L1 ⚛ L1-121 ⊙ Testnet

Magnetic Flux Leakage (MFL) — pipeline & rail inspection

Industrial Inspection · Ferromagnetic defect detection via DC flux

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⬇ L1-121.md

# ⚛ L1 Principle — Magnetic Flux Leakage (MFL) — pipeline & rail inspection **ID:** `L1-121` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *Ferromagnetic defect detection via DC flux* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D defect geometry > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554212 --- ## 🧠 1. Introduction **Magnetic Flux Leakage (MFL) — pipeline & rail inspection** is a **nonlinear inverse problem** whose unknown lives in **2D defect geometry** space, within the **Ferromagnetic defect detection via DC flux** sub-domain of **Industrial Inspection**. Measurements consist of radio-frequency electromagnetic waves via a **magnetic flux leakage** sensing mechanism. The forward operator applies, in order: L · dc magnetize operator; L · flux leakage operator; D · hall sensor operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D defect geometry 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 ~= 10); liftoff_variation dominates the stability cliff; magnetization_non_uniformity 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 · dc magnetize → L · flux leakage → D · hall sensor → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.hall_sensor` `L.flux_leakage` `L.dc_magnetize` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.dc_magnetize` | L · dc magnetize operator | | `L.flux_leakage` | L · flux leakage operator | | `D.hall_sensor` | D · hall sensor operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | Ferromagnetic defect detection via DC flux | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_defect_geometry | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered 2D defect geometry 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 ~= 10); liftoff_variation dominates the stability cliff; magnetization_non_uniformity 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:** `mfl` · **Forward operator:** `mfl_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 4096 | | Snr db | dB | 20 | | N sensors | — | 32 | | Lift off mm | mm | 1 | | Velocity mps | — | 1 | | Liftoff variation | — | 0 | | External interference | — | 0 | | Magnetization non uniformity | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 1024 | | W | px | 512 – 32768 | | Snr db | dB | 0.0 – 35.0 | | N sensors | — | 8 – 256 | | Lift off mm | mm | 0.1 – 10.0 | | Velocity mps | — | 0.1 – 20.0 | | Velocity effect | — | 0.0 – 0.3 | | Liftoff variation | — | 0.0 – 0.5 | | External interference | — | 0.0 – 0.3 | | Magnetization non uniformity | — | 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 = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x825452763bb821cbdb2021524f16bb0d0ae640804f619069ff7658a3da0bba70` - **Chain tx hash:** `0xe6800207eb22ce423a47944c47e17e8517582d6471756da23512a785c82074d6` - **Chain block:** `41554212` --- ## File Mapping This bundle consists of: `L1-121.md`, `L1-121.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-121.md` | Source of truth — edit this | Human or LLM | | `L1-121.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 `L1-121`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-121.md).
Regenerate L1-121.json so every field matches the Markdown.
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L2-121-001 Magnetic Flux Leakage (MFL) — pipeline & rail inspection Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Industrial Inspection",
  "hardness_fn": {
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    "noise_model": "gaussian",
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    "sensing_mechanism": "magnetic_flux_leakage",
    "solution_space": "2D_defect_geometry",
    "sub_domain": "Ferromagnetic defect detection via DC flux",
    "title": "Magnetic Flux Leakage (MFL) \u2014 pipeline \u0026 rail inspection"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Ferromagnetic defect detection via DC flux",
  "title": "Magnetic Flux Leakage (MFL) \u2014 pipeline \u0026 rail inspection"
}

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