L1 ⚛ L1-239 ⊙ Testnet

Waveguide Modes — dispersion and S-parameter analysis

Electromagnetics · Rectangular/coax/photonic waveguide eigenmodes

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⬇ L1-239.md

# ⚛ L1 Principle — Waveguide Modes — dispersion and S-parameter analysis **ID:** `L1-239` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Rectangular/coax/photonic waveguide eigenmodes* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** modal fields and S params > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553988 --- ## 🧠 1. Introduction **Waveguide Modes — dispersion and S-parameter analysis** is a **linear inverse problem** whose unknown lives in **modal fields and S params** space, within the **Rectangular/coax/photonic waveguide eigenmodes** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **vna** sensing mechanism. The forward operator applies, in order: L · eigenmode solve operator; L · propagate operator; L · S param extract 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 · eigenmode solve → L · propagate → L · S param extract → Frequency integration → **y** (detector). ``` y = ∫dω `L.S_param_extract` `L.propagate` `L.eigenmode_solve` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.eigenmode_solve` | L · eigenmode solve operator | | `L.propagate` | L · propagate operator | | `L.S_param_extract` | L · s param extract operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Rectangular/coax/photonic waveguide eigenmodes | | Carrier | em | | Problem class | linear_inverse | | Solution space | modal_fields_and_S_params | | Noise model | gaussian | | Integration axis | frequency | | 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:** `waveguide` · **Forward operator:** `waveguide_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 40 | | N freqs | — | 401 | | N modes | — | 5 | | Dim error | — | 0 | | Freq ghz max | — | 40 | | Permittivity error | — | 0 | | Conductor loss error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 10 – 60 | | N freqs | — | 11 – 10001 | | N modes | — | 1 – 50 | | Dim error | — | 0.0 – 0.02 | | Freq ghz max | — | 0.1 – 500 | | Permittivity error | — | 0.0 – 0.1 | | Conductor loss error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2541b4c36b163d361b5e9cb6075371dc9f8930b168893777df997918e12d003c` - **Chain tx hash:** `0x16f6b3d47dd165786fe984a72ea9c4af02e4698f8e96e47df1e10e43fb8760b4` - **Chain block:** `41553988` --- ## File Mapping This bundle consists of: `L1-239.md`, `L1-239.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-239.md` | Source of truth — edit this | Human or LLM | | `L1-239.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 `L1-239`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-239.md).
Regenerate L1-239.json so every field matches the Markdown.
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L2-239-001 Waveguide Modes — dispersion and S-parameter analysis Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-239",
  "chain_block": 41553988,
  "chain_hash": "0x2541b4c36b163d361b5e9cb6075371dc9f8930b168893777df997918e12d003c",
  "chain_tx_hash": "0x16f6b3d47dd165786fe984a72ea9c4af02e4698f8e96e47df1e10e43fb8760b4",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "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": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.eigenmode_solve",
      "L.propagate",
      "L.S_param_extract",
      "int.frequency"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "vna",
    "solution_space": "modal_fields_and_S_params",
    "sub_domain": "Rectangular/coax/photonic waveguide eigenmodes",
    "title": "Waveguide Modes \u2014 dispersion and S-parameter analysis"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "waveguide_forward"
    ],
    "allowed_omega_dimensions": [
      "N_modes",
      "N_freqs",
      "freq_GHz_max",
      "SNR_dB",
      "dim_error",
      "permittivity_error",
      "conductor_loss_error",
      "dim_error",
      "permittivity_error",
      "conductor_loss_error"
    ],
    "allowed_problem_classes": [
      "waveguide"
    ],
    "center_spec": {
      "epsilon_fn_center": "28.0",
      "forward_operator": "waveguide_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_freqs": 401,
        "N_modes": 5,
        "SNR_dB": 40,
        "conductor_loss_error": 0.0,
        "dim_error": 0.0,
        "freq_GHz_max": 40,
        "permittivity_error": 0.0
      },
      "problem_class": "waveguide"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_freqs": [
        11,
        10001
      ],
      "N_modes": [
        1,
        50
      ],
      "SNR_dB": [
        10,
        60
      ],
      "conductor_loss_error": [
        0.0,
        0.3
      ],
      "dim_error": [
        0.0,
        0.02
      ],
      "freq_GHz_max": [
        0.1,
        500
      ],
      "permittivity_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rectangular/coax/photonic waveguide eigenmodes",
  "title": "Waveguide Modes \u2014 dispersion and S-parameter analysis"
}

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