L1 ⚛ L1-249 ⊙ Testnet

Metamaterial / Metasurface — effective medium inversion

Electromagnetics · Effective permittivity/permeability retrieval

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⬇ L1-249.md

# ⚛ L1 Principle — Metamaterial / Metasurface — effective medium inversion **ID:** `L1-249` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Effective permittivity/permeability retrieval* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** effective medium params > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554000 --- ## 🧠 1. Introduction **Metamaterial / Metasurface — effective medium inversion** is a **nonlinear inverse problem** whose unknown lives in **effective medium params** space, within the **Effective permittivity/permeability retrieval** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **s params** sensing mechanism. The forward operator applies, in order: L · unit cell sim operator; L · s param extract operator; L · n eff retrieve 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 · unit cell sim → L · s param extract → L · n eff retrieve → Frequency integration → **y** (detector). ``` y = ∫dω `L.n_eff_retrieve` `L.s_param_extract` `L.unit_cell_sim` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.unit_cell_sim` | L · unit cell sim operator | | `L.s_param_extract` | L · s param extract operator | | `L.n_eff_retrieve` | L · n eff retrieve operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Effective permittivity/permeability retrieval | | Carrier | em | | Problem class | nonlinear_inverse | | Solution space | effective_medium_params | | 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:** `meta_extract` · **Forward operator:** `meta_extract_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 40 | | N freqs | — | 401 | | Loss error | — | 0 | | N unit cells | — | 10 | | Spatial dispersion error | — | 0 | | Unit cell geometry error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 10 – 60 | | N freqs | — | 11 – 10001 | | Loss error | — | 0.0 – 0.2 | | N unit cells | — | 1 – 100 | | Spatial dispersion error | — | 0.0 – 0.3 | | Unit cell geometry error | — | 0.0 – 0.05 | ## 🎯 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 = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x278bbded77fad6e6683db5bebd02f9cc8f1c00bac9f1f7a1255a65b088bd3e81` - **Chain tx hash:** `0xc3b109b584d22aa9766a55fbeab03feb9d9d35d0b26e8a7754da93344992ae3c` - **Chain block:** `41554000` --- ## File Mapping This bundle consists of: `L1-249.md`, `L1-249.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-249.md` | Source of truth — edit this | Human or LLM | | `L1-249.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 `L1-249`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-249.md).
Regenerate L1-249.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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L2-249-001 Metamaterial / Metasurface — effective medium inversion Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-249",
  "chain_block": 41554000,
  "chain_hash": "0x278bbded77fad6e6683db5bebd02f9cc8f1c00bac9f1f7a1255a65b088bd3e81",
  "chain_tx_hash": "0xc3b109b584d22aa9766a55fbeab03feb9d9d35d0b26e8a7754da93344992ae3c",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "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": 3.2,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.unit_cell_sim",
      "L.s_param_extract",
      "L.n_eff_retrieve",
      "int.frequency"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "s_params",
    "solution_space": "effective_medium_params",
    "sub_domain": "Effective permittivity/permeability retrieval",
    "title": "Metamaterial / Metasurface \u2014 effective medium inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "meta_extract_forward"
    ],
    "allowed_omega_dimensions": [
      "N_freqs",
      "N_unit_cells",
      "SNR_dB",
      "unit_cell_geometry_error",
      "spatial_dispersion_error",
      "loss_error",
      "unit_cell_geometry_error",
      "spatial_dispersion_error",
      "loss_error"
    ],
    "allowed_problem_classes": [
      "meta_extract"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "meta_extract_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_freqs": 401,
        "N_unit_cells": 10,
        "SNR_dB": 40,
        "loss_error": 0.0,
        "spatial_dispersion_error": 0.0,
        "unit_cell_geometry_error": 0.0
      },
      "problem_class": "meta_extract"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_freqs": [
        11,
        10001
      ],
      "N_unit_cells": [
        1,
        100
      ],
      "SNR_dB": [
        10,
        60
      ],
      "loss_error": [
        0.0,
        0.2
      ],
      "spatial_dispersion_error": [
        0.0,
        0.3
      ],
      "unit_cell_geometry_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Effective permittivity/permeability retrieval",
  "title": "Metamaterial / Metasurface \u2014 effective medium inversion"
}

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