L1 ⚛ L1-153 ⊙ Testnet

Ghost Imaging (correlated-photon imaging)

Quantum Imaging · Imaging via photon-pair correlations between bucket and reference

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⬇ L1-153.md

# ⚛ L1 Principle — Ghost Imaging (correlated-photon imaging) **ID:** `L1-153` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Imaging — *Imaging via photon-pair correlations between bucket and reference* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554241 --- ## 🧠 1. Introduction **Ghost Imaging (correlated-photon imaging)** is a **nonlinear inverse problem** whose unknown lives in **2D intensity** space, within the **Imaging via photon-pair correlations between bucket and reference** sub-domain of **Quantum Imaging**. Measurements consist of photons collected by an optical detector via a **photon correlation imaging** sensing mechanism. The forward operator applies, in order: L · photon pair source operator; D · bucket detector operator; D · reference imaging operator; L · correlation operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); photon_pair_rate dominates the stability cliff; accidental_coincidences and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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 · photon pair source → D · bucket detector → D · reference imaging → L · correlation → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.correlation` `D.reference_imaging` `D.bucket_detector` `L.photon_pair_source` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.photon_pair_source` | L · photon pair source operator | | `D.bucket_detector` | D · bucket detector operator | | `D.reference_imaging` | D · reference imaging operator | | `L.correlation` | L · correlation operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Imaging | | Sub domain | Imaging via photon-pair correlations between bucket and reference | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_intensity | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 4.2 | ## 📡 4. Measurement Model Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); photon_pair_rate dominates the stability cliff; accidental_coincidences and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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:** `ghost_imaging` · **Forward operator:** `ghost_imaging_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | N pairs | — | 100000 | | Bucket snr db | dB | 10 | | Photon pair rate | — | 1 | | Reference calibration | — | 1 | | Accidental coincidences | — | 0.1 | | Environmental decoherence | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 | | W | px | 32 | | N pairs | — | 1000 – 100000000 | | Bucket snr db | dB | 0.0 – 30.0 | | Photon pair rate | — | 0.1 – 10.0 | | Reference calibration | — | 0.3 – 1.0 | | Accidental coincidences | — | 0.0 – 0.5 | | Environmental decoherence | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 18.0 | 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:** `0xb06391d95e4843afb8624a137b2b120388b1074027095e55a1dbb3f498d016ef` - **Chain tx hash:** `0x69513649625e504ee17741b4df3ab31017e91ac64380a6bb2596f338396eb455` - **Chain block:** `41554241` --- ## File Mapping This bundle consists of: `L1-153.md`, `L1-153.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-153.md` | Source of truth — edit this | Human or LLM | | `L1-153.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 `L1-153`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-153.md).
Regenerate L1-153.json so every field matches the Markdown.
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L2-153-001 Ghost Imaging (correlated-photon imaging) Mismatch-Only Spec

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📋 JSON metadata

{
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  "chain_block": 41554241,
  "chain_hash": "0xb06391d95e4843afb8624a137b2b120388b1074027095e55a1dbb3f498d016ef",
  "chain_tx_hash": "0x69513649625e504ee17741b4df3ab31017e91ac64380a6bb2596f338396eb455",
  "domain": "Quantum Imaging",
  "hardness_fn": {
    "delta": 10,
    "kappa": 600,
    "metric": "PSNR_dB",
    "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": "PSNR_dB",
    "regime": "Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); photon_pair_rate dominates the stability cliff; accidental_coincidences and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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": 4.2,
    "carrier": "photon",
    "difficulty_delta": 10,
    "domain": "Quantum Imaging",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.photon_pair_source",
      "D.bucket_detector",
      "D.reference_imaging",
      "L.correlation",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "photon_correlation_imaging",
    "solution_space": "2D_intensity",
    "sub_domain": "Imaging via photon-pair correlations between bucket and reference",
    "title": "Ghost Imaging (correlated-photon imaging)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ghost_imaging_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_pairs",
      "bucket_SNR_dB",
      "photon_pair_rate",
      "accidental_coincidences",
      "reference_calibration",
      "environmental_decoherence",
      "photon_pair_rate",
      "accidental_coincidences",
      "reference_calibration",
      "environmental_decoherence"
    ],
    "allowed_problem_classes": [
      "ghost_imaging"
    ],
    "center_spec": {
      "epsilon_fn_center": "18.0",
      "forward_operator": "ghost_imaging_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_pairs": 100000,
        "W": 128,
        "accidental_coincidences": 0.1,
        "bucket_SNR_dB": 10,
        "environmental_decoherence": 0.0,
        "photon_pair_rate": 1.0,
        "reference_calibration": 1.0
      },
      "problem_class": "ghost_imaging"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": 32,
      "N_pairs": [
        1000,
        100000000
      ],
      "W": 32,
      "accidental_coincidences": [
        0.0,
        0.5
      ],
      "bucket_SNR_dB": [
        0.0,
        30.0
      ],
      "environmental_decoherence": [
        0.0,
        0.5
      ],
      "photon_pair_rate": [
        0.1,
        10.0
      ],
      "reference_calibration": [
        0.3,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Imaging via photon-pair correlations between bucket and reference",
  "title": "Ghost Imaging (correlated-photon imaging)"
}

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