L1 ⚛ L1-114 ⊙ Testnet

Eddy-Current Testing (near-surface metallic defect detection)

Industrial Inspection · Electromagnetic induction NDT

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⬇ L1-114.md

# ⚛ L1 Principle — Eddy-Current Testing (near-surface metallic defect detection) **ID:** `L1-114` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *Electromagnetic induction NDT* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D conductivity map > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554199 --- ## 🧠 1. Introduction **Eddy-Current Testing (near-surface metallic defect detection)** is a **nonlinear inverse problem** whose unknown lives in **2D conductivity map** space, within the **Electromagnetic induction NDT** sub-domain of **Industrial Inspection**. Measurements consist of radio-frequency electromagnetic waves via a **eddy current impedance** sensing mechanism. The forward operator applies, in order: L · induce eddy current operator; L · secondary field operator; D · coil impedance operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D conductivity 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 ~= 10); lift_off_variation dominates the stability cliff; conductivity_variation 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 · induce eddy current → L · secondary field → D · coil impedance → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.coil_impedance` `L.secondary_field` `L.induce_eddy_current` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.induce_eddy_current` | L · induce eddy current operator | | `L.secondary_field` | L · secondary field operator | | `D.coil_impedance` | D · coil impedance operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | Electromagnetic induction NDT | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_conductivity_map | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 4. Measurement Model Existence of the recovered 2D conductivity 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 ~= 10); lift_off_variation dominates the stability cliff; conductivity_variation 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:** `eddy_current` · **Forward operator:** `eddy_current_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | F khz | kHz | 100 | | Snr db | dB | 25 | | Probe tilt | — | 0 | | Lift off mm | mm | 0.5 | | Lift off variation | — | 0 | | Conductivity variation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | W | px | 64 – 2048 | | F khz | kHz | 1 – 10000 | | Snr db | dB | 0.0 – 40.0 | | Probe tilt | — | 0.0 – 0.1 | | Edge effect | — | 0.0 – 0.3 | | Lift off mm | mm | 0.1 – 10.0 | | Lift off variation | — | 0.0 – 0.5 | | Conductivity variation | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | 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:** `0x78c128f1be5e55258ceb95273440343eaf9642fe82d1a703b459db13149524af` - **Chain tx hash:** `0x487b8f5c2ff8aab9fb21450660ba841b2bae9d83f6fd3dfe70f062e9ae2f1ec0` - **Chain block:** `41554199` --- ## File Mapping This bundle consists of: `L1-114.md`, `L1-114.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-114.md` | Source of truth — edit this | Human or LLM | | `L1-114.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 `L1-114`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-114.md).
Regenerate L1-114.json so every field matches the Markdown.
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L2-114-001 Eddy-Current Testing (near-surface metallic defect detection) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554199,
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  "chain_tx_hash": "0x487b8f5c2ff8aab9fb21450660ba841b2bae9d83f6fd3dfe70f062e9ae2f1ec0",
  "domain": "Industrial Inspection",
  "hardness_fn": {
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    "kappa": 200,
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    "noise_model": "gaussian",
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    "sub_domain": "Electromagnetic induction NDT",
    "title": "Eddy-Current Testing (near-surface metallic defect detection)"
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Electromagnetic induction NDT",
  "title": "Eddy-Current Testing (near-surface metallic defect detection)"
}

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