L1 ⚛ L1-111 ⊙ Testnet

Industrial Computed Tomography (high-res x-ray CT for NDT)

Industrial Inspection · Micro-/nano-CT non-destructive inspection

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⬇ L1-111.md

# ⚛ L1 Principle — Industrial Computed Tomography (high-res x-ray CT for NDT) **ID:** `L1-111` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *Micro-/nano-CT non-destructive inspection* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D attenuation > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554199 --- ## 🧠 1. Introduction **Industrial Computed Tomography (high-res x-ray CT for NDT)** is a **linear inverse problem** whose unknown lives in **3D attenuation** space, within the **Micro-/nano-CT non-destructive inspection** sub-domain of **Industrial Inspection**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **xray ct** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; rotates source / detector to acquire different projections; exponential attenuation along the propagation path; spreads measurements back along source rays (adjoint operator); integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D attenuation 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 ~= 18); beam_hardening dominates the stability cliff; scatter and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → Angular scan → Beer-Lambert attenuation → Angular integration → **y** (detector). ``` y = ∫dΩ exp(-∫µ dl) R(θ) I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `S.scan.angular` | Rotates source / detector to acquire different projections | | `L.beer_lambert` | Exponential attenuation along the propagation path | | `int.angular` | Integration over the solid angle of incidence/emission | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `L.backproject` | Spreads measurements back along source rays (adjoint operator) | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | Micro-/nano-CT non-destructive inspection | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | 3D_attenuation | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 3D attenuation 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 ~= 18); beam_hardening dominates the stability cliff; scatter and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `industrial_ct` · **Forward operator:** `industrial_ct_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Z | — | 512 | | Kv | — | 150 | | Scatter | — | 0 | | Pixel um | µm | 50 | | Misalignment | — | 0 | | N projections | — | 720 | | Beam hardening | — | 0 | | Photon count per ray | — | 10000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 8192 | | W | px | 512 – 8192 | | Z | — | 64 – 4096 | | Kv | — | 20 – 450 | | Scatter | — | 0.0 – 0.4 | | Pixel um | µm | 0.5 – 500 | | Misalignment | — | 0.0 – 5.0 | | N projections | — | 180 – 4320 | | Ring artifact | — | 0.0 – 0.2 | | Beam hardening | — | 0.0 – 0.3 | | Photon count per ray | — | 100 – 100000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7b559b400db1df155a398cb129f8e36a0278ccc22d8a27905ead9b4e0641ce27` - **Chain tx hash:** `0x100aad798be7b7621886dff4347810c1c3dc6bf1934b65809a7b6f0378d8d6c0` - **Chain block:** `41554199` --- ## File Mapping This bundle consists of: `L1-111.md`, `L1-111.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-111.md` | Source of truth — edit this | Human or LLM | | `L1-111.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 `L1-111`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-111-001 Industrial Computed Tomography (high-res x-ray CT for NDT) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554199,
  "chain_hash": "0x7b559b400db1df155a398cb129f8e36a0278ccc22d8a27905ead9b4e0641ce27",
  "chain_tx_hash": "0x100aad798be7b7621886dff4347810c1c3dc6bf1934b65809a7b6f0378d8d6c0",
  "domain": "Industrial Inspection",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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  "observable_profile": {
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    "regime": "Existence of the recovered 3D attenuation 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 ~= 18); beam_hardening dominates the stability cliff; scatter and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
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    "difficulty_delta": 5,
    "domain": "Industrial Inspection",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
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      "S.scan.angular",
      "L.beer_lambert",
      "L.backproject",
      "int.angular"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "xray_ct",
    "solution_space": "3D_attenuation",
    "sub_domain": "Micro-/nano-CT non-destructive inspection",
    "title": "Industrial Computed Tomography (high-res x-ray CT for NDT)"
  },
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    "allowed_problem_classes": [
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    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
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        "N_projections": 720,
        "W": 2048,
        "Z": 512,
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        "pixel_um": 50,
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      "N_projections": [
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      "W": [
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      ],
      "Z": [
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      ],
      "beam_hardening": [
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        0.3
      ],
      "kV": [
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      ],
      "misalignment": [
        0.0,
        5.0
      ],
      "photon_count_per_ray": [
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      "pixel_um": [
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      ],
      "ring_artifact": [
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        0.2
      ],
      "scatter": [
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        0.4
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Micro-/nano-CT non-destructive inspection",
  "title": "Industrial Computed Tomography (high-res x-ray CT for NDT)"
}

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