L1 ⚛ L1-011 ⊙ Testnet

PALM / STORM (single-molecule localization microscopy)

Microscopy · Single-molecule localization super-resolution

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⬇ L1-011.md

# ⚛ L1 Principle — PALM / STORM (single-molecule localization microscopy) **ID:** `L1-011` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Single-molecule localization super-resolution* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** point list > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554155 --- ## 🧠 1. Introduction **PALM / STORM (single-molecule localization microscopy)** is a **nonlinear inverse problem** whose unknown lives in **point list** space, within the **Single-molecule localization 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: convolution with the Airy disk of a circular aperture; D · threshold · isolated operator; 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 ~= 30); drift_nm_per_frame dominates the stability cliff; multi_emitter_overlap 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** → Airy PSF convolution → D · threshold · isolated → L · gaussian fit → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.gaussian_fit` `D.threshold.isolated` K_Airy * x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.psf.airy` | Convolution with the airy disk of a circular aperture | | `D.threshold.isolated` | D · threshold · isolated operator | | `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 | Single-molecule localization super-resolution | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | point_list | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 4.2 | ## 📡 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 ~= 30); drift_nm_per_frame dominates the stability cliff; multi_emitter_overlap 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:** `smlm` · **Forward operator:** `smlm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Na | — | 1.49 | | T frames | — | 10000 | | Pixel nm | nm | 160 | | Background bias | — | 50 | | Drift nm per frame | — | 0 | | N emitters per frame | — | 50 | | Photons per molecule | — | 3000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | W | px | 64 – 2048 | | Na | — | 1.3 – 1.49 | | T frames | — | 1000 – 100000 | | Pixel nm | nm | 80 – 300 | | Background bias | — | 10 – 500 | | Blinking kinetics | — | 0.0 – 0.2 | | Drift nm per frame | — | 0.0 – 5.0 | | N emitters per frame | — | 5 – 500 | | Photons per molecule | — | 500 – 20000 | | Multi emitter overlap | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15.0 | Metric | Range | |---|---| | Localization nm | 0.5 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **localization_precision_nm**, with κ = `600` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9500e1c2916952fa19efc571aa507dfa579922aece34a60e32b8d25664d5fe42` - **Chain tx hash:** `0xf0725c4e2ead287799c36b1cd3c3aefef5bd5ba4a27a561860b90e8fa4db446e` - **Chain block:** `41554155` --- ## File Mapping This bundle consists of: `L1-011.md`, `L1-011.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-011.md` | Source of truth — edit this | Human or LLM | | `L1-011.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 `L1-011`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-011.md).
Regenerate L1-011.json so every field matches the Markdown.
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L2-011-001 PALM / STORM (single-molecule localization microscopy) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Microscopy",
  "hardness_fn": {
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    "kappa": 600,
    "metric": "localization_precision_nm",
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    "sensing_mechanism": "single_molecule_localization",
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    "sub_domain": "Single-molecule localization super-resolution",
    "title": "PALM / STORM (single-molecule localization microscopy)"
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      "drift_nm_per_frame": [
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      "multi_emitter_overlap": [
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      ],
      "photons_per_molecule": [
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      ],
      "pixel_nm": [
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        300
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Single-molecule localization super-resolution",
  "title": "PALM / STORM (single-molecule localization microscopy)"
}

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