L1 ⚛ L1-384 ⊙ Testnet

Image Inpainting (masked region recovery)

Signal Processing · Spatial hole-filling / occlusion removal

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Markdown — human-readable source of truth

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⬇ L1-384.md

# ⚛ L1 Principle — Image Inpainting (masked region recovery) **ID:** `L1-384` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Signal Processing — *Spatial hole-filling / occlusion removal* > **🎯 Problem class:** linear inverse masked · **🧮 Solution space:** 2D image > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555197 --- ## 🧠 1. Introduction **Image Inpainting (masked region recovery)** is a **linear inverse masked** whose unknown lives in **2D image** space, within the **Spatial hole-filling / occlusion removal** sub-domain of **Signal Processing**. Measurements consist of photons collected by an optical detector via a **binary masking** sensing mechanism. The forward operator applies, in order: D · mask · spatial operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Strictly underdetermined inside mask; uniqueness is prior-induced (TV, non-local similarity, learned). Stability decreases super-linearly with mask_ratio and hole diameter. ## ⚙ 2. Forward Model Physical chain: **x** → D · mask · spatial → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.mask.spatial` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.mask.spatial` | D · mask · spatial operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Signal Processing | | Sub domain | Spatial hole-filling / occlusion removal | | Carrier | photon | | Problem class | linear_inverse_masked | | Solution space | 2D_image | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2 | ## 📡 4. Measurement Model Strictly underdetermined inside mask; uniqueness is prior-induced (TV, non-local similarity, learned). Stability decreases super-linearly with mask_ratio and hole diameter. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `freeform_inpainting` · **Forward operator:** `binary_mask` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Mask ratio | — | 0.25 | | Mask shape | — | freeform | | Noise level | — | 0 | | Boundary dilation | — | 0 | | Hole diameter max | — | 64 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Mask ratio | — | 0.05 – 0.75 | | Noise level | — | 0.0 – 0.05 | | Boundary dilation | — | 0 – 8 | | Hole diameter max | — | 8 – 512 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 15.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `10000` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x551cdda785b03feb489e1a6bac709df7aa9b1bf03d78f5a6b00ef07de2bdb994` - **Chain tx hash:** `0x3ea98f5fe15d7f904ee4043488a94956404a5991648292fe1a3a64a99d2606f5` - **Chain block:** `41555197` --- ## File Mapping This bundle consists of: `L1-384.md`, `L1-384.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-384.md` | Source of truth — edit this | Human or LLM | | `L1-384.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 `L1-384`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Prompt to give your LLM

Read the attached Markdown (L1-384.md).
Regenerate L1-384.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

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L2-384-001 Image Inpainting Freeform-Mask Spec (Places2 / CelebA-HQ family)

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📋 JSON metadata

{
  "artifact_id": "L1-384",
  "chain_block": 41555197,
  "chain_hash": "0x551cdda785b03feb489e1a6bac709df7aa9b1bf03d78f5a6b00ef07de2bdb994",
  "chain_tx_hash": "0x3ea98f5fe15d7f904ee4043488a94956404a5991648292fe1a3a64a99d2606f5",
  "domain": "Signal Processing",
  "hardness_fn": {
    "delta": 3,
    "kappa": 10000,
    "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": "Strictly underdetermined inside mask; uniqueness is prior-induced (TV, non-local similarity, learned). Stability decreases super-linearly with mask_ratio and hole diameter.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Signal Processing",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "D.mask.spatial",
      "int.spatial"
    ],
    "problem_class": "linear_inverse_masked",
    "sensing_mechanism": "binary_masking",
    "solution_space": "2D_image",
    "sub_domain": "Spatial hole-filling / occlusion removal",
    "title": "Image Inpainting (masked region recovery)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "binary_mask",
      "soft_mask"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "mask_ratio",
      "hole_diameter_max",
      "mask_shape",
      "boundary_dilation",
      "noise_level"
    ],
    "allowed_problem_classes": [
      "freeform_inpainting",
      "rectangular_inpainting",
      "object_removal"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0 dB PSNR",
      "forward_operator": "binary_mask",
      "input_format": "measurement_plus_mask",
      "omega": {
        "H": 512,
        "W": 512,
        "boundary_dilation": 0,
        "hole_diameter_max": 64,
        "mask_ratio": 0.25,
        "mask_shape": "freeform",
        "noise_level": 0.0
      },
      "problem_class": "freeform_inpainting"
    },
    "epsilon_bounds": {
      "psnr_db": [
        15.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        2048
      ],
      "W": [
        128,
        2048
      ],
      "boundary_dilation": [
        0,
        8
      ],
      "hole_diameter_max": [
        8,
        512
      ],
      "mask_ratio": [
        0.05,
        0.75
      ],
      "noise_level": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Spatial hole-filling / occlusion removal",
  "title": "Image Inpainting (masked region recovery)"
}

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