L1 ⚛ L1-234 ⊙ Testnet

FDTD — finite-difference time-domain Maxwell

Electromagnetics · Yee-grid explicit FDTD

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⬇ L1-234.md

# ⚛ L1 Principle — FDTD — finite-difference time-domain Maxwell **ID:** `L1-234` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Yee-grid explicit FDTD* > **🎯 Problem class:** forward · **🧮 Solution space:** 3D E H field spacetime > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553987 --- ## 🧠 1. Introduction **FDTD — finite-difference time-domain Maxwell** is a **forward-model simulation** whose unknown lives in **3D E H field spacetime** space, within the **Yee-grid explicit FDTD** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **near field probes** sensing mechanism. The forward operator applies, in order: L · yee grid update operator; L · pml absorb operator; L · source inject operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · yee grid update → L · pml absorb → L · source inject → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.source_inject` `L.pml_absorb` `L.yee_grid_update` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.yee_grid_update` | L · yee grid update operator | | `L.pml_absorb` | L · pml absorb operator | | `L.source_inject` | L · source inject operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Yee-grid explicit FDTD | | Carrier | em | | Problem class | forward | | Solution space | 3D_E_H_field_spacetime | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 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:** `fdtd` · **Forward operator:** `fdtd_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Dt fs | — | 1 | | Snr db | dB | 30 | | N samples | — | 2000 | | Pml error | — | 0 | | Dispersion error | — | 0 | | Grid aniso error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | W | px | 64 – 2048 | | Z | — | 32 – 1024 | | Dt fs | — | 0.01 – 1000 | | Snr db | dB | 0 – 40 | | N samples | — | 100 – 100000 | | Pml error | — | 0.0 – 0.2 | | Dispersion error | — | 0.0 – 0.2 | | Grid aniso error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb05b69946152894d0562cf92ee6b9e93fa41b0db402a549fa3072367b256f224` - **Chain tx hash:** `0x9b1fab6c7e685e8c74648e83c47ae5545e2d1227a5004b97666c2242effc6b3f` - **Chain block:** `41553987` --- ## File Mapping This bundle consists of: `L1-234.md`, `L1-234.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-234.md` | Source of truth — edit this | Human or LLM | | `L1-234.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 `L1-234`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-234.md).
Regenerate L1-234.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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L2-234-001 FDTD — finite-difference time-domain Maxwell Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-234",
  "chain_block": 41553987,
  "chain_hash": "0xb05b69946152894d0562cf92ee6b9e93fa41b0db402a549fa3072367b256f224",
  "chain_tx_hash": "0x9b1fab6c7e685e8c74648e83c47ae5545e2d1227a5004b97666c2242effc6b3f",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.yee_grid_update",
      "L.pml_absorb",
      "L.source_inject",
      "int.temporal"
    ],
    "problem_class": "forward",
    "sensing_mechanism": "near_field_probes",
    "solution_space": "3D_E_H_field_spacetime",
    "sub_domain": "Yee-grid explicit FDTD",
    "title": "FDTD \u2014 finite-difference time-domain Maxwell"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fdtd_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_samples",
      "dt_fs",
      "SNR_dB",
      "grid_aniso_error",
      "pml_error",
      "dispersion_error",
      "grid_aniso_error",
      "pml_error",
      "dispersion_error"
    ],
    "allowed_problem_classes": [
      "fdtd"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "fdtd_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_samples": 2000,
        "SNR_dB": 30,
        "W": 256,
        "Z": 128,
        "dispersion_error": 0.0,
        "dt_fs": 1.0,
        "grid_aniso_error": 0.0,
        "pml_error": 0.0
      },
      "problem_class": "fdtd"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        2048
      ],
      "N_samples": [
        100,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        2048
      ],
      "Z": [
        32,
        1024
      ],
      "dispersion_error": [
        0.0,
        0.2
      ],
      "dt_fs": [
        0.01,
        1000
      ],
      "grid_aniso_error": [
        0.0,
        0.1
      ],
      "pml_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Yee-grid explicit FDTD",
  "title": "FDTD \u2014 finite-difference time-domain Maxwell"
}

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