L1 ⚛ L1-254 ⊙ Testnet

X-ray Phase Contrast — propagation / grating / analyzer

Electromagnetics · X-ray phase and attenuation imaging

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Markdown — human-readable source of truth

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⬇ L1-254.md

# ⚛ L1 Principle — X-ray Phase Contrast — propagation / grating / analyzer **ID:** `L1-254` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *X-ray phase and attenuation imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D refractive index delta beta > **📡 Carrier:** em · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554001 --- ## 🧠 1. Introduction **X-ray Phase Contrast — propagation / grating / analyzer** is a **linear inverse problem** whose unknown lives in **3D refractive index delta beta** space, within the **X-ray phase and attenuation imaging** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **xray ccd** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; L · refract sample operator; L · propagate operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → L · refract sample → L · propagate → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.propagate` `L.refract_sample` I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `L.refract_sample` | L · refract sample operator | | `L.propagate` | L · propagate operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | X-ray phase and attenuation imaging | | Carrier | em | | Problem class | linear_inverse | | Solution space | 3D_refractive_index_delta_beta | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `xray_pc` · **Forward operator:** `xray_pc_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Z | — | 128 | | Snr db | dB | 30 | | Z error | — | 0 | | N distances | — | 3 | | Coherence error | — | 0 | | Beam harmonics error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 8192 | | W | px | 256 – 8192 | | Z | — | 32 – 1024 | | Snr db | dB | 0 – 40 | | Z error | — | 0.0 – 0.1 | | N distances | — | 1 – 50 | | Coherence error | — | 0.0 – 0.3 | | Beam harmonics error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf3df13574937e5b2987af88ac19d4520895b2819e64c29616282a70955a7fde8` - **Chain tx hash:** `0x630fccc1c8e7fdbbe95916e6199752865d47f2449ed24e02ac4bde7fd134dab0` - **Chain block:** `41554001` --- ## File Mapping This bundle consists of: `L1-254.md`, `L1-254.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-254.md` | Source of truth — edit this | Human or LLM | | `L1-254.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 `L1-254`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Prompt to give your LLM

Read the attached Markdown (L1-254.md).
Regenerate L1-254.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

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L2-254-001 X-ray Phase Contrast — propagation / grating / analyzer Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-254",
  "chain_block": 41554001,
  "chain_hash": "0xf3df13574937e5b2987af88ac19d4520895b2819e64c29616282a70955a7fde8",
  "chain_tx_hash": "0x630fccc1c8e7fdbbe95916e6199752865d47f2449ed24e02ac4bde7fd134dab0",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.xray_source",
      "L.refract_sample",
      "L.propagate",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "xray_ccd",
    "solution_space": "3D_refractive_index_delta_beta",
    "sub_domain": "X-ray phase and attenuation imaging",
    "title": "X-ray Phase Contrast \u2014 propagation / grating / analyzer"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "xray_pc_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_distances",
      "SNR_dB",
      "z_error",
      "coherence_error",
      "beam_harmonics_error",
      "z_error",
      "coherence_error",
      "beam_harmonics_error"
    ],
    "allowed_problem_classes": [
      "xray_pc"
    ],
    "center_spec": {
      "epsilon_fn_center": "25.0",
      "forward_operator": "xray_pc_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 2048,
        "N_distances": 3,
        "SNR_dB": 30,
        "W": 2048,
        "Z": 128,
        "beam_harmonics_error": 0.0,
        "coherence_error": 0.0,
        "z_error": 0.0
      },
      "problem_class": "xray_pc"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        256,
        8192
      ],
      "N_distances": [
        1,
        50
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        256,
        8192
      ],
      "Z": [
        32,
        1024
      ],
      "beam_harmonics_error": [
        0.0,
        0.2
      ],
      "coherence_error": [
        0.0,
        0.3
      ],
      "z_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "X-ray phase and attenuation imaging",
  "title": "X-ray Phase Contrast \u2014 propagation / grating / analyzer"
}

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