L1 ⚛ L1-116 ⊙ Testnet

Terahertz Imaging (0.1-10 THz time-domain / CW)

Industrial Inspection · THz non-ionizing NDT for dielectrics

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⬇ L1-116.md

# ⚛ L1 Principle — Terahertz Imaging (0.1-10 THz time-domain / CW) **ID:** `L1-116` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *THz non-ionizing NDT for dielectrics* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D complex permittivity > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554200 --- ## 🧠 1. Introduction **Terahertz Imaging (0.1-10 THz time-domain / CW)** is a **linear inverse problem** whose unknown lives in **2D complex permittivity** space, within the **THz non-ionizing NDT for dielectrics** sub-domain of **Industrial Inspection**. Measurements consist of photons collected by an optical detector via a **terahertz time domain** sensing mechanism. The forward operator applies, in order: L · thz source operator; L · transmit sample operator; D · thz detector operator; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D complex permittivity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 14); water_absorption dominates the stability cliff; scattering_at_defects and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · thz source → L · transmit sample → D · thz detector → Spectral integration → **y** (detector). ``` y = Σ_λ `D.thz_detector` `L.transmit_sample` `L.thz_source` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.thz_source` | L · thz source operator | | `L.transmit_sample` | L · transmit sample operator | | `D.thz_detector` | D · thz detector operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | THz non-ionizing NDT for dielectrics | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_complex_permittivity | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Existence of the recovered 2D complex permittivity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 14); water_absorption dominates the stability cliff; scattering_at_defects and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `thz_tds` · **Forward operator:** `thz_tds_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | N freq | — | 512 | | Snr db | dB | 25 | | F thz range | — | 0.1 – 3.0 | | Dispersive media | — | 0 | | Water absorption | — | 0 | | Scattering at defects | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 1024 | | W | px | 64 – 1024 | | N freq | — | 64 – 2048 | | Snr db | dB | 5.0 – 40.0 | | Dispersive media | — | 0.0 – 0.5 | | Water absorption | — | 0.0 – 0.5 | | Power fluctuation | — | 0.0 – 0.2 | | Scattering at defects | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `280` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x839cd1b98c3b3cbdbacaeaa4d3d04a75a42c879d3fceb2de3e4f5af6d94feb8a` - **Chain tx hash:** `0x836aca69bc1e555bfa41b3bb9763e89c14834f8937db6d60ce16951a4e4bbb5c` - **Chain block:** `41554200` --- ## File Mapping This bundle consists of: `L1-116.md`, `L1-116.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-116.md` | Source of truth — edit this | Human or LLM | | `L1-116.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 `L1-116`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-116.md).
Regenerate L1-116.json so every field matches the Markdown.
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L2-116-001 Terahertz Imaging (0.1-10 THz time-domain / CW) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554200,
  "chain_hash": "0x839cd1b98c3b3cbdbacaeaa4d3d04a75a42c879d3fceb2de3e4f5af6d94feb8a",
  "chain_tx_hash": "0x836aca69bc1e555bfa41b3bb9763e89c14834f8937db6d60ce16951a4e4bbb5c",
  "domain": "Industrial Inspection",
  "hardness_fn": {
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    "kappa": 280,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "regime": "Existence of the recovered 2D complex permittivity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 14); water_absorption dominates the stability cliff; scattering_at_defects and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
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    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Industrial Inspection",
    "integration_axis": "spectral",
    "noise_model": "gaussian",
    "primitives": [
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      "L.transmit_sample",
      "D.thz_detector",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "terahertz_time_domain",
    "solution_space": "2D_complex_permittivity",
    "sub_domain": "THz non-ionizing NDT for dielectrics",
    "title": "Terahertz Imaging (0.1-10 THz time-domain / CW)"
  },
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      "W",
      "N_freq",
      "f_THz_range",
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      "water_absorption",
      "scattering_at_defects",
      "dispersive_media",
      "water_absorption",
      "scattering_at_defects",
      "dispersive_media",
      "power_fluctuation"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
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        "dispersive_media": 0.0,
        "f_THz_range": [
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        "water_absorption": 0.0
      },
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        40.0
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      "N_freq": [
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        2048
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      "SNR_dB": [
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        40.0
      ],
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        1024
      ],
      "dispersive_media": [
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        0.5
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      "power_fluctuation": [
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        0.2
      ],
      "scattering_at_defects": [
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        0.3
      ],
      "water_absorption": [
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        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "THz non-ionizing NDT for dielectrics",
  "title": "Terahertz Imaging (0.1-10 THz time-domain / CW)"
}

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