L1 ⚛ L1-243 ⊙ Testnet

Mie Scattering — rigorous spherical-particle scattering

Electromagnetics · Particle size distribution from Mie pattern

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⬇ L1-243.md

# ⚛ L1 Principle — Mie Scattering — rigorous spherical-particle scattering **ID:** `L1-243` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Particle size distribution from Mie pattern* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** particle size distribution > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553989 --- ## 🧠 1. Introduction **Mie Scattering — rigorous spherical-particle scattering** is a **nonlinear inverse problem** whose unknown lives in **particle size distribution** space, within the **Particle size distribution from Mie pattern** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **angular scatter detector** sensing mechanism. The forward operator applies, in order: L · mie coeff operator; L · series sum operator; L · polydispersity average 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 · mie coeff → L · series sum → L · polydispersity average → Angular integration → **y** (detector). ``` y = ∫dΩ `L.polydispersity_average` `L.series_sum` `L.mie_coeff` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.mie_coeff` | L · mie coeff operator | | `L.series_sum` | L · series sum operator | | `L.polydispersity_average` | L · polydispersity average operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Particle size distribution from Mie pattern | | Carrier | em | | Problem class | nonlinear_inverse | | Solution space | particle_size_distribution | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 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:** `mie` · **Forward operator:** `mie_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N angles | — | 360 | | N wavelengths | — | 3 | | N complex error | — | 0 | | Concentration error | — | 0 | | Polydispersity width error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N angles | — | 18 – 3600 | | N wavelengths | — | 1 – 50 | | N complex error | — | 0.0 – 0.05 | | Concentration error | — | 0.0 – 0.3 | | Polydispersity width error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xeb1ac9320f533261622240766b5919a639edc4323dd50764cd76131aa2b665c2` - **Chain tx hash:** `0x466091f9732a9a9834e3540b87e6f0cb4f54be175bc2725f77669214a54c6e6a` - **Chain block:** `41553989` --- ## File Mapping This bundle consists of: `L1-243.md`, `L1-243.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-243.md` | Source of truth — edit this | Human or LLM | | `L1-243.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 `L1-243`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-243.md).
Regenerate L1-243.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-243-001 Mie Scattering — rigorous spherical-particle scattering Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-243",
  "chain_block": 41553989,
  "chain_hash": "0xeb1ac9320f533261622240766b5919a639edc4323dd50764cd76131aa2b665c2",
  "chain_tx_hash": "0x466091f9732a9a9834e3540b87e6f0cb4f54be175bc2725f77669214a54c6e6a",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Electromagnetics",
    "integration_axis": "angular",
    "noise_model": "gaussian",
    "primitives": [
      "L.mie_coeff",
      "L.series_sum",
      "L.polydispersity_average",
      "int.angular"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "angular_scatter_detector",
    "solution_space": "particle_size_distribution",
    "sub_domain": "Particle size distribution from Mie pattern",
    "title": "Mie Scattering \u2014 rigorous spherical-particle scattering"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mie_forward"
    ],
    "allowed_omega_dimensions": [
      "N_angles",
      "N_wavelengths",
      "SNR_dB",
      "n_complex_error",
      "polydispersity_width_error",
      "concentration_error",
      "n_complex_error",
      "polydispersity_width_error",
      "concentration_error"
    ],
    "allowed_problem_classes": [
      "mie"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "mie_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_angles": 360,
        "N_wavelengths": 3,
        "SNR_dB": 30,
        "concentration_error": 0.0,
        "n_complex_error": 0.0,
        "polydispersity_width_error": 0.0
      },
      "problem_class": "mie"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_angles": [
        18,
        3600
      ],
      "N_wavelengths": [
        1,
        50
      ],
      "SNR_dB": [
        0,
        40
      ],
      "concentration_error": [
        0.0,
        0.3
      ],
      "n_complex_error": [
        0.0,
        0.05
      ],
      "polydispersity_width_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Particle size distribution from Mie pattern",
  "title": "Mie Scattering \u2014 rigorous spherical-particle scattering"
}

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