L1 ⚛ L1-162 ⊙ Testnet

Atomic Force Microscopy (AFM)

Scanning Probe · Cantilever-tip topography

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Markdown — human-readable source of truth

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⬇ L1-162.md

# ⚛ L1 Principle — Atomic Force Microscopy (AFM) **ID:** `L1-162` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Scanning Probe — *Cantilever-tip topography* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D topography > **📡 Carrier:** none · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554242 --- ## 🧠 1. Introduction **Atomic Force Microscopy (AFM)** is a **nonlinear inverse problem** whose unknown lives in **2D topography** space, within the **Cantilever-tip topography** sub-domain of **Scanning Probe**. Measurements consist of none via a **atomic force microscopy** sensing mechanism. The forward operator applies, in order: L · cantilever oscillator operator; ordered pixel-by-pixel sampling; D · laser deflection operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D topography 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 ~= 12); tip_convolution dominates the stability cliff; thermal_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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** → L · cantilever oscillator → Raster scan → D · laser deflection → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.laser_deflection` S_raster `L.cantilever_oscillator` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.cantilever_oscillator` | L · cantilever oscillator operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `D.laser_deflection` | D · laser deflection operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Scanning Probe | | Sub domain | Cantilever-tip topography | | Carrier | none | | Problem class | nonlinear_inverse | | Solution space | 2D_topography | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered 2D topography 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 ~= 12); tip_convolution dominates the stability cliff; thermal_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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:** `afm` · **Forward operator:** `afm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 30 | | Pixel nm | nm | 2 | | Tip wear | — | 0 | | Thermal drift | — | 0 | | Tip radius nm | nm | 5 | | Tip convolution | — | 0 | | Nonlinear response | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Snr db | dB | 0.0 – 40.0 | | Pixel nm | nm | 0.1 – 100 | | Tip wear | — | 0.0 – 0.5 | | Thermal drift | — | 0.0 – 10 | | Tip radius nm | nm | 1 – 100 | | Tip convolution | — | 0.0 – 0.5 | | Nonlinear response | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3fcf235db9b4136a596c788864ecece37e46c781e5310c6939d9db3260c050ca` - **Chain tx hash:** `0x247e631b2b7c81daaae99bcc2e4381d9ccbcc12d28717404ddbc7df44d0add58` - **Chain block:** `41554242` --- ## File Mapping This bundle consists of: `L1-162.md`, `L1-162.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-162.md` | Source of truth — edit this | Human or LLM | | `L1-162.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 `L1-162`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-162.md).
Regenerate L1-162.json so every field matches the Markdown.
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L2-162-001 Atomic Force Microscopy (AFM) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554242,
  "chain_hash": "0x3fcf235db9b4136a596c788864ecece37e46c781e5310c6939d9db3260c050ca",
  "chain_tx_hash": "0x247e631b2b7c81daaae99bcc2e4381d9ccbcc12d28717404ddbc7df44d0add58",
  "domain": "Scanning Probe",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D topography 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 ~= 12); tip_convolution dominates the stability cliff; thermal_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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": 3.0,
    "carrier": "none",
    "difficulty_delta": 3,
    "domain": "Scanning Probe",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.cantilever_oscillator",
      "S.scan.raster",
      "D.laser_deflection",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "atomic_force_microscopy",
    "solution_space": "2D_topography",
    "sub_domain": "Cantilever-tip topography",
    "title": "Atomic Force Microscopy (AFM)"
  },
  "size_tiers": {
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      "W",
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      "tip_radius_nm",
      "tip_convolution",
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      "tip_wear",
      "nonlinear_response",
      "SNR_dB",
      "tip_convolution",
      "thermal_drift",
      "tip_wear",
      "nonlinear_response"
    ],
    "allowed_problem_classes": [
      "afm"
    ],
    "center_spec": {
      "epsilon_fn_center": "28.0",
      "forward_operator": "afm_forward",
      "input_format": "measurement_only",
      "omega": {
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        "SNR_dB": 30,
        "W": 512,
        "nonlinear_response": 0.0,
        "pixel_nm": 2,
        "thermal_drift": 0.0,
        "tip_convolution": 0.0,
        "tip_radius_nm": 5,
        "tip_wear": 0.0
      },
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    "epsilon_bounds": {
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        40.0
      ]
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    "omega_bounds": {
      "H": 128,
      "SNR_dB": [
        0.0,
        40.0
      ],
      "W": 128,
      "nonlinear_response": [
        0.0,
        0.3
      ],
      "pixel_nm": [
        0.1,
        100
      ],
      "thermal_drift": [
        0.0,
        10
      ],
      "tip_convolution": [
        0.0,
        0.5
      ],
      "tip_radius_nm": [
        1,
        100
      ],
      "tip_wear": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cantilever-tip topography",
  "title": "Atomic Force Microscopy (AFM)"
}

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