L1 ⚛ L1-255 ⊙ Testnet

Microwave Imaging — permittivity imaging for biomed/NDE

Electromagnetics · Microwave tomography (biomedical/NDT)

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-255.md

# ⚛ L1 Principle — Microwave Imaging — permittivity imaging for biomed/NDE **ID:** `L1-255` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Microwave tomography (biomedical/NDT)* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D permittivity conductivity > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554001 --- ## 🧠 1. Introduction **Microwave Imaging — permittivity imaging for biomed/NDE** is a **nonlinear inverse problem** whose unknown lives in **3D permittivity conductivity** space, within the **Microwave tomography (biomedical/NDT)** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **antenna array** sensing mechanism. The forward operator applies, in order: L · incident field operator; L · scatter equation operator; L · born contrast operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Ill-posed, non-linear; limited data coverage typical. ## ⚙ 2. Forward Model Physical chain: **x** → L · incident field → L · scatter equation → L · born contrast → Frequency integration → **y** (detector). ``` y = ∫dω `L.born_contrast` `L.scatter_equation` `L.incident_field` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.incident_field` | L · incident field operator | | `L.scatter_equation` | L · scatter equation operator | | `L.born_contrast` | L · born contrast operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Microwave tomography (biomedical/NDT) | | Carrier | em | | Problem class | nonlinear_inverse | | Solution space | 3D_permittivity_conductivity | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Ill-posed, non-linear; limited data coverage typical. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `microwave_tomo` · **Forward operator:** `microwave_tomo_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 | | Snr db | dB | 25 | | N freqs | — | 16 | | N antennas | — | 16 | | Antenna pos error | — | 0 | | Skin effect error | — | 0 | | Coupling medium error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 8 – 512 | | Snr db | dB | -5 – 40 | | N freqs | — | 1 – 256 | | N antennas | — | 4 – 256 | | Antenna pos error | — | 0.0 – 0.05 | | Skin effect error | — | 0.0 – 0.3 | | Coupling medium error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x0d32f5f98bad358432597ff247ae7dcdf16e8bc1def752c1ab7d0bf1be4e4b8a` - **Chain tx hash:** `0x20f7ac378c74b2f0823163e759a924415974a215b15006a9d92d934c0f2c47c6` - **Chain block:** `41554001` --- ## File Mapping This bundle consists of: `L1-255.md`, `L1-255.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-255.md` | Source of truth — edit this | Human or LLM | | `L1-255.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 `L1-255`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-255.md).
Regenerate L1-255.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.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-255-001 Microwave Imaging — permittivity imaging for biomed/NDE Mismatch-Only Spec

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-255",
  "chain_block": 41554001,
  "chain_hash": "0x0d32f5f98bad358432597ff247ae7dcdf16e8bc1def752c1ab7d0bf1be4e4b8a",
  "chain_tx_hash": "0x20f7ac378c74b2f0823163e759a924415974a215b15006a9d92d934c0f2c47c6",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 800,
    "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": "Ill-posed, non-linear; limited data coverage typical.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.incident_field",
      "L.scatter_equation",
      "L.born_contrast",
      "int.frequency"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "antenna_array",
    "solution_space": "3D_permittivity_conductivity",
    "sub_domain": "Microwave tomography (biomedical/NDT)",
    "title": "Microwave Imaging \u2014 permittivity imaging for biomed/NDE"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "microwave_tomo_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_antennas",
      "N_freqs",
      "SNR_dB",
      "coupling_medium_error",
      "antenna_pos_error",
      "skin_effect_error",
      "coupling_medium_error",
      "antenna_pos_error",
      "skin_effect_error"
    ],
    "allowed_problem_classes": [
      "microwave_tomo"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "microwave_tomo_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_antennas": 16,
        "N_freqs": 16,
        "SNR_dB": 25,
        "W": 128,
        "Z": 32,
        "antenna_pos_error": 0.0,
        "coupling_medium_error": 0.0,
        "skin_effect_error": 0.0
      },
      "problem_class": "microwave_tomo"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "N_antennas": [
        4,
        256
      ],
      "N_freqs": [
        1,
        256
      ],
      "SNR_dB": [
        -5,
        40
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        8,
        512
      ],
      "antenna_pos_error": [
        0.0,
        0.05
      ],
      "coupling_medium_error": [
        0.0,
        0.2
      ],
      "skin_effect_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Microwave tomography (biomedical/NDT)",
  "title": "Microwave Imaging \u2014 permittivity imaging for biomed/NDE"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.