L1 ⚛ L1-133 ⊙ Testnet

WAXS — Wide-Angle X-ray Scattering

Scientific Instrumentation · X-ray scattering probing Å-scale structure

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⬇ L1-133.md

# ⚛ L1 Principle — WAXS — Wide-Angle X-ray Scattering **ID:** `L1-133` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Scientific Instrumentation — *X-ray scattering probing Å-scale structure* > **🎯 Problem class:** inverse fourier scatter · **🧮 Solution space:** radial structure function > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554214 --- ## 🧠 1. Introduction **WAXS — Wide-Angle X-ray Scattering** is a **inverse fourier scatter** whose unknown lives in **radial structure function** space, within the **X-ray scattering probing Å-scale structure** sub-domain of **Scientific Instrumentation**. Measurements consist of photons collected by an optical detector via a **xray wide angle scatter** sensing mechanism. The forward operator applies, in order: L · scatter · elastic operator; L · project · q operator; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Fourier inversion is ill-conditioned for truncated q-range; regularization (max-entropy, oversampling) stabilizes. Mismatch: background subtraction, termination ripples. ## ⚙ 2. Forward Model Physical chain: **x** → L · scatter · elastic → L · project · q → Angular integration → **y** (detector). ``` y = ∫dΩ `L.project.q` `L.scatter.elastic` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.scatter.elastic` | L · scatter · elastic operator | | `L.project.q` | L · project · q operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Scientific Instrumentation | | Sub domain | X-ray scattering probing Å-scale structure | | Carrier | photon | | Problem class | inverse_fourier_scatter | | Solution space | radial_structure_function | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 3 | | L dag | 2.7 | ## 📡 4. Measurement Model Fourier inversion is ill-conditioned for truncated q-range; regularization (max-entropy, oversampling) stabilizes. Mismatch: background subtraction, termination ripples. | Metric | Value | |---|---| | Metric | g_r_NMSE | | Secondary | Rwp_rietveld | ## 📏 5. Operating Range (Ω) **Center problem class:** `waxs_polymer_analysis` · **Forward operator:** `waxs_iq_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N q | — | 800 | | Q max | — | 30 | | Q min | — | 5 | | Sample thickness um | µm | 100 | | Background subtraction | — | 0.05 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N q | — | 100 – 5000 | | Q max | — | 15 – 50 | | Q min | — | 1 – 10 | | Q truncation | — | 0.0 – 0.5 | | Sample thickness um | µm | 1 – 1000 | | Termination ripples | — | 0.0 – 0.3 | | Beam profile mismatch | — | 0.0 – 0.2 | | Preferred orientation | — | 0.0 – 0.5 | | Background subtraction | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** g(r) NMSE 5e-3 | Metric | Range | |---|---| | G r nmse | 0.0001 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **g_r_NMSE**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x03efadead8ee044135c98acd73d0a6aead576d7b75d7141b0c8fbd6c32b5f664` - **Chain tx hash:** `0x7416be9e99e0ab6284a27b574c8a532a8786a68ce691caae4f03c1553b76afd8` - **Chain block:** `41554214` --- ## File Mapping This bundle consists of: `L1-133.md`, `L1-133.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-133.md` | Source of truth — edit this | Human or LLM | | `L1-133.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 `L1-133`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-133.md).
Regenerate L1-133.json so every field matches the Markdown.
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L2-133-001 WAXS Polymer/Structure Spec

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📋 JSON metadata

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  "artifact_id": "L1-133",
  "chain_block": 41554214,
  "chain_hash": "0x03efadead8ee044135c98acd73d0a6aead576d7b75d7141b0c8fbd6c32b5f664",
  "chain_tx_hash": "0x7416be9e99e0ab6284a27b574c8a532a8786a68ce691caae4f03c1553b76afd8",
  "domain": "Scientific Instrumentation",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "g_r_NMSE",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "g_r_NMSE",
    "regime": "Fourier inversion is ill-conditioned for truncated q-range; regularization (max-entropy, oversampling) stabilizes. Mismatch: background subtraction, termination ripples.",
    "secondary": "Rwp_rietveld"
  },
  "physics_fingerprint": {
    "L_DAG": 2.7,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Scientific Instrumentation",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.scatter.elastic",
      "L.project.q",
      "int.angular"
    ],
    "problem_class": "inverse_fourier_scatter",
    "sensing_mechanism": "xray_wide_angle_scatter",
    "solution_space": "radial_structure_function",
    "sub_domain": "X-ray scattering probing \u00c5-scale structure",
    "title": "WAXS \u2014 Wide-Angle X-ray Scattering"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "waxs_iq_forward",
      "giwaxs_2d_forward"
    ],
    "allowed_omega_dimensions": [
      "N_q",
      "q_min",
      "q_max",
      "sample_thickness_um",
      "background_subtraction",
      "q_truncation",
      "termination_ripples",
      "beam_profile_mismatch",
      "preferred_orientation"
    ],
    "allowed_problem_classes": [
      "waxs_polymer_analysis",
      "waxs_crystal_fraction",
      "waxs_nano_crystal_size"
    ],
    "center_spec": {
      "epsilon_fn_center": "g(r) NMSE 5e-3",
      "forward_operator": "waxs_iq_forward",
      "input_format": "scattering_pattern",
      "omega": {
        "N_q": 800,
        "background_subtraction": 0.05,
        "q_max": 30,
        "q_min": 5,
        "sample_thickness_um": 100
      },
      "problem_class": "waxs_polymer_analysis"
    },
    "epsilon_bounds": {
      "g_r_nmse": [
        0.0001,
        0.3
      ]
    },
    "omega_bounds": {
      "N_q": [
        100,
        5000
      ],
      "background_subtraction": [
        0.0,
        0.3
      ],
      "beam_profile_mismatch": [
        0.0,
        0.2
      ],
      "preferred_orientation": [
        0.0,
        0.5
      ],
      "q_max": [
        15,
        50
      ],
      "q_min": [
        1,
        10
      ],
      "q_truncation": [
        0.0,
        0.5
      ],
      "sample_thickness_um": [
        1,
        1000
      ],
      "termination_ripples": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "X-ray scattering probing \u00c5-scale structure",
  "title": "WAXS \u2014 Wide-Angle X-ray Scattering"
}

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