d1555e365520aa5620795915d1b2370904d5daa35",
  "domain": "Astronomy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 1000000.0,
    "metric": "chi2_reduced",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "chi2_reduced",
    "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 declared priors. Stability is conditionally stable (kappa_eff ~= 1000); station_gain_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Thermal gaussian sets the irreducible data-fidelity floor.",
    "secondary": "image_fidelity_score"
  },
  "physics_fingerprint": {
    "L_DAG": 4.5,
    "carrier": "radio_wave",
    "difficulty_delta": 5,
    "domain": "Astronomy",
    "integration_axis": "uv_plane",
    "noise_model": "thermal_gaussian",
    "primitives": [
      "F.fourier.nufft",
      "S.closure.phase",
      "O.regularize",
      "O.chi2.visibility"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "vlbi_sparse_aperture",
    "solution_space": "2D_brightness_temperature",
    "sub_domain": "Radio interferometry",
    "title": "Event Horizon Telescope (VLBI) Imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "vlbi_sparse_aperture"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_baselines",
      "uv_fraction",
      "noise_sigma_Jy"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "1.2 chi2_reduced",
      "forward_operator": "vlbi_sparse_aperture",
      "input_format": "measurement_only",
      "omega": {
        "H": 64,
        "N_baselines": 15,
        "W": 64,
        "noise_sigma_Jy": 0.1,
        "uv_fraction": 0.001
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "chi2_reduced": [
        0.8,
        3.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        512
      ],
      "N_baselines": [
        6,
        50
      ],
      "W": [
        32,
        512
      ],
      "noise_sigma_Jy": [
        0.01,
        1.0
      ],
      "uv_fraction": [
        0.0001,
        0.01
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Radio interferometry",
  "title": "Event Horizon Telescope (VLBI) Imaging"
}

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