L1 ⚛ L1-016 ⊙ Testnet

Image Scanning Microscopy (ISM) — pixel reassignment super-resolution

Microscopy · Confocal with small-pinhole detector array

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⬇ L1-016.md

# ⚛ L1 Principle — Image Scanning Microscopy (ISM) — pixel reassignment super-resolution **ID:** `L1-016` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Confocal with small-pinhole detector array* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554156 --- ## 🧠 1. Introduction **Image Scanning Microscopy (ISM) — pixel reassignment super-resolution** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Confocal with small-pinhole detector array** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **airy scan detector array** sensing mechanism. The forward operator applies, in order: K · psf · confocal operator; ordered pixel-by-pixel sampling; L · pixel reassign operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 9); detector_registration dominates the stability cliff; pinhole_size_AU and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → K · psf · confocal → Raster scan → L · pixel reassign → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.pixel_reassign` S_raster `K.psf.confocal` x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.psf.confocal` | K · psf · confocal operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `L.pixel_reassign` | L · pixel reassign operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Confocal with small-pinhole detector array | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | poisson_gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 9); detector_registration dominates the stability cliff; pinhole_size_AU and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `ism` · **Forward operator:** `ism_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Na | — | 1.4 | | N det | — | 32 | | Pixel nm | nm | 40 | | Pinhole au | — | 0.2 | | Peak photons | photons | 300 | | Detector registration | — | 0 | | Reassignment kernel drift | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Na | — | 1.0 – 1.49 | | N det | — | 4 – 100 | | Pixel nm | nm | 20 – 100 | | Pinhole au | — | 0.1 – 1.0 | | Peak photons | photons | 30 – 3000 | | Detector registration | — | 0.0 – 0.1 | | Reassignment kernel drift | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `180` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7733790aa6235469f6240481753e2e0d6acb727353fe8f75919cad7c305955c6` - **Chain tx hash:** `0x0d3681ee5f259ff05977e7df1e15429adbc5fdb9646cb74f7f6869f9766ab629` - **Chain block:** `41554156` --- ## File Mapping This bundle consists of: `L1-016.md`, `L1-016.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-016.md` | Source of truth — edit this | Human or LLM | | `L1-016.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 `L1-016`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Regenerate L1-016.json so every field matches the Markdown.
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L2-016-001 Image Scanning Microscopy (ISM) — pixel reassignment super-resolution Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554156,
  "chain_hash": "0x7733790aa6235469f6240481753e2e0d6acb727353fe8f75919cad7c305955c6",
  "chain_tx_hash": "0x0d3681ee5f259ff05977e7df1e15429adbc5fdb9646cb74f7f6869f9766ab629",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 180,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 9); detector_registration dominates the stability cliff; pinhole_size_AU and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "poisson_gaussian",
    "primitives": [
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      "S.scan.raster",
      "L.pixel_reassign",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "airy_scan_detector_array",
    "solution_space": "2D_intensity",
    "sub_domain": "Confocal with small-pinhole detector array",
    "title": "Image Scanning Microscopy (ISM) \u2014 pixel reassignment super-resolution"
  },
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    "allowed_omega_dimensions": [
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      "W",
      "N_det",
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      "NA",
      "pinhole_AU",
      "peak_photons",
      "detector_registration",
      "reassignment_kernel_drift",
      "detector_registration",
      "pinhole_size_AU",
      "reassignment_kernel_drift"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
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        "NA": 1.4,
        "N_det": 32,
        "W": 1024,
        "detector_registration": 0.0,
        "peak_photons": 300,
        "pinhole_AU": 0.2,
        "pixel_nm": 40,
        "reassignment_kernel_drift": 0.0
      },
      "problem_class": "ism"
    },
    "epsilon_bounds": {
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        42.0
      ]
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        4096
      ],
      "NA": [
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      ],
      "N_det": [
        4,
        100
      ],
      "W": [
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        4096
      ],
      "detector_registration": [
        0.0,
        0.1
      ],
      "peak_photons": [
        30,
        3000
      ],
      "pinhole_AU": [
        0.1,
        1.0
      ],
      "pixel_nm": [
        20,
        100
      ],
      "reassignment_kernel_drift": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Confocal with small-pinhole detector array",
  "title": "Image Scanning Microscopy (ISM) \u2014 pixel reassignment super-resolution"
}

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