L1 ⚛ L1-368 ⊙ Testnet

Strong Gravitational Lensing Inversion

Astrophysics · Gravitational lensing

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⬇ L1-368.md

# ⚛ L1 Principle — Strong Gravitational Lensing Inversion **ID:** `L1-368` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Astrophysics — *Gravitational lensing* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D lens mass distribution > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41555177 --- ## 🧠 1. Introduction **Strong Gravitational Lensing Inversion** is a **nonlinear inverse problem** whose unknown lives in **2D lens mass distribution** space, within the **Gravitational lensing** sub-domain of **Astrophysics**. Measurements consist of photons collected by an optical detector via a **gravitational deflection mapping** sensing mechanism. The forward operator applies, in order: an unspecified linear measurement operator; S · source · pixelization operator; O · chi2 · image plane operator. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D_lens_mass_distribution 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 ~= 5000); PSF_mismatch dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Generic linear operator → S · source · pixelization → O · chi2 · image plane → **y** (detector). ``` y = `O.chi2.image_plane` `S.source.pixelization` A x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.linear_op` | An unspecified linear measurement operator | | `S.source.pixelization` | S · source · pixelization operator | | `O.chi2.image_plane` | O · chi2 · image plane operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Astrophysics | | Sub domain | Gravitational lensing | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_lens_mass_distribution | | Noise model | shot_poisson | | Integration axis | lens_plane | | Difficulty delta | 10 | | L dag | 4.2 | ## 📡 4. Measurement Model Existence of the recovered 2D_lens_mass_distribution 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 ~= 5000); PSF_mismatch dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Shot poisson sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | image_chi2_reduced | | Secondary | source_plane_regularization | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `gravitational_deflection_mapping` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 100 | | W | px | 100 | | Gamma shear | — | 0.05 | | E ellipticity | — | 0.2 | | Theta e arcsec | — | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 50 – 500 | | W | px | 50 – 500 | | Gamma shear | — | 0.0 – 0.2 | | E ellipticity | — | 0.0 – 0.5 | | Theta e arcsec | — | 0.2 – 3.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 1.1 image_chi2_reduced | Metric | Range | |---|---| | Image chi2 reduced | 0.9 – 3.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **image_chi2_reduced**, with κ = `1000000.0` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5aaa44ef61f3e528988c3dbc9fec6cd9bb3e57684a35106e8d08a6da2cf84b57` - **Chain tx hash:** `0x99e3ed8a5c176fbda7d6117d9fa9ac408e30313985a3022e43bc306840ec3ec2` - **Chain block:** `41555177` --- ## File Mapping This bundle consists of: `L1-368.md`, `L1-368.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-368.md` | Source of truth — edit this | Human or LLM | | `L1-368.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 `L1-368`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-368.md).
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L2-368-001 Strong Gravitational Lensing Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Astrophysics",
  "hardness_fn": {
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  "physics_fingerprint": {
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    "carrier": "photon",
    "difficulty_delta": 10,
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    "integration_axis": "lens_plane",
    "noise_model": "shot_poisson",
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      "S.source.pixelization",
      "O.chi2.image_plane"
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    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "gravitational_deflection_mapping",
    "solution_space": "2D_lens_mass_distribution",
    "sub_domain": "Gravitational lensing",
    "title": "Strong Gravitational Lensing Inversion"
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    "allowed_problem_classes": [
      "nonlinear_inverse"
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    "center_spec": {
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      "forward_operator": "gravitational_deflection_mapping",
      "input_format": "measurement_only",
      "omega": {
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        "theta_E_arcsec": 1.0
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    },
    "epsilon_bounds": {
      "image_chi2_reduced": [
        0.9,
        3.0
      ]
    },
    "omega_bounds": {
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        500
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      "W": [
        50,
        500
      ],
      "e_ellipticity": [
        0.0,
        0.5
      ],
      "gamma_shear": [
        0.0,
        0.2
      ],
      "theta_E_arcsec": [
        0.2,
        3.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Gravitational lensing",
  "title": "Strong Gravitational Lensing Inversion"
}

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