L1 ⚛ L1-094 ⊙ Testnet

STEM-EDX — X-ray energy-dispersive elemental mapping

Electron Microscopy · Chemical composition via characteristic X-rays

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⬇ L1-094.md

# ⚛ L1 Principle — STEM-EDX — X-ray energy-dispersive elemental mapping **ID:** `L1-094` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Chemical composition via characteristic X-rays* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** elemental concentration map > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554185 --- ## 🧠 1. Introduction **STEM-EDX — X-ray energy-dispersive elemental mapping** is a **linear inverse problem** whose unknown lives in **elemental concentration map** space, within the **Chemical composition via characteristic X-rays** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **edx characteristic xray** sensing mechanism. The forward operator applies, in order: L · illumination · convergent probe operator; ordered pixel-by-pixel sampling; D · edx detector 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); detector_dead_time dominates the stability cliff; peak_overlap 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 · illumination · convergent probe → Raster scan → D · edx detector → Spectral integration → **y** (detector). ``` y = Σ_λ `D.edx_detector` S_raster `L.illumination.convergent_probe` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.illumination.convergent_probe` | L · illumination · convergent probe operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `D.edx_detector` | D · edx detector operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Chemical composition via characteristic X-rays | | Carrier | electron | | Problem class | linear_inverse | | Solution space | elemental_concentration_map | | Noise model | shot_poisson | | Integration axis | spectral | | Difficulty delta | 3 | | L dag | 3.4 | ## 📡 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); detector_dead_time dominates the stability cliff; peak_overlap 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:** `stem_edx` · **Forward operator:** `stem_edx_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Kv | — | 200 | | Dwell ms | ms | 5 | | N elements | — | 6 | | Peak overlap | — | 0 | | Peak electrons | — | 1000 | | Detector dead time | — | 0.1 | | Absorption correction | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Kv | — | 60 – 300 | | Dwell ms | ms | 0.1 – 1000 | | N elements | — | 2 – 30 | | Peak overlap | — | 0.0 – 0.5 | | Peak electrons | — | 50 – 100000 | | Detector dead time | — | 0.0 – 0.5 | | Absorption correction | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 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:** `0x9e7ec6f14b81d585009a8ebebd67a34c5ae7609a79cd195746e71996cb81c2c0` - **Chain tx hash:** `0xff096da21fdb8ac871c47eb8415020407f18667343b8f0c1bde7a89eb2b5cf80` - **Chain block:** `41554185` --- ## File Mapping This bundle consists of: `L1-094.md`, `L1-094.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-094.md` | Source of truth — edit this | Human or LLM | | `L1-094.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 `L1-094`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-094.md).
Regenerate L1-094.json so every field matches the Markdown.
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L2-094-001 STEM-EDX — X-ray energy-dispersive elemental mapping Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-094",
  "chain_block": 41554185,
  "chain_hash": "0x9e7ec6f14b81d585009a8ebebd67a34c5ae7609a79cd195746e71996cb81c2c0",
  "chain_tx_hash": "0xff096da21fdb8ac871c47eb8415020407f18667343b8f0c1bde7a89eb2b5cf80",
  "domain": "Electron Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
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  "observable_profile": {
    "metric": "PSNR_dB",
    "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); detector_dead_time dominates the stability cliff; peak_overlap 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": {
    "L_DAG": 3.4,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Electron Microscopy",
    "integration_axis": "spectral",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.illumination.convergent_probe",
      "S.scan.raster",
      "D.edx_detector",
      "int.spectral"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "edx_characteristic_xray",
    "solution_space": "elemental_concentration_map",
    "sub_domain": "Chemical composition via characteristic X-rays",
    "title": "STEM-EDX \u2014 X-ray energy-dispersive elemental mapping"
  },
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      "W",
      "N_elements",
      "kV",
      "dwell_ms",
      "peak_electrons",
      "detector_dead_time",
      "peak_overlap",
      "absorption_correction",
      "detector_dead_time",
      "peak_overlap",
      "absorption_correction"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "forward_operator": "stem_edx_forward",
      "input_format": "measurement_only",
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        "N_elements": 6,
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        "absorption_correction": 0.0,
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        "peak_electrons": 1000,
        "peak_overlap": 0.0
      },
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    "epsilon_bounds": {
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        40.0
      ]
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      "H": [
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        2048
      ],
      "N_elements": [
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        30
      ],
      "W": [
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        2048
      ],
      "absorption_correction": [
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        0.3
      ],
      "detector_dead_time": [
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        0.5
      ],
      "dwell_ms": [
        0.1,
        1000
      ],
      "kV": [
        60,
        300
      ],
      "peak_electrons": [
        50,
        100000
      ],
      "peak_overlap": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Chemical composition via characteristic X-rays",
  "title": "STEM-EDX \u2014 X-ray energy-dispersive elemental mapping"
}

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