L1 ⚛ L1-244 ⊙ Testnet

Rayleigh Scattering — molecular / small-particle scattering

Electromagnetics · Rayleigh regime optical scattering

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⬇ L1-244.md

# ⚛ L1 Principle — Rayleigh Scattering — molecular / small-particle scattering **ID:** `L1-244` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Rayleigh regime optical scattering* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** molecular density or aerosol > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553989 --- ## 🧠 1. Introduction **Rayleigh Scattering — molecular / small-particle scattering** is a **linear inverse problem** whose unknown lives in **molecular density or aerosol** space, within the **Rayleigh regime optical scattering** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **photometer** sensing mechanism. The forward operator applies, in order: L · small particle dipole operator; L · sigma lambda 4 operator; L · polarization operator; integration over the solid angle of incidence/emission. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · small particle dipole → L · sigma lambda 4 → L · polarization → Angular integration → **y** (detector). ``` y = ∫dΩ `L.polarization` `L.sigma_lambda_4` `L.small_particle_dipole` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.small_particle_dipole` | L · small particle dipole operator | | `L.sigma_lambda_4` | L · sigma lambda 4 operator | | `L.polarization` | L · polarization operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Rayleigh regime optical scattering | | Carrier | em | | Problem class | linear_inverse | | Solution space | molecular_density_or_aerosol | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 3 | | L dag | 2.8 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `rayleigh` · **Forward operator:** `rayleigh_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N angles | — | 16 | | N wavelengths | — | 10 | | Wavelength error | — | 0 | | Path length error | — | 0 | | Polarizability error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N angles | — | 1 – 256 | | N wavelengths | — | 1 – 200 | | Wavelength error | — | 0.0 – 0.01 | | Path length error | — | 0.0 – 0.05 | | Polarizability error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x45ddcc0e2a287a60e5231ec9777ff591b668f03b2bec096b3601ab329ca393dc` - **Chain tx hash:** `0xc7a705a4da829a1f06329330ed168b9c38d152cf5607f393f6b554c96205b99c` - **Chain block:** `41553989` --- ## File Mapping This bundle consists of: `L1-244.md`, `L1-244.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-244.md` | Source of truth — edit this | Human or LLM | | `L1-244.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 `L1-244`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-244.md).
Regenerate L1-244.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-244-001 Rayleigh Scattering — molecular / small-particle scattering Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-244",
  "chain_block": 41553989,
  "chain_hash": "0x45ddcc0e2a287a60e5231ec9777ff591b668f03b2bec096b3601ab329ca393dc",
  "chain_tx_hash": "0xc7a705a4da829a1f06329330ed168b9c38d152cf5607f393f6b554c96205b99c",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.8,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "angular",
    "noise_model": "gaussian",
    "primitives": [
      "L.small_particle_dipole",
      "L.sigma_lambda_4",
      "L.polarization",
      "int.angular"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "photometer",
    "solution_space": "molecular_density_or_aerosol",
    "sub_domain": "Rayleigh regime optical scattering",
    "title": "Rayleigh Scattering \u2014 molecular / small-particle scattering"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "rayleigh_forward"
    ],
    "allowed_omega_dimensions": [
      "N_wavelengths",
      "N_angles",
      "SNR_dB",
      "polarizability_error",
      "path_length_error",
      "wavelength_error",
      "polarizability_error",
      "path_length_error",
      "wavelength_error"
    ],
    "allowed_problem_classes": [
      "rayleigh"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "rayleigh_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_angles": 16,
        "N_wavelengths": 10,
        "SNR_dB": 30,
        "path_length_error": 0.0,
        "polarizability_error": 0.0,
        "wavelength_error": 0.0
      },
      "problem_class": "rayleigh"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_angles": [
        1,
        256
      ],
      "N_wavelengths": [
        1,
        200
      ],
      "SNR_dB": [
        0,
        40
      ],
      "path_length_error": [
        0.0,
        0.05
      ],
      "polarizability_error": [
        0.0,
        0.1
      ],
      "wavelength_error": [
        0.0,
        0.01
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rayleigh regime optical scattering",
  "title": "Rayleigh Scattering \u2014 molecular / small-particle scattering"
}

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