L1 ⚛ L1-246 ⊙ Testnet

Holographic Reconstruction — wavefront from interference

Electromagnetics · Digital holography reconstruction

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-246.md

# ⚛ L1 Principle — Holographic Reconstruction — wavefront from interference **ID:** `L1-246` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Digital holography reconstruction* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex 2D field > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553989 --- ## 🧠 1. Introduction **Holographic Reconstruction — wavefront from interference** is a **linear inverse problem** whose unknown lives in **complex 2D field** space, within the **Digital holography reconstruction** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **ccd** sensing mechanism. The forward operator applies, in order: L · interference operator; L · fft reconstruct operator; L · demultiplex operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · interference → L · fft reconstruct → L · demultiplex → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.demultiplex` `L.fft_reconstruct` `L.interference` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.interference` | L · interference operator | | `L.fft_reconstruct` | L · fft reconstruct operator | | `L.demultiplex` | L · demultiplex operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Digital holography reconstruction | | Carrier | em | | Problem class | linear_inverse | | Solution space | complex_2D_field | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `holo_recon` · **Forward operator:** `holo_recon_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Z m | m | 0.1 | | Snr db | dB | 30 | | Lambda nm | nm | 633 | | Z focus error | — | 0 | | Twin image error | — | 0 | | Ref beam tilt error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 4096 | | W | px | 128 – 4096 | | Z m | m | 0.001 – 10 | | Snr db | dB | 0 – 40 | | Lambda nm | nm | 100 – 10000 | | Z focus error | — | 0.0 – 0.05 | | Twin image error | — | 0.0 – 0.3 | | Ref beam tilt error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x35de961792cda4d255ec9ccf0a19c1ce44171c2983ee7c7ab5dcaf8f9dd76058` - **Chain tx hash:** `0xfa9f79900a4a9d80660866a020442ee88231cf7478533f642bf6320b2158e623` - **Chain block:** `41553989` --- ## File Mapping This bundle consists of: `L1-246.md`, `L1-246.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-246.md` | Source of truth — edit this | Human or LLM | | `L1-246.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 `L1-246`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-246.md).
Regenerate L1-246.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

↓ L2 Spec 1 child ▾

L2-246-001 Holographic Reconstruction — wavefront from interference Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-246",
  "chain_block": 41553989,
  "chain_hash": "0x35de961792cda4d255ec9ccf0a19c1ce44171c2983ee7c7ab5dcaf8f9dd76058",
  "chain_tx_hash": "0xfa9f79900a4a9d80660866a020442ee88231cf7478533f642bf6320b2158e623",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "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": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.interference",
      "L.fft_reconstruct",
      "L.demultiplex",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "ccd",
    "solution_space": "complex_2D_field",
    "sub_domain": "Digital holography reconstruction",
    "title": "Holographic Reconstruction \u2014 wavefront from interference"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "holo_recon_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "lambda_nm",
      "z_m",
      "SNR_dB",
      "ref_beam_tilt_error",
      "z_focus_error",
      "twin_image_error",
      "ref_beam_tilt_error",
      "z_focus_error",
      "twin_image_error"
    ],
    "allowed_problem_classes": [
      "holo_recon"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0",
      "forward_operator": "holo_recon_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 1024,
        "SNR_dB": 30,
        "W": 1024,
        "lambda_nm": 633,
        "ref_beam_tilt_error": 0.0,
        "twin_image_error": 0.0,
        "z_focus_error": 0.0,
        "z_m": 0.1
      },
      "problem_class": "holo_recon"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        4096
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        128,
        4096
      ],
      "lambda_nm": [
        100,
        10000
      ],
      "ref_beam_tilt_error": [
        0.0,
        0.1
      ],
      "twin_image_error": [
        0.0,
        0.3
      ],
      "z_focus_error": [
        0.0,
        0.05
      ],
      "z_m": [
        0.001,
        10
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Digital holography reconstruction",
  "title": "Holographic Reconstruction \u2014 wavefront from interference"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.