L1 ⚛ L1-147 ⊙ Testnet

XAS / EXAFS — X-ray Absorption & Extended X-ray Absorption Fine Structure

Spectroscopy · Inner-shell X-ray absorption + multiple scattering oscillations

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⬇ L1-147.md

# ⚛ L1 Principle — XAS / EXAFS — X-ray Absorption & Extended X-ray Absorption Fine Structure **ID:** `L1-147` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Spectroscopy — *Inner-shell X-ray absorption + multiple scattering oscillations* > **🎯 Problem class:** nonlinear inverse structural · **🧮 Solution space:** radial coordination > **📡 Carrier:** photon · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554228 --- ## 🧠 1. Introduction **XAS / EXAFS — X-ray Absorption & Extended X-ray Absorption Fine Structure** is a **nonlinear inverse structural** whose unknown lives in **radial coordination** space, within the **Inner-shell X-ray absorption + multiple scattering oscillations** sub-domain of **Spectroscopy**. Measurements consist of photons collected by an optical detector via a **xray core absorption** sensing mechanism. The forward operator applies, in order: L · absorb · photoionization operator; L · scatter · multiple operator; detector sums all spectral bands. Observations are corrupted by Poisson counting noise. Fourier-transform EXAFS inversion is linear; parameter fitting (R_j, N_j, sigma_j^2) is nonlinear; correlation among N, S_0, sigma is a major ill-conditioning source. ## ⚙ 2. Forward Model Physical chain: **x** → L · absorb · photoionization → L · scatter · multiple → Spectral integration → **y** (detector). ``` y = Σ_λ `L.scatter.multiple` `L.absorb.photoionization` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.absorb.photoionization` | L · absorb · photoionization operator | | `L.scatter.multiple` | L · scatter · multiple operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Spectroscopy | | Sub domain | Inner-shell X-ray absorption + multiple scattering oscillations | | Carrier | photon | | Problem class | nonlinear_inverse_structural | | Solution space | radial_coordination | | Noise model | poisson | | Integration axis | spectral | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Fourier-transform EXAFS inversion is linear; parameter fitting (R_j, N_j, sigma_j^2) is nonlinear; correlation among N, S_0, sigma is a major ill-conditioning source. | Metric | Value | |---|---| | Metric | R_j_RMSE_angstrom | | Secondary | N_j_NMSE | ## 📏 5. Operating Range (Ω) **Center problem class:** `exafs_radial_fit` · **Forward operator:** `feff_exafs_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N e | — | 400 | | K max | — | 10 | | Snr db | dB | 30 | | K shells | — | 3 | | S 0 squared | — | 0.85 | | E0 shift ev | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N e | — | 50 – 2000 | | K max | — | 4 – 16 | | Snr db | dB | -5 – 45 | | K shells | — | 1 – 10 | | S 0 squared | — | 0.5 – 1.0 | | E0 shift ev | — | -5 – 5 | | Detector saturation | — | 0.0 – 0.2 | | Self absorption correction | — | 0.0 – 0.3 | | Multiple scattering truncation | — | 1 – 5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.01 A R-RMSE | Metric | Range | |---|---| | Rmse angstrom | 0.001 – 0.2 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **R_j_RMSE_angstrom**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6236f942e037e4657879721e22d5d874827bda83260a000ac570672d28dd0418` - **Chain tx hash:** `0x8d99ca2b6521ca569bb6db1bd5f20f2baadb5662beebbfefdbe56b1493f31a2c` - **Chain block:** `41554228` --- ## File Mapping This bundle consists of: `L1-147.md`, `L1-147.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-147.md` | Source of truth — edit this | Human or LLM | | `L1-147.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 `L1-147`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

{
  "artifact_id": "L1-147",
  "chain_block": 41554228,
  "chain_hash": "0x6236f942e037e4657879721e22d5d874827bda83260a000ac570672d28dd0418",
  "chain_tx_hash": "0x8d99ca2b6521ca569bb6db1bd5f20f2baadb5662beebbfefdbe56b1493f31a2c",
  "domain": "Spectroscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "R_j_RMSE_angstrom",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "R_j_RMSE_angstrom",
    "regime": "Fourier-transform EXAFS inversion is linear; parameter fitting (R_j, N_j, sigma_j^2) is nonlinear; correlation among N, S_0, sigma is a major ill-conditioning source.",
    "secondary": "N_j_NMSE"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Spectroscopy",
    "integration_axis": "spectral",
    "noise_model": "poisson",
    "primitives": [
      "L.absorb.photoionization",
      "L.scatter.multiple",
      "int.spectral"
    ],
    "problem_class": "nonlinear_inverse_structural",
    "sensing_mechanism": "xray_core_absorption",
    "solution_space": "radial_coordination",
    "sub_domain": "Inner-shell X-ray absorption + multiple scattering oscillations",
    "title": "XAS / EXAFS \u2014 X-ray Absorption \u0026 Extended X-ray Absorption Fine Structure"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "feff_exafs_forward",
      "ab_initio_xanes_forward"
    ],
    "allowed_omega_dimensions": [
      "N_E",
      "k_max",
      "K_shells",
      "SNR_dB",
      "S_0_squared",
      "e0_shift_eV",
      "multiple_scattering_truncation",
      "self_absorption_correction",
      "detector_saturation"
    ],
    "allowed_problem_classes": [
      "exafs_radial_fit",
      "xanes_fingerprint",
      "operando_xas_reaction"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.01 A R-RMSE",
      "forward_operator": "feff_exafs_forward",
      "input_format": "absorption_vs_energy",
      "omega": {
        "K_shells": 3,
        "N_E": 400,
        "SNR_dB": 30,
        "S_0_squared": 0.85,
        "e0_shift_eV": 0.0,
        "k_max": 10
      },
      "problem_class": "exafs_radial_fit"
    },
    "epsilon_bounds": {
      "rmse_angstrom": [
        0.001,
        0.2
      ]
    },
    "omega_bounds": {
      "K_shells": [
        1,
        10
      ],
      "N_E": [
        50,
        2000
      ],
      "SNR_dB": [
        -5,
        45
      ],
      "S_0_squared": [
        0.5,
        1.0
      ],
      "detector_saturation": [
        0.0,
        0.2
      ],
      "e0_shift_eV": [
        -5,
        5
      ],
      "k_max": [
        4,
        16
      ],
      "multiple_scattering_truncation": [
        1,
        5
      ],
      "self_absorption_correction": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Inner-shell X-ray absorption + multiple scattering oscillations",
  "title": "XAS / EXAFS \u2014 X-ray Absorption \u0026 Extended X-ray Absorption Fine Structure"
}

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