L1 ⚛ L1-125 ⊙ Testnet

X-ray Crystallography (single-crystal diffraction)

Scientific Instrumentation · Atomic-resolution crystal structure determination

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⬇ L1-125.md

# ⚛ L1 Principle — X-ray Crystallography (single-crystal diffraction) **ID:** `L1-125` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Scientific Instrumentation — *Atomic-resolution crystal structure determination* > **🎯 Problem class:** phase retrieval inverse · **🧮 Solution space:** electron density > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554213 --- ## 🧠 1. Introduction **X-ray Crystallography (single-crystal diffraction)** is a **phase retrieval inverse** whose unknown lives in **electron density** space, within the **Atomic-resolution crystal structure determination** sub-domain of **Scientific Instrumentation**. Measurements consist of photons collected by an optical detector via a **xray diffraction** sensing mechanism. The forward operator applies, in order: L · diffract · bragg operator; L · project · rescipocal operator; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Phase problem fundamentally ill-posed from intensities alone; experimental phasing (MAD/SAD) adds constraints. Well-posed at atomic resolution (<1.2 Å) via direct methods. ## ⚙ 2. Forward Model Physical chain: **x** → L · diffract · bragg → L · project · rescipocal → Angular integration → **y** (detector). ``` y = ∫dΩ `L.project.rescipocal` `L.diffract.bragg` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.diffract.bragg` | L · diffract · bragg operator | | `L.project.rescipocal` | L · project · rescipocal operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Scientific Instrumentation | | Sub domain | Atomic-resolution crystal structure determination | | Carrier | photon | | Problem class | phase_retrieval_inverse | | Solution space | electron_density | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Phase problem fundamentally ill-posed from intensities alone; experimental phasing (MAD/SAD) adds constraints. Well-posed at atomic resolution (<1.2 Å) via direct methods. | Metric | Value | |---|---| | Metric | R_free | | Secondary | atomic_coord_RMSD_angstrom | ## 📏 5. Operating Range (Ω) **Center problem class:** `sad_phasing_refinement` · **Forward operator:** `xrd_bragg_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N refl | — | 50000 | | N atoms | — | 1000 | | Resolution a | — | 2 | | Mosaicity deg | deg | 0.3 | | Radiation damage | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N refl | — | 100 – 1000000 | | N atoms | — | 10 – 100000 | | Resolution a | — | 0.8 – 4.0 | | Mosaicity deg | deg | 0.05 – 2.0 | | Radiation damage | — | 0.0 – 1.0 | | Twinning fraction | — | 0.0 – 0.5 | | Absorption anisotropy | — | 0.0 – 0.3 | | Crystal size variability | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** R_free 0.22 | Metric | Range | |---|---| | R free | 0.15 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **R_free**, with κ = `1000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x4578dd83185a94e3d1c8032fcdb46c12dd20d6bda35d7a107ac5bbbe60ae7049` - **Chain tx hash:** `0xd56d1d748d8253073d6526feeb18173c43487ebf92bc6094a2965abfa4dec1fc` - **Chain block:** `41554213` --- ## File Mapping This bundle consists of: `L1-125.md`, `L1-125.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-125.md` | Source of truth — edit this | Human or LLM | | `L1-125.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 `L1-125`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-125-001 X-ray Crystallography SAD-Phasing Spec

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📋 JSON metadata

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  "chain_block": 41554213,
  "chain_hash": "0x4578dd83185a94e3d1c8032fcdb46c12dd20d6bda35d7a107ac5bbbe60ae7049",
  "chain_tx_hash": "0xd56d1d748d8253073d6526feeb18173c43487ebf92bc6094a2965abfa4dec1fc",
  "domain": "Scientific Instrumentation",
  "hardness_fn": {
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    "kappa": 1000,
    "metric": "R_free",
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    "regime": "Phase problem fundamentally ill-posed from intensities alone; experimental phasing (MAD/SAD) adds constraints. Well-posed at atomic resolution (\u003c1.2 \u00c5) via direct methods.",
    "secondary": "atomic_coord_RMSD_angstrom"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Scientific Instrumentation",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
    "primitives": [
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      "L.project.rescipocal",
      "int.angular"
    ],
    "problem_class": "phase_retrieval_inverse",
    "sensing_mechanism": "xray_diffraction",
    "solution_space": "electron_density",
    "sub_domain": "Atomic-resolution crystal structure determination",
    "title": "X-ray Crystallography (single-crystal diffraction)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "xrd_bragg_forward",
      "xfel_serial_forward"
    ],
    "allowed_omega_dimensions": [
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      "N_refl",
      "N_atoms",
      "mosaicity_deg",
      "radiation_damage",
      "twinning_fraction",
      "absorption_anisotropy",
      "crystal_size_variability"
    ],
    "allowed_problem_classes": [
      "sad_phasing_refinement",
      "molecular_replacement",
      "ab_initio_direct_methods",
      "twin_refinement"
    ],
    "center_spec": {
      "epsilon_fn_center": "R_free 0.22",
      "forward_operator": "xrd_bragg_forward",
      "input_format": "integrated_intensities",
      "omega": {
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        "N_refl": 50000,
        "mosaicity_deg": 0.3,
        "radiation_damage": 0.0,
        "resolution_A": 2.0
      },
      "problem_class": "sad_phasing_refinement"
    },
    "epsilon_bounds": {
      "r_free": [
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        0.5
      ]
    },
    "omega_bounds": {
      "N_atoms": [
        10,
        100000
      ],
      "N_refl": [
        100,
        1000000
      ],
      "absorption_anisotropy": [
        0.0,
        0.3
      ],
      "crystal_size_variability": [
        0.0,
        0.5
      ],
      "mosaicity_deg": [
        0.05,
        2.0
      ],
      "radiation_damage": [
        0.0,
        1.0
      ],
      "resolution_A": [
        0.8,
        4.0
      ],
      "twinning_fraction": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Atomic-resolution crystal structure determination",
  "title": "X-ray Crystallography (single-crystal diffraction)"
}

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