L1 ⚛ L1-113 ⊙ Testnet

Phased-Array Ultrasonic Testing (PAUT)

Industrial Inspection · Electronically steered ultrasonic NDT

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⬇ L1-113.md

# ⚛ L1 Principle — Phased-Array Ultrasonic Testing (PAUT) **ID:** `L1-113` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *Electronically steered ultrasonic NDT* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D acoustic reflectivity > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554199 --- ## 🧠 1. Introduction **Phased-Array Ultrasonic Testing (PAUT)** is a **linear inverse problem** whose unknown lives in **2D acoustic reflectivity** space, within the **Electronically steered ultrasonic NDT** sub-domain of **Industrial Inspection**. Measurements consist of acoustic pressure waves recorded by transducers via a **phased array ultrasonics** sensing mechanism. The forward operator applies, in order: L · emit · acoustic pulse operator; S · scan · beam operator; L · beamform operator; L · time of flight operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D acoustic reflectivity 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 ~= 15); wedge_coupling dominates the stability cliff; surface_curvature 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 · emit · acoustic pulse → S · scan · beam → L · beamform → L · time of flight → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.time_of_flight` `L.beamform` `S.scan.beam` `L.emit.acoustic_pulse` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.acoustic_pulse` | L · emit · acoustic pulse operator | | `S.scan.beam` | S · scan · beam operator | | `L.beamform` | L · beamform operator | | `L.time_of_flight` | L · time of flight operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | Electronically steered ultrasonic NDT | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | 2D_acoustic_reflectivity | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 2D acoustic reflectivity 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 ~= 15); wedge_coupling dominates the stability cliff; surface_curvature 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:** `phased_array_ut` · **Forward operator:** `phased_array_ut_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | F mhz | MHz | 5 | | Snr db | dB | 20 | | N angles | — | 41 | | Range mm | mm | 50 | | N elements | — | 64 | | Wedge coupling | — | 1 | | Surface curvature | — | 0 | | Sound speed uncertainty | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | F mhz | MHz | 0.5 – 25 | | Snr db | dB | 0.0 – 30.0 | | N angles | — | 11 – 181 | | Range mm | mm | 5 – 500 | | N elements | — | 16 – 256 | | Grain noise | — | 0.0 – 0.3 | | Wedge coupling | — | 0.3 – 1.0 | | Surface curvature | — | 0.0 – 0.5 | | Sound speed uncertainty | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x04b9ce328cccc779c8cf7a86aeb316631fbee998d4028e1e77906c41921f0fdd` - **Chain tx hash:** `0x1144f8a7e13835f72ab1069eee668feab474ebf3f871988bf68365b4e3aa68c8` - **Chain block:** `41554199` --- ## File Mapping This bundle consists of: `L1-113.md`, `L1-113.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-113.md` | Source of truth — edit this | Human or LLM | | `L1-113.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 `L1-113`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-113.md).
Regenerate L1-113.json so every field matches the Markdown.
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L2-113-001 Phased-Array Ultrasonic Testing (PAUT) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554199,
  "chain_hash": "0x04b9ce328cccc779c8cf7a86aeb316631fbee998d4028e1e77906c41921f0fdd",
  "chain_tx_hash": "0x1144f8a7e13835f72ab1069eee668feab474ebf3f871988bf68365b4e3aa68c8",
  "domain": "Industrial Inspection",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "PSNR_dB",
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    "secondary": "SSIM"
  },
  "physics_fingerprint": {
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    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Industrial Inspection",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
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      "S.scan.beam",
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      "int.temporal"
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    "sensing_mechanism": "phased_array_ultrasonics",
    "solution_space": "2D_acoustic_reflectivity",
    "sub_domain": "Electronically steered ultrasonic NDT",
    "title": "Phased-Array Ultrasonic Testing (PAUT)"
  },
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      "range_mm",
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      "surface_curvature",
      "sound_speed_uncertainty",
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      "grain_noise"
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      "input_format": "measurement_only",
      "omega": {
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        "N_elements": 64,
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        "wedge_coupling": 1.0
      },
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        40.0
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        181
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      "N_elements": [
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      "SNR_dB": [
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      ],
      "f_MHz": [
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      "range_mm": [
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      ],
      "sound_speed_uncertainty": [
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        0.05
      ],
      "surface_curvature": [
        0.0,
        0.5
      ],
      "wedge_coupling": [
        0.3,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Electronically steered ultrasonic NDT",
  "title": "Phased-Array Ultrasonic Testing (PAUT)"
}

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