L1 ⚛ L1-519 ⊙ Testnet

X-ray Diffraction Crystal Space-Group Classification (PWDR)

Materials Science · Crystal symmetry classification from XRD lattice + structure-factor recovery

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⬇ L1-519.md

# ⚛ L1 Principle — X-ray Diffraction Crystal Space-Group Classification (PWDR) **ID:** `L1-519` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Materials Science — *Crystal symmetry classification from XRD lattice + structure-factor recovery* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D space group label > **📡 Carrier:** x_ray · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554142 --- ## 🧠 1. Introduction **X-ray Diffraction Crystal Space-Group Classification (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D space group label** space, within the **Crystal symmetry classification from XRD lattice + structure-factor recovery** sub-domain of **Materials Science**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **bragg diffraction with space group classifier** sensing mechanism. The forward operator applies, in order: polyenergetic X-ray emission spectrum; L · bragg diffraction operator; L · structure factor operator; L · lattice parameter recovery operator; L · systematic absence test operator; L · space group decision tree operator; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson counting noise. Existence and uniqueness inherited from L1-518 with additional constraint: pseudosymmetry can cause space-group ambiguity (e.g., P2_1/n vs Pn — distinguishing requires additional statistics or chemistry constraint). Stability inherits L1-518's high condition number plus additive systematic_absence_threshold_uncertainty. Joint Hadamard well-posedness for the space-group classification established by Hahn 2005 (International Tables Vol A), Cromer-Liberman 1970 (anomalous scattering for centrosymmetry tests), Le Bail 2005 (powder indexing), Kabsch 2010 (XDS for space-group determination), Spek 2003 (PLATON ADDSYM). ## ⚙ 2. Forward Model Physical chain: **x** → X-ray source → L · bragg diffraction → L · structure factor → L · lattice parameter recovery → L · systematic absence test → L · space group decision tree → Angular integration → **y** (detector). ``` y = ∫dΩ `L.space_group_decision_tree` `L.systematic_absence_test` `L.lattice_parameter_recovery` `L.structure_factor` `L.bragg_diffraction` I₀(E) x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.xray_source` | Polyenergetic x-ray emission spectrum | | `L.bragg_diffraction` | L · bragg diffraction operator | | `L.structure_factor` | L · structure factor operator | | `L.lattice_parameter_recovery` | L · lattice parameter recovery operator | | `L.systematic_absence_test` | L · systematic absence test operator | | `L.space_group_decision_tree` | L · space group decision tree operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Materials Science | | Sub domain | Crystal symmetry classification from XRD lattice + structure-factor recovery | | Carrier | x_ray | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_space_group_label | | Noise model | poisson | | Integration axis | angular_spatial | | Difficulty delta | 5 | | L dag | 6.8 | ## 📡 4. Measurement Model Existence and uniqueness inherited from L1-518 with additional constraint: pseudosymmetry can cause space-group ambiguity (e.g., P2_1/n vs Pn — distinguishing requires additional statistics or chemistry constraint). Stability inherits L1-518's high condition number plus additive systematic_absence_threshold_uncertainty. Joint Hadamard well-posedness for the space-group classification established by Hahn 2005 (International Tables Vol A), Cromer-Liberman 1970 (anomalous scattering for centrosymmetry tests), Le Bail 2005 (powder indexing), Kabsch 2010 (XDS for space-group determination), Spek 2003 (PLATON ADDSYM). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | top_3_accuracy | ## 📏 5. Operating Range (Ω) **Center problem class:** `xrd_space_group_pwdr` · **Forward operator:** `xrd_space_group_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Two theta max | — | 120 | | Two theta min | — | 5 | | Two theta step | — | 0.02 | | Lambda angstrom | — | 1.5418 | | Twinning artifact | — | 0 | | Instrumental broadening | — | 0.05 | | Pseudosymmetry ambiguity | — | 0 | | Modulation or superlattice | — | 0 | | Lattice parameter uncertainty | — | 0 | | Systematic absence threshold uncertainty | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Two theta max | — | 60 – 160 | | Two theta min | — | 1 – 30 | | Lambda angstrom | — | 0.4 – 2.5 | | Instrumental broadening | — | 0.01 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.85_accuracy | Metric | Range | |---|---| | Categorical accuracy | 0.3 – 0.99 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xeecb4fc500389a8009bfab9a6b2e0ddb83b0b17ed2ade9f3f25506d88e0d71a7` - **Chain tx hash:** `0xecefcf2feafe0b852896a9ab692100199979b48b3c591987bb3aa9d43b794dda` - **Chain block:** `41554142` --- ## File Mapping This bundle consists of: `L1-519.md`, `L1-519.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-519.md` | Source of truth — edit this | Human or LLM | | `L1-519.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 `L1-519`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-519.md).
Regenerate L1-519.json so every field matches the Markdown.
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L2-519-001 X-ray Diffraction Crystal Space-Group Classification (PWDR) — Spec Skeleton

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📋 JSON metadata

{
  "artifact_id": "L1-519",
  "chain_block": 41554142,
  "chain_hash": "0xeecb4fc500389a8009bfab9a6b2e0ddb83b0b17ed2ade9f3f25506d88e0d71a7",
  "chain_tx_hash": "0xecefcf2feafe0b852896a9ab692100199979b48b3c591987bb3aa9d43b794dda",
  "domain": "Materials Science",
  "hardness_fn": {
    "delta": 5,
    "kappa": 600,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "categorical_accuracy",
    "regime": "Existence and uniqueness inherited from L1-518 with additional constraint: pseudosymmetry can cause space-group ambiguity (e.g., P2_1/n vs Pn \u2014 distinguishing requires additional statistics or chemistry constraint). Stability inherits L1-518\u0027s high condition number plus additive systematic_absence_threshold_uncertainty. Joint Hadamard well-posedness for the space-group classification established by Hahn 2005 (International Tables Vol A), Cromer-Liberman 1970 (anomalous scattering for centrosymmetry tests), Le Bail 2005 (powder indexing), Kabsch 2010 (XDS for space-group determination), Spek 2003 (PLATON ADDSYM).",
    "secondary": "top_3_accuracy"
  },
  "physics_fingerprint": {
    "L_DAG": 6.8,
    "carrier": "x_ray",
    "difficulty_delta": 5,
    "domain": "Materials Science",
    "integration_axis": "angular_spatial",
    "noise_model": "poisson",
    "primitives": [
      "L.xray_source",
      "L.bragg_diffraction",
      "L.structure_factor",
      "L.lattice_parameter_recovery",
      "L.systematic_absence_test",
      "L.space_group_decision_tree",
      "int.angular"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "bragg_diffraction_with_space_group_classifier",
    "solution_space": "1D_space_group_label",
    "sub_domain": "Crystal symmetry classification from XRD lattice + structure-factor recovery",
    "title": "X-ray Diffraction Crystal Space-Group Classification (PWDR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "xrd_space_group_pwdr_forward",
      "xrd_crystal_system_pwdr_forward",
      "xrd_bravais_pwdr_forward",
      "xrd_point_group_pwdr_forward"
    ],
    "allowed_omega_dimensions": [
      "lambda_angstrom",
      "two_theta_min",
      "two_theta_max",
      "two_theta_step",
      "instrumental_broadening",
      "lattice_parameter_uncertainty",
      "systematic_absence_threshold_uncertainty",
      "twinning_artifact",
      "modulation_or_superlattice",
      "pseudosymmetry_ambiguity"
    ],
    "allowed_problem_classes": [
      "xrd_space_group_pwdr",
      "xrd_crystal_system_pwdr",
      "xrd_bravais_pwdr",
      "xrd_point_group_pwdr",
      "xrd_centrosymmetry_pwdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.85_accuracy",
      "forward_operator": "xrd_space_group_pwdr_forward",
      "input_format": "powder_xrd_pattern_with_space_group_label",
      "omega": {
        "instrumental_broadening": 0.05,
        "lambda_angstrom": 1.5418,
        "lattice_parameter_uncertainty": 0.0,
        "modulation_or_superlattice": 0.0,
        "pseudosymmetry_ambiguity": 0.0,
        "systematic_absence_threshold_uncertainty": 0.0,
        "twinning_artifact": 0.0,
        "two_theta_max": 120,
        "two_theta_min": 5,
        "two_theta_step": 0.02
      },
      "problem_class": "xrd_space_group_pwdr"
    },
    "epsilon_bounds": {
      "categorical_accuracy": [
        0.3,
        0.99
      ]
    },
    "omega_bounds": {
      "instrumental_broadening": [
        0.01,
        0.5
      ],
      "lambda_angstrom": [
        0.4,
        2.5
      ],
      "two_theta_max": [
        60,
        160
      ],
      "two_theta_min": [
        1,
        30
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Crystal symmetry classification from XRD lattice + structure-factor recovery",
  "title": "X-ray Diffraction Crystal Space-Group Classification (PWDR)"
}

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