L1 ⚛ L1-238 ⊙ Testnet

Eddy Currents — conductor inversion from induced fields

Electromagnetics · Quasi-static eddy-current inspection

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⬇ L1-238.md

# ⚛ L1 Principle — Eddy Currents — conductor inversion from induced fields **ID:** `L1-238` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Quasi-static eddy-current inspection* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** conductivity 3D map > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553988 --- ## 🧠 1. Introduction **Eddy Currents — conductor inversion from induced fields** is a **linear inverse problem** whose unknown lives in **conductivity 3D map** space, within the **Quasi-static eddy-current inspection** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **induction coil** sensing mechanism. The forward operator applies, in order: L · induced current operator; L · quasi static operator; L · diffuse through conductor operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · induced current → L · quasi static → L · diffuse through conductor → Frequency integration → **y** (detector). ``` y = ∫dω `L.diffuse_through_conductor` `L.quasi_static` `L.induced_current` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.induced_current` | L · induced current operator | | `L.quasi_static` | L · quasi static operator | | `L.diffuse_through_conductor` | L · diffuse through conductor operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Quasi-static eddy-current inspection | | Carrier | em | | Problem class | linear_inverse | | Solution space | conductivity_3D_map | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | 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 | 128 | | W | px | 128 | | Z | — | 32 | | N pos | — | 64 | | Snr db | dB | 30 | | N freqs | — | 16 | | Mu r error | — | 0 | | Sigma error | — | 0 | | Coil pos error | — | 0 | | Coil lift off error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 8 – 512 | | N pos | — | 4 – 1024 | | Snr db | dB | 0 – 40 | | N freqs | — | 1 – 256 | | Mu r error | — | 0.0 – 0.1 | | Sigma error | — | 0.0 – 0.1 | | Coil pos error | — | 0.0 – 0.02 | | Coil lift off error | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb42e8313c53bfab8498afd7c391ceb25e2c6cd9b6b7bdbbfaf33b3c408a3c5fd` - **Chain tx hash:** `0x0f46e71c1b23d7f577aad33fbfa2c5f675ad7a646fdd10054790d6ed4ef3c4fc` - **Chain block:** `41553988` --- ## File Mapping This bundle consists of: `L1-238.md`, `L1-238.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-238.md` | Source of truth — edit this | Human or LLM | | `L1-238.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 `L1-238`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-238.md).
Regenerate L1-238.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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L2-238-001 Eddy Currents — conductor inversion from induced fields Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553988,
  "chain_hash": "0xb42e8313c53bfab8498afd7c391ceb25e2c6cd9b6b7bdbbfaf33b3c408a3c5fd",
  "chain_tx_hash": "0x0f46e71c1b23d7f577aad33fbfa2c5f675ad7a646fdd10054790d6ed4ef3c4fc",
  "domain": "Electromagnetics",
  "hardness_fn": {
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    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
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  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
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      "L.diffuse_through_conductor",
      "int.frequency"
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    "sensing_mechanism": "induction_coil",
    "solution_space": "conductivity_3D_map",
    "sub_domain": "Quasi-static eddy-current inspection",
    "title": "Eddy Currents \u2014 conductor inversion from induced fields"
  },
  "size_tiers": {
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        "W": 128,
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      "W": [
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      "Z": [
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      "mu_r_error": [
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      "sigma_error": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Quasi-static eddy-current inspection",
  "title": "Eddy Currents \u2014 conductor inversion from induced fields"
}

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