L1 ⚛ L1-112 ⊙ Testnet

X-ray Non-Destructive Testing (2D radiography)

Industrial Inspection · 2D projection radiography for defect detection

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⬇ L1-112.md

# ⚛ L1 Principle — X-ray Non-Destructive Testing (2D radiography) **ID:** `L1-112` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *2D projection radiography for defect detection* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D attenuation projection > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554199 --- ## 🧠 1. Introduction **X-ray Non-Destructive Testing (2D radiography)** is a **linear inverse problem** whose unknown lives in **2D attenuation projection** space, within the **2D projection radiography for defect detection** sub-domain of **Industrial Inspection**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **xray projection** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; exponential attenuation along the propagation path; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D attenuation projection 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 well-conditioned (kappa_eff ~= 8); 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 mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → Beer-Lambert attenuation → Spatial integration → **y** (detector). ``` y = ∫_A dA exp(-∫µ dl) I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `L.beer_lambert` | Exponential attenuation along the propagation path | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | 2D projection radiography for defect detection | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | 2D_attenuation_projection | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered 2D attenuation projection 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 well-conditioned (kappa_eff ~= 8); 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 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:** `xray_ndt` · **Forward operator:** `xray_ndt_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Kv | — | 150 | | Scatter | — | 0 | | Pixel um | µm | 100 | | Photon count | — | 5000 | | Beam hardening | — | 0 | | Thickness variation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 8192 | | W | px | 512 – 8192 | | Kv | — | 20 – 450 | | Scatter | — | 0.0 – 0.4 | | Pixel um | µm | 1 – 500 | | Photon count | — | 100 – 100000 | | Beam hardening | — | 0.0 – 0.3 | | Thickness variation | — | 0.0 – 0.5 | | Source intensity drift | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x45ae0a0745a91fb54ed4ea22c7385cd1c7c8987636f0b49d00f54529f86ede3b` - **Chain tx hash:** `0xefd2535572644fe7ea98926b807253d2982b005655e87797e178e56372fc1791` - **Chain block:** `41554199` --- ## File Mapping This bundle consists of: `L1-112.md`, `L1-112.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-112.md` | Source of truth — edit this | Human or LLM | | `L1-112.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 `L1-112`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Regenerate L1-112.json so every field matches the Markdown.
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L2-112-001 X-ray Non-Destructive Testing (2D radiography) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Industrial Inspection",
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  "physics_fingerprint": {
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    "title": "X-ray Non-Destructive Testing (2D radiography)"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "2D projection radiography for defect detection",
  "title": "X-ray Non-Destructive Testing (2D radiography)"
}

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