L1 ⚛ L1-024 ⊙ Testnet

DNA-PAINT (transient DNA-hybridization localization microscopy)

Microscopy · Programmable-blinking single-molecule super-resolution

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⬇ L1-024.md

# ⚛ L1 Principle — DNA-PAINT (transient DNA-hybridization localization microscopy) **ID:** `L1-024` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Programmable-blinking single-molecule super-resolution* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** point list > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554169 --- ## 🧠 1. Introduction **DNA-PAINT (transient DNA-hybridization localization microscopy)** is a **nonlinear inverse problem** whose unknown lives in **point list** space, within the **Programmable-blinking single-molecule super-resolution** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **single molecule localization** sensing mechanism. The forward operator applies, in order: L · dna hybridization blinking operator; convolution with the Airy disk of a circular aperture; L · gaussian fit operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered point list 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 ~= 28); docking_strand_concentration dominates the stability cliff; drift_nm_per_frame 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 · dna hybridization blinking → Airy PSF convolution → L · gaussian fit → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.gaussian_fit` K_Airy * `L.dna_hybridization_blinking` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.dna_hybridization_blinking` | L · dna hybridization blinking operator | | `K.psf.airy` | Convolution with the airy disk of a circular aperture | | `L.gaussian_fit` | L · gaussian fit operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Programmable-blinking single-molecule super-resolution | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | point_list | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered point list 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 ~= 28); docking_strand_concentration dominates the stability cliff; drift_nm_per_frame 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 | localization_precision_nm | | Secondary | detection_recall | ## 📏 5. Operating Range (Ω) **Center problem class:** `dnapaint` · **Forward operator:** `dnapaint_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Na | — | 1.49 | | T frames | — | 30000 | | Pixel nm | nm | 160 | | Drift nm per frame | — | 0 | | Photons per binding | — | 5000 | | Non specific binding | — | 0.02 | | Strand concentration nm | nm | 5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | W | px | 64 – 2048 | | Na | — | 1.3 – 1.49 | | T frames | — | 5000 – 200000 | | Pixel nm | nm | 80 – 300 | | Drift nm per frame | — | 0.0 – 3.0 | | Photons per binding | — | 500 – 50000 | | Non specific binding | — | 0.0 – 0.2 | | Strand concentration nm | nm | 0.5 – 50 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 8.0 | Metric | Range | |---|---| | Localization nm | 0.5 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **localization_precision_nm**, with κ = `560` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4edb8ecb50a6b1edb2f3b4f786698438c74036348e3bd3f3737100858e1b4fa6` - **Chain tx hash:** `0xc1190d7b1d1a36d54875331e7c64136ada552c562d976632d12d21f58d60c84e` - **Chain block:** `41554169` --- ## File Mapping This bundle consists of: `L1-024.md`, `L1-024.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-024.md` | Source of truth — edit this | Human or LLM | | `L1-024.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 `L1-024`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-024.md).
Regenerate L1-024.json so every field matches the Markdown.
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L2-024-001 DNA-PAINT (transient DNA-hybridization localization microscopy) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Microscopy",
  "hardness_fn": {
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    "kappa": 560,
    "metric": "localization_precision_nm",
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    "regime": "Existence of the recovered point list 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 ~= 28); docking_strand_concentration dominates the stability cliff; drift_nm_per_frame 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.",
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    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "single_molecule_localization",
    "solution_space": "point_list",
    "sub_domain": "Programmable-blinking single-molecule super-resolution",
    "title": "DNA-PAINT (transient DNA-hybridization localization microscopy)"
  },
  "size_tiers": {
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      "drift_nm_per_frame",
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      "drift_nm_per_frame",
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        "pixel_nm": 160,
        "strand_concentration_nM": 5
      },
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      "drift_nm_per_frame": [
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      ],
      "non_specific_binding": [
        0.0,
        0.2
      ],
      "photons_per_binding": [
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        50000
      ],
      "pixel_nm": [
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        300
      ],
      "strand_concentration_nM": [
        0.5,
        50
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Programmable-blinking single-molecule super-resolution",
  "title": "DNA-PAINT (transient DNA-hybridization localization microscopy)"
}

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