L1 ⚛ L1-165 ⊙ Testnet

Magnetic Force Microscopy (MFM)

Scanning Probe · Magnetic cantilever probe for domain imaging

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⬇ L1-165.md

# ⚛ L1 Principle — Magnetic Force Microscopy (MFM) **ID:** `L1-165` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Scanning Probe — *Magnetic cantilever probe for domain imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D magnetization map > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554243 --- ## 🧠 1. Introduction **Magnetic Force Microscopy (MFM)** is a **nonlinear inverse problem** whose unknown lives in **2D magnetization map** space, within the **Magnetic cantilever probe for domain imaging** sub-domain of **Scanning Probe**. Measurements consist of radio-frequency electromagnetic waves via a **magnetic force microscopy** sensing mechanism. The forward operator applies, in order: L · magnetic cantilever operator; ordered pixel-by-pixel sampling; D · frequency shift operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D magnetization map 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 ~= 13); crosstalk_topography dominates the stability cliff; stray_field 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 · magnetic cantilever → Raster scan → D · frequency shift → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.frequency_shift` S_raster `L.magnetic_cantilever` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.magnetic_cantilever` | L · magnetic cantilever operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `D.frequency_shift` | D · frequency shift operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Scanning Probe | | Sub domain | Magnetic cantilever probe for domain imaging | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_magnetization_map | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Existence of the recovered 2D magnetization map 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 ~= 13); crosstalk_topography dominates the stability cliff; stray_field 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:** `mfm` · **Forward operator:** `mfm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 25 | | Pixel nm | nm | 20 | | Vibration | — | 0 | | Stray field | — | 0 | | Tip radius nm | nm | 30 | | Lift height nm | nm | 50 | | Crosstalk topography | — | 0 | | Tip magnetization drift | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 | | W | px | 64 | | Snr db | dB | 0.0 – 40.0 | | Pixel nm | nm | 2 – 500 | | Vibration | — | 0.0 – 0.3 | | Stray field | — | 0.0 – 0.3 | | Tip radius nm | nm | 5 – 200 | | Lift height nm | nm | 10 – 500 | | Crosstalk topography | — | 0.0 – 0.5 | | Tip magnetization drift | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `260` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x048b15a7a1b67344a1dbe9b1f26abb0db8f6f100361ced09a11621a64a8c9b10` - **Chain tx hash:** `0x8e4d93c8afe6fa828e687dd317430946dcaf68e7af60a5eddce68b250f3731dd` - **Chain block:** `41554243` --- ## File Mapping This bundle consists of: `L1-165.md`, `L1-165.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-165.md` | Source of truth — edit this | Human or LLM | | `L1-165.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 `L1-165`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-165.md).
Regenerate L1-165.json so every field matches the Markdown.
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L2-165-001 Magnetic Force Microscopy (MFM) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-165",
  "chain_block": 41554243,
  "chain_hash": "0x048b15a7a1b67344a1dbe9b1f26abb0db8f6f100361ced09a11621a64a8c9b10",
  "chain_tx_hash": "0x8e4d93c8afe6fa828e687dd317430946dcaf68e7af60a5eddce68b250f3731dd",
  "domain": "Scanning Probe",
  "hardness_fn": {
    "delta": 3,
    "kappa": 260,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D magnetization map 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 ~= 13); crosstalk_topography dominates the stability cliff; stray_field 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": 3.3,
    "carrier": "radio_wave",
    "difficulty_delta": 3,
    "domain": "Scanning Probe",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.magnetic_cantilever",
      "S.scan.raster",
      "D.frequency_shift",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "magnetic_force_microscopy",
    "solution_space": "2D_magnetization_map",
    "sub_domain": "Magnetic cantilever probe for domain imaging",
    "title": "Magnetic Force Microscopy (MFM)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mfm_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_nm",
      "lift_height_nm",
      "tip_radius_nm",
      "SNR_dB",
      "crosstalk_topography",
      "stray_field",
      "tip_magnetization_drift",
      "vibration",
      "crosstalk_topography",
      "stray_field",
      "tip_magnetization_drift",
      "vibration"
    ],
    "allowed_problem_classes": [
      "mfm"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "mfm_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "SNR_dB": 25,
        "W": 512,
        "crosstalk_topography": 0.0,
        "lift_height_nm": 50,
        "pixel_nm": 20,
        "stray_field": 0.0,
        "tip_magnetization_drift": 0.0,
        "tip_radius_nm": 30,
        "vibration": 0.0
      },
      "problem_class": "mfm"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": 64,
      "SNR_dB": [
        0.0,
        40.0
      ],
      "W": 64,
      "crosstalk_topography": [
        0.0,
        0.5
      ],
      "lift_height_nm": [
        10,
        500
      ],
      "pixel_nm": [
        2,
        500
      ],
      "stray_field": [
        0.0,
        0.3
      ],
      "tip_magnetization_drift": [
        0.0,
        0.3
      ],
      "tip_radius_nm": [
        5,
        200
      ],
      "vibration": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Magnetic cantilever probe for domain imaging",
  "title": "Magnetic Force Microscopy (MFM)"
}

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