L1 ⚛ L1-232 ⊙ Testnet

Maxwell Full-Wave — time-domain 3D Maxwell equations

Electromagnetics · 3D vector Maxwell time-domain simulation

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⬇ L1-232.md

# ⚛ L1 Principle — Maxwell Full-Wave — time-domain 3D Maxwell equations **ID:** `L1-232` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *3D vector Maxwell time-domain simulation* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D E H field spacetime > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41553987 --- ## 🧠 1. Introduction **Maxwell Full-Wave — time-domain 3D Maxwell equations** is a **linear inverse problem** whose unknown lives in **3D E H field spacetime** space, within the **3D vector Maxwell time-domain simulation** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **near field probes** sensing mechanism. The forward operator applies, in order: L · source injection operator; L · curl curl operator; L · constitutive operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. CFL-stable explicit time stepping; ill-posed inverse for full 3D eps(x) reconstruction. ## ⚙ 2. Forward Model Physical chain: **x** → L · source injection → L · curl curl → L · constitutive → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.constitutive` `L.curl_curl` `L.source_injection` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.source_injection` | L · source injection operator | | `L.curl_curl` | L · curl curl operator | | `L.constitutive` | L · constitutive operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | 3D vector Maxwell time-domain simulation | | Carrier | em | | Problem class | linear_inverse | | Solution space | 3D_E_H_field_spacetime | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model CFL-stable explicit time stepping; ill-posed inverse for full 3D eps(x) reconstruction. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `maxwell_tm` · **Forward operator:** `maxwell_tm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 128 | | Snr db | dB | 30 | | N probes | — | 16 | | Mu error | — | 0 | | N samples | — | 512 | | Eps error | — | 0 | | Sigma error | — | 0 | | Boundary pml error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 32 – 1024 | | Snr db | dB | 0 – 40 | | N probes | — | 4 – 1024 | | Mu error | — | 0.0 – 0.05 | | N samples | — | 64 – 10000 | | Eps error | — | 0.0 – 0.1 | | Sigma error | — | 0.0 – 0.1 | | Boundary pml error | — | 0.0 – 0.2 | ## 🎯 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 = `1600` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x177babd070bb2e7be404fa90e2b0d96b63b48882e2d15ade5f0cc4a6167b8549` - **Chain tx hash:** `0x57a5672d690bb3e38a9ddc1a2f7d34b146ca09665ce82986a7a2123cd863b89c` - **Chain block:** `41553987` --- ## File Mapping This bundle consists of: `L1-232.md`, `L1-232.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-232.md` | Source of truth — edit this | Human or LLM | | `L1-232.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 `L1-232`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-232.md).
Regenerate L1-232.json so every field matches the Markdown.
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L2-232-001 Maxwell Full-Wave — time-domain 3D Maxwell equations Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553987,
  "chain_hash": "0x177babd070bb2e7be404fa90e2b0d96b63b48882e2d15ade5f0cc4a6167b8549",
  "chain_tx_hash": "0x57a5672d690bb3e38a9ddc1a2f7d34b146ca09665ce82986a7a2123cd863b89c",
  "domain": "Electromagnetics",
  "hardness_fn": {
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    "kappa": 1600,
    "metric": "PSNR_dB",
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    "regime": "CFL-stable explicit time stepping; ill-posed inverse for full 3D eps(x) reconstruction.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "em",
    "difficulty_delta": 10,
    "domain": "Electromagnetics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.source_injection",
      "L.curl_curl",
      "L.constitutive",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "near_field_probes",
    "solution_space": "3D_E_H_field_spacetime",
    "sub_domain": "3D vector Maxwell time-domain simulation",
    "title": "Maxwell Full-Wave \u2014 time-domain 3D Maxwell equations"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "W",
      "Z",
      "N_samples",
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      "SNR_dB",
      "eps_error",
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      "sigma_error",
      "boundary_PML_error",
      "eps_error",
      "mu_error",
      "sigma_error",
      "boundary_PML_error"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "maxwell_tm_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_probes": 16,
        "N_samples": 512,
        "SNR_dB": 30,
        "W": 128,
        "Z": 128,
        "boundary_PML_error": 0.0,
        "eps_error": 0.0,
        "mu_error": 0.0,
        "sigma_error": 0.0
      },
      "problem_class": "maxwell_tm"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "N_probes": [
        4,
        1024
      ],
      "N_samples": [
        64,
        10000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        32,
        1024
      ],
      "boundary_PML_error": [
        0.0,
        0.2
      ],
      "eps_error": [
        0.0,
        0.1
      ],
      "mu_error": [
        0.0,
        0.05
      ],
      "sigma_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "3D vector Maxwell time-domain simulation",
  "title": "Maxwell Full-Wave \u2014 time-domain 3D Maxwell equations"
}

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