L1 ⚛ L1-164 ⊙ Testnet

Near-Field Scanning Optical Microscopy (NSOM/SNOM)

Scanning Probe · Sub-diffraction optical microscopy via near-field aperture

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⬇ L1-164.md

# ⚛ L1 Principle — Near-Field Scanning Optical Microscopy (NSOM/SNOM) **ID:** `L1-164` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Scanning Probe — *Sub-diffraction optical microscopy via near-field aperture* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554243 --- ## 🧠 1. Introduction **Near-Field Scanning Optical Microscopy (NSOM/SNOM)** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Sub-diffraction optical microscopy via near-field aperture** sub-domain of **Scanning Probe**. Measurements consist of photons collected by an optical detector via a **near field scanning optical** sensing mechanism. The forward operator applies, in order: L · aperture near field operator; L · evanescent coupling operator; ordered pixel-by-pixel sampling; pixel-level spatial averaging on the detector. 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 holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 18); tip_sample_distance dominates the stability cliff; aperture_contamination 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 · aperture near field → L · evanescent coupling → Raster scan → Spatial integration → **y** (detector). ``` y = ∫_A dA S_raster `L.evanescent_coupling` `L.aperture_near_field` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.aperture_near_field` | L · aperture near field operator | | `L.evanescent_coupling` | L · evanescent coupling operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Scanning Probe | | Sub domain | Sub-diffraction optical microscopy via near-field aperture | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 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 moderately conditioned (kappa_eff ~= 18); tip_sample_distance dominates the stability cliff; aperture_contamination 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:** `nsom` · **Forward operator:** `nsom_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Snr db | dB | 25 | | Pixel nm | nm | 10 | | Aperture nm | nm | 50 | | Peak photons | photons | 500 | | Optical coupling | — | 1 | | Vibrational noise | — | 0 | | Tip sample distance | — | 5 | | Aperture contamination | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 | | W | px | 64 | | Snr db | dB | 0.0 – 40.0 | | Pixel nm | nm | 1 – 100 | | Aperture nm | nm | 10 – 500 | | Peak photons | photons | 10 – 10000 | | Optical coupling | — | 0.3 – 1.0 | | Vibrational noise | — | 0.0 – 0.3 | | Tip sample distance | — | 1 – 50 | | Aperture contamination | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x99d8c798110fcc57cd10d3c2a763abb60f2c31edd3dc4e1f80295042b154c2df` - **Chain tx hash:** `0x46f6816e4e09df7fb3aa235f506bd68228aca9ca9f8ab6640fe53c8770914266` - **Chain block:** `41554243` --- ## File Mapping This bundle consists of: `L1-164.md`, `L1-164.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-164.md` | Source of truth — edit this | Human or LLM | | `L1-164.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 `L1-164`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-164.md).
Regenerate L1-164.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-164-001 Near-Field Scanning Optical Microscopy (NSOM/SNOM) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-164",
  "chain_block": 41554243,
  "chain_hash": "0x99d8c798110fcc57cd10d3c2a763abb60f2c31edd3dc4e1f80295042b154c2df",
  "chain_tx_hash": "0x46f6816e4e09df7fb3aa235f506bd68228aca9ca9f8ab6640fe53c8770914266",
  "domain": "Scanning Probe",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "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 moderately conditioned (kappa_eff ~= 18); tip_sample_distance dominates the stability cliff; aperture_contamination 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": 3.8,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Scanning Probe",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.aperture_near_field",
      "L.evanescent_coupling",
      "S.scan.raster",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "near_field_scanning_optical",
    "solution_space": "2D_intensity",
    "sub_domain": "Sub-diffraction optical microscopy via near-field aperture",
    "title": "Near-Field Scanning Optical Microscopy (NSOM/SNOM)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "nsom_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "aperture_nm",
      "pixel_nm",
      "peak_photons",
      "tip_sample_distance",
      "aperture_contamination",
      "vibrational_noise",
      "optical_coupling",
      "SNR_dB",
      "tip_sample_distance",
      "aperture_contamination",
      "vibrational_noise",
      "optical_coupling"
    ],
    "allowed_problem_classes": [
      "nsom"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "nsom_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "SNR_dB": 25,
        "W": 256,
        "aperture_contamination": 0.0,
        "aperture_nm": 50,
        "optical_coupling": 1.0,
        "peak_photons": 500,
        "pixel_nm": 10,
        "tip_sample_distance": 5,
        "vibrational_noise": 0.0
      },
      "problem_class": "nsom"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": 64,
      "SNR_dB": [
        0.0,
        40.0
      ],
      "W": 64,
      "aperture_contamination": [
        0.0,
        0.5
      ],
      "aperture_nm": [
        10,
        500
      ],
      "optical_coupling": [
        0.3,
        1.0
      ],
      "peak_photons": [
        10,
        10000
      ],
      "pixel_nm": [
        1,
        100
      ],
      "tip_sample_distance": [
        1,
        50
      ],
      "vibrational_noise": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Sub-diffraction optical microscopy via near-field aperture",
  "title": "Near-Field Scanning Optical Microscopy (NSOM/SNOM)"
}

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