L1 ⚛ L1-118 ⊙ Testnet

X-Ray Fluorescence (XRF) Mapping

Industrial Inspection · Elemental mapping via characteristic X-ray fluorescence

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⬇ L1-118.md

# ⚛ L1 Principle — X-Ray Fluorescence (XRF) Mapping **ID:** `L1-118` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *Elemental mapping via characteristic X-ray fluorescence* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** elemental concentration map > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554200 --- ## 🧠 1. Introduction **X-Ray Fluorescence (XRF) Mapping** is a **linear inverse problem** whose unknown lives in **elemental concentration map** space, within the **Elemental mapping via characteristic X-ray fluorescence** sub-domain of **Industrial Inspection**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **xrf characteristic xray** sensing mechanism. The forward operator applies, in order: L · xray excitation operator; L · fluorescence emission operator; D · energy dispersive operator; detector sums all spectral bands. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered elemental concentration map 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 ~= 10); matrix_effect dominates the stability cliff; detector_dead_time 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** → L · xray excitation → L · fluorescence emission → D · energy dispersive → Spectral integration → **y** (detector). ``` y = Σ_λ `D.energy_dispersive` `L.fluorescence_emission` `L.xray_excitation` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_excitation` | L · xray excitation operator | | `L.fluorescence_emission` | L · fluorescence emission operator | | `D.energy_dispersive` | D · energy dispersive operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | Elemental mapping via characteristic X-ray fluorescence | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | elemental_concentration_map | | Noise model | shot_poisson | | Integration axis | spectral | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered elemental concentration map 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 ~= 10); matrix_effect dominates the stability cliff; detector_dead_time 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:** `xrf_mapping` · **Forward operator:** `xrf_mapping_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Kv | — | 30 | | Dwell ms | ms | 100 | | N elements | — | 10 | | Peak counts | — | 1000 | | Peak overlap | — | 0 | | Matrix effect | — | 0 | | Detector dead time | — | 0.05 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 4096 | | W | px | 64 – 4096 | | Kv | — | 10 – 50 | | Dwell ms | ms | 1 – 10000 | | N elements | — | 2 – 30 | | Peak counts | — | 20 – 100000 | | Peak overlap | — | 0.0 – 0.5 | | Matrix effect | — | 0.0 – 0.3 | | Self absorption | — | 0.0 – 0.5 | | Detector dead time | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xcf09b2dc819f67c811fd9056d3087ec4dbd8966173db2fa3f7e6b1669f849d9d` - **Chain tx hash:** `0x07d27827c55f2a2ada2a79815290bca084c190e32e3fc9f542ff8dbf35146971` - **Chain block:** `41554200` --- ## File Mapping This bundle consists of: `L1-118.md`, `L1-118.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-118.md` | Source of truth — edit this | Human or LLM | | `L1-118.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 `L1-118`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-118.md).
Regenerate L1-118.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-118-001 X-Ray Fluorescence (XRF) Mapping Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554200,
  "chain_hash": "0xcf09b2dc819f67c811fd9056d3087ec4dbd8966173db2fa3f7e6b1669f849d9d",
  "chain_tx_hash": "0x07d27827c55f2a2ada2a79815290bca084c190e32e3fc9f542ff8dbf35146971",
  "domain": "Industrial Inspection",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "regime": "Existence of the recovered elemental concentration map 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 ~= 10); matrix_effect dominates the stability cliff; detector_dead_time 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.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
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    "carrier": "x_ray",
    "difficulty_delta": 3,
    "domain": "Industrial Inspection",
    "integration_axis": "spectral",
    "noise_model": "shot_poisson",
    "primitives": [
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      "L.fluorescence_emission",
      "D.energy_dispersive",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "xrf_characteristic_xray",
    "solution_space": "elemental_concentration_map",
    "sub_domain": "Elemental mapping via characteristic X-ray fluorescence",
    "title": "X-Ray Fluorescence (XRF) Mapping"
  },
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      "peak_overlap",
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      "detector_dead_time",
      "peak_overlap",
      "self_absorption"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "xrf_mapping_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_elements": 10,
        "W": 512,
        "detector_dead_time": 0.05,
        "dwell_ms": 100,
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        "matrix_effect": 0.0,
        "peak_counts": 1000,
        "peak_overlap": 0.0
      },
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    },
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      ]
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      "N_elements": [
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      "detector_dead_time": [
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      "dwell_ms": [
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      ],
      "kV": [
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        50
      ],
      "matrix_effect": [
        0.0,
        0.3
      ],
      "peak_counts": [
        20,
        100000
      ],
      "peak_overlap": [
        0.0,
        0.5
      ],
      "self_absorption": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Elemental mapping via characteristic X-ray fluorescence",
  "title": "X-Ray Fluorescence (XRF) Mapping"
}

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