L1 ⚛ L1-126 ⊙ Testnet

SAXS — Small-Angle X-ray Scattering

Scientific Instrumentation · Nanoscale structural scattering (1-100 nm)

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⬇ L1-126.md

# ⚛ L1 Principle — SAXS — Small-Angle X-ray Scattering **ID:** `L1-126` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Scientific Instrumentation — *Nanoscale structural scattering (1-100 nm)* > **🎯 Problem class:** inverse fourier scatter · **🧮 Solution space:** pair distribution or envelope > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554213 --- ## 🧠 1. Introduction **SAXS — Small-Angle X-ray Scattering** is a **inverse fourier scatter** whose unknown lives in **pair distribution or envelope** space, within the **Nanoscale structural scattering (1-100 nm)** sub-domain of **Scientific Instrumentation**. Measurements consist of photons collected by an optical detector via a **xray small 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. Inverse Fourier transform from I(q) to P(r) is ill-posed (ATSAS-GNOM uses regularization); shape reconstruction requires ab-initio bead models. Mismatch: aggregation, polydispersity, buffer mismatch. ## ⚙ 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 | Nanoscale structural scattering (1-100 nm) | | Carrier | photon | | Problem class | inverse_fourier_scatter | | Solution space | pair_distribution_or_envelope | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 3 | | L dag | 2.7 | ## 📡 4. Measurement Model Inverse Fourier transform from I(q) to P(r) is ill-posed (ATSAS-GNOM uses regularization); shape reconstruction requires ab-initio bead models. Mismatch: aggregation, polydispersity, buffer mismatch. | Metric | Value | |---|---| | Metric | Rg_RMSE_nm | | Secondary | chi2_reduced | ## 📏 5. Operating Range (Ω) **Center problem class:** `biosaxs_globular_protein` · **Forward operator:** `saxs_iq_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N q | — | 400 | | Rg nm | nm | 2 | | Q max | — | 0.5 | | Q min | — | 0.01 | | Concentration mg ml | — | 1 | | Aggregation fraction | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N q | — | 50 – 2000 | | Rg nm | nm | 0.5 – 50 | | Q max | — | 0.1 – 1.0 | | Q min | — | 0.001 – 0.1 | | Beam damage | — | 0.0 – 0.5 | | Polydispersity | — | 0.0 – 0.5 | | Buffer mismatch | — | 0.0 – 0.3 | | Q range truncation | — | 0.0 – 0.5 | | Concentration mg ml | — | 0.1 – 20 | | Aggregation fraction | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.05 nm Rg RMSE | Metric | Range | |---|---| | Rg rmse nm | 0.01 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **Rg_RMSE_nm**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6ea68f7f1986db6a5ed685b31657281b924c5f5c3a38a47cae6b5e03d6b986ae` - **Chain tx hash:** `0x671a3fa51d16ae2af60593a60dbc756a1ec43d71c82ba0962cef38eb9f046716` - **Chain block:** `41554213` --- ## File Mapping This bundle consists of: `L1-126.md`, `L1-126.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-126.md` | Source of truth — edit this | Human or LLM | | `L1-126.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 `L1-126`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-126.md).
Regenerate L1-126.json so every field matches the Markdown.
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L2-126-001 SAXS BioSAXS Indirect-FT Spec

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📋 JSON metadata

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  "artifact_id": "L1-126",
  "chain_block": 41554213,
  "chain_hash": "0x6ea68f7f1986db6a5ed685b31657281b924c5f5c3a38a47cae6b5e03d6b986ae",
  "chain_tx_hash": "0x671a3fa51d16ae2af60593a60dbc756a1ec43d71c82ba0962cef38eb9f046716",
  "domain": "Scientific Instrumentation",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "Rg_RMSE_nm",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "Rg_RMSE_nm",
    "regime": "Inverse Fourier transform from I(q) to P(r) is ill-posed (ATSAS-GNOM uses regularization); shape reconstruction requires ab-initio bead models. Mismatch: aggregation, polydispersity, buffer mismatch.",
    "secondary": "chi2_reduced"
  },
  "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_small_angle_scatter",
    "solution_space": "pair_distribution_or_envelope",
    "sub_domain": "Nanoscale structural scattering (1-100 nm)",
    "title": "SAXS \u2014 Small-Angle X-ray Scattering"
  },
  "size_tiers": {
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      "saxs_iq_forward",
      "waxs_iq_forward"
    ],
    "allowed_omega_dimensions": [
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      "q_min",
      "q_max",
      "Rg_nm",
      "concentration_mg_ml",
      "aggregation_fraction",
      "polydispersity",
      "buffer_mismatch",
      "beam_damage",
      "q_range_truncation"
    ],
    "allowed_problem_classes": [
      "biosaxs_globular_protein",
      "biosaxs_imp_flexible",
      "saxs_nanoparticle",
      "waxs_fiber"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.05 nm Rg RMSE",
      "forward_operator": "saxs_iq_forward",
      "input_format": "scattering_curve_plus_buffer",
      "omega": {
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        "Rg_nm": 2.0,
        "aggregation_fraction": 0.0,
        "concentration_mg_ml": 1.0,
        "q_max": 0.5,
        "q_min": 0.01
      },
      "problem_class": "biosaxs_globular_protein"
    },
    "epsilon_bounds": {
      "rg_rmse_nm": [
        0.01,
        1.0
      ]
    },
    "omega_bounds": {
      "N_q": [
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        2000
      ],
      "Rg_nm": [
        0.5,
        50
      ],
      "aggregation_fraction": [
        0.0,
        0.5
      ],
      "beam_damage": [
        0.0,
        0.5
      ],
      "buffer_mismatch": [
        0.0,
        0.3
      ],
      "concentration_mg_ml": [
        0.1,
        20
      ],
      "polydispersity": [
        0.0,
        0.5
      ],
      "q_max": [
        0.1,
        1.0
      ],
      "q_min": [
        0.001,
        0.1
      ],
      "q_range_truncation": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Nanoscale structural scattering (1-100 nm)",
  "title": "SAXS \u2014 Small-Angle X-ray Scattering"
}

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