L1 ⚛ L1-015 ⊙ Testnet

MINFLUX (minimum-photon single-molecule localization)

Microscopy · Doughnut-beam nanometer localization

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⬇ L1-015.md

# ⚛ L1 Principle — MINFLUX (minimum-photon single-molecule localization) **ID:** `L1-015` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Doughnut-beam nanometer localization* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** point list > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554155 --- ## 🧠 1. Introduction **MINFLUX (minimum-photon single-molecule localization)** is a **nonlinear inverse problem** whose unknown lives in **point list** space, within the **Doughnut-beam nanometer localization** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **minflux targeted donut** sensing mechanism. The forward operator applies, in order: L · excitation · donut array operator; D · threshold · photon 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 ~= 25); beam_position_error dominates the stability cliff; background_count 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 · excitation · donut array → D · threshold · photon → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.threshold.photon` `L.excitation.donut_array` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.donut_array` | L · excitation · donut array operator | | `D.threshold.photon` | D · threshold · photon operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Doughnut-beam nanometer localization | | 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 ~= 25); beam_position_error dominates the stability cliff; background_count 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:** `minflux` · **Forward operator:** `minflux_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 64 | | W | px | 64 | | L nm | nm | 150 | | N beams | — | 4 | | Drift nm | nm | 0 | | Background count | — | 1 | | Beam position error | — | 0.5 | | Photons per localization | — | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 256 | | W | px | 32 – 256 | | L nm | nm | 50 – 500 | | N beams | — | 4 – 6 | | Drift nm | nm | 0.0 – 3.0 | | Background count | — | 0 – 20 | | Beam position error | — | 0.0 – 3.0 | | Photons per localization | — | 20 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 2.0 | Metric | Range | |---|---| | Localization nm | 0.5 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **localization_precision_nm**, with κ = `500` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc32ce518f71665e922e0374cfc7b018ee616877f51c91c373920de517797d27b` - **Chain tx hash:** `0x6ad96130aad7b4193086cad654f43635971823d6429461f37116baa706e4a95a` - **Chain block:** `41554155` --- ## File Mapping This bundle consists of: `L1-015.md`, `L1-015.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-015.md` | Source of truth — edit this | Human or LLM | | `L1-015.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 `L1-015`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-015-001 MINFLUX (minimum-photon single-molecule localization) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Microscopy",
  "hardness_fn": {
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    "integration_axis": "temporal",
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    "sensing_mechanism": "minflux_targeted_donut",
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    "sub_domain": "Doughnut-beam nanometer localization",
    "title": "MINFLUX (minimum-photon single-molecule localization)"
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      "beam_position_error",
      "background_count",
      "drift_nm"
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    "allowed_problem_classes": [
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    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
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        "L_nm": 150,
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      "beam_position_error": [
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      ],
      "drift_nm": [
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        3.0
      ],
      "photons_per_localization": [
        20,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Doughnut-beam nanometer localization",
  "title": "MINFLUX (minimum-photon single-molecule localization)"
}

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