L1 ⚛ L1-235 ⊙ Testnet

Method of Moments (MoM) — integral-equation EM

Electromagnetics · Surface/volume integral-equation MoM

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⬇ L1-235.md

# ⚛ L1 Principle — Method of Moments (MoM) — integral-equation EM **ID:** `L1-235` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Surface/volume integral-equation MoM* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** surface currents and rcs > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553987 --- ## 🧠 1. Introduction **Method of Moments (MoM) — integral-equation EM** is a **linear inverse problem** whose unknown lives in **surface currents and rcs** space, within the **Surface/volume integral-equation MoM** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **far field antenna** sensing mechanism. The forward operator applies, in order: L · efie mfie operator; L · rwg expand operator; L · linear solve 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 · efie mfie → L · rwg expand → L · linear solve → Frequency integration → **y** (detector). ``` y = ∫dω `L.linear_solve` `L.rwg_expand` `L.efie_mfie` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.efie_mfie` | L · efie mfie operator | | `L.rwg_expand` | L · rwg expand operator | | `L.linear_solve` | L · linear solve operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Surface/volume integral-equation MoM | | Carrier | em | | Problem class | linear_inverse | | Solution space | surface_currents_and_rcs | | 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:** `mom` · **Forward operator:** `mom_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N mesh | — | 10000 | | Snr db | dB | 30 | | N freqs | — | 16 | | Bc error | — | 0 | | N angles | — | 256 | | Mesh error | — | 0 | | Material error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N mesh | — | 100 – 1000000 | | Snr db | dB | 0 – 40 | | N freqs | — | 1 – 256 | | Bc error | — | 0.0 – 0.2 | | N angles | — | 16 – 4096 | | Mesh error | — | 0.0 – 0.1 | | Material error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xac55197b2796857a918394a278f96b1393e62a9abf97b5ef91c933988f63eb89` - **Chain tx hash:** `0x3e6b80bcaf774329b736d26a28e3bd016474af7295377d7a6fee61a0148aa730` - **Chain block:** `41553987` --- ## File Mapping This bundle consists of: `L1-235.md`, `L1-235.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-235.md` | Source of truth — edit this | Human or LLM | | `L1-235.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 `L1-235`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-235.md).
Regenerate L1-235.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-235-001 Method of Moments (MoM) — integral-equation EM Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-235",
  "chain_block": 41553987,
  "chain_hash": "0xac55197b2796857a918394a278f96b1393e62a9abf97b5ef91c933988f63eb89",
  "chain_tx_hash": "0x3e6b80bcaf774329b736d26a28e3bd016474af7295377d7a6fee61a0148aa730",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.efie_mfie",
      "L.rwg_expand",
      "L.linear_solve",
      "int.frequency"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "far_field_antenna",
    "solution_space": "surface_currents_and_rcs",
    "sub_domain": "Surface/volume integral-equation MoM",
    "title": "Method of Moments (MoM) \u2014 integral-equation EM"
  },
  "size_tiers": {
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      "mom_forward"
    ],
    "allowed_omega_dimensions": [
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      "N_freqs",
      "N_angles",
      "SNR_dB",
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      "material_error",
      "mesh_error",
      "BC_error",
      "material_error"
    ],
    "allowed_problem_classes": [
      "mom"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "mom_forward",
      "input_format": "measurement_only",
      "omega": {
        "BC_error": 0.0,
        "N_angles": 256,
        "N_freqs": 16,
        "N_mesh": 10000,
        "SNR_dB": 30,
        "material_error": 0.0,
        "mesh_error": 0.0
      },
      "problem_class": "mom"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "BC_error": [
        0.0,
        0.2
      ],
      "N_angles": [
        16,
        4096
      ],
      "N_freqs": [
        1,
        256
      ],
      "N_mesh": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "material_error": [
        0.0,
        0.1
      ],
      "mesh_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Surface/volume integral-equation MoM",
  "title": "Method of Moments (MoM) \u2014 integral-equation EM"
}

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