L1 ⚛ L1-236 ⊙ Testnet

Antenna Analysis — radiation pattern inversion

Electromagnetics · Antenna near/far-field pattern synthesis

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⬇ L1-236.md

# ⚛ L1 Principle — Antenna Analysis — radiation pattern inversion **ID:** `L1-236` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Antenna near/far-field pattern synthesis* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** radiation pattern 2D > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553987 --- ## 🧠 1. Introduction **Antenna Analysis — radiation pattern inversion** is a **linear inverse problem** whose unknown lives in **radiation pattern 2D** space, within the **Antenna near/far-field pattern synthesis** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **anechoic chamber** sensing mechanism. The forward operator applies, in order: L · source current operator; L · array factor operator; L · radiate farfield operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · source current → L · array factor → L · radiate farfield → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.radiate_farfield` `L.array_factor` `L.source_current` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.source_current` | L · source current operator | | `L.array_factor` | L · array factor operator | | `L.radiate_farfield` | L · radiate farfield operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Antenna near/far-field pattern synthesis | | Carrier | em | | Problem class | linear_inverse | | Solution space | radiation_pattern_2D | | Noise model | gaussian | | Integration axis | spatial | | 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:** `antenna_radiation` · **Forward operator:** `antenna_radiation_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N phi | — | 361 | | Snr db | dB | 30 | | N theta | — | 361 | | Freq ghz | GHz | 10 | | Pos error | — | 0 | | N elements | — | 16 | | Phase error | — | 0 | | Amplitude error | — | 0 | | Mutual coupling error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N phi | — | 36 – 3600 | | Snr db | dB | 0 – 40 | | N theta | — | 36 – 3600 | | Freq ghz | GHz | 0.1 – 300 | | Pos error | — | 0.0 – 0.05 | | N elements | — | 1 – 4096 | | Phase error | — | 0.0 – 0.2 | | Amplitude error | — | 0.0 – 0.2 | | Mutual coupling error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5f8661333309273fc67e41a7edf222ddbdc9139419daa91591ae219c8aaac3ac` - **Chain tx hash:** `0x3c0214ed248c0967874325a64faca642db9500843041c074f6e85467c6ba0597` - **Chain block:** `41553987` --- ## File Mapping This bundle consists of: `L1-236.md`, `L1-236.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-236.md` | Source of truth — edit this | Human or LLM | | `L1-236.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 `L1-236`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-236.md).
Regenerate L1-236.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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L2-236-001 Antenna Analysis — radiation pattern inversion Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553987,
  "chain_hash": "0x5f8661333309273fc67e41a7edf222ddbdc9139419daa91591ae219c8aaac3ac",
  "chain_tx_hash": "0x3c0214ed248c0967874325a64faca642db9500843041c074f6e85467c6ba0597",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
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  "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": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.source_current",
      "L.array_factor",
      "L.radiate_farfield",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "anechoic_chamber",
    "solution_space": "radiation_pattern_2D",
    "sub_domain": "Antenna near/far-field pattern synthesis",
    "title": "Antenna Analysis \u2014 radiation pattern inversion"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "N_theta",
      "N_phi",
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      "mutual_coupling_error",
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      "mutual_coupling_error"
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    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "antenna_radiation_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_phi": 361,
        "N_theta": 361,
        "SNR_dB": 30,
        "amplitude_error": 0.0,
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        "phase_error": 0.0,
        "pos_error": 0.0
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    "epsilon_bounds": {
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    "omega_bounds": {
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      ],
      "N_phi": [
        36,
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      ],
      "N_theta": [
        36,
        3600
      ],
      "SNR_dB": [
        0,
        40
      ],
      "amplitude_error": [
        0.0,
        0.2
      ],
      "freq_GHz": [
        0.1,
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      ],
      "mutual_coupling_error": [
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      ],
      "phase_error": [
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        0.2
      ],
      "pos_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Antenna near/far-field pattern synthesis",
  "title": "Antenna Analysis \u2014 radiation pattern inversion"
}

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