L1 ⚛ L1-241 ⊙ Testnet

Fresnel Diffraction — paraxial wave propagation

Electromagnetics · Paraxial (Fresnel) diffraction integral

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⬇ principle.md ⬇ principle.json

Fork L1-241

⬇ L1-241.md ⬇ L1-241.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-241 (Fresnel Diffraction — paraxial wave propagation) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-241.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-241.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = ∫_A dA `L.intensity_capture` `L.fresnel_convolve` `L.paraxial_propagate` x + n,    n ~ 𝒩(0, σ²)

world state x (complex 2D field)

→

L · paraxial propagate `L.paraxial_propagate`

→

L · fresnel convolve `L.fresnel_convolve`

→

L · intensity capture `L.intensity_capture`

→

Spatial integration ∫_A dA

→

observation y (em detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-241.md

# ⚛ L1 Principle — Fresnel Diffraction — paraxial wave propagation **ID:** `L1-241` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Paraxial (Fresnel) diffraction integral* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex 2D field > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553988 --- ## 🧠 1. Introduction **Fresnel Diffraction — paraxial wave propagation** is a **linear inverse problem** whose unknown lives in **complex 2D field** space, within the **Paraxial (Fresnel) diffraction integral** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **intensity camera** sensing mechanism. The forward operator applies, in order: L · paraxial propagate operator; L · fresnel convolve operator; L · intensity capture operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · paraxial propagate → L · fresnel convolve → L · intensity capture → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.intensity_capture` `L.fresnel_convolve` `L.paraxial_propagate` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.paraxial_propagate` | L · paraxial propagate operator | | `L.fresnel_convolve` | L · fresnel convolve operator | | `L.intensity_capture` | L · intensity capture operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Paraxial (Fresnel) diffraction integral | | Carrier | em | | Problem class | linear_inverse | | Solution space | complex_2D_field | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 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:** `fresnel` · **Forward operator:** `fresnel_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z m | m | 1 | | Snr db | dB | 30 | | Lambda nm | nm | 633 | | Z dist error | — | 0 | | Aperture error | — | 0 | | Wavelength error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 4096 | | W | px | 64 – 4096 | | Z m | m | 0.001 – 1000 | | Snr db | dB | 0 – 40 | | Lambda nm | nm | 1 – 10000 | | Z dist error | — | 0.0 – 0.05 | | Aperture error | — | 0.0 – 0.1 | | Wavelength error | — | 0.0 – 0.02 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x962286a8a0878837f180eb1ef49a26fe3456eebd93ac875ffe3719696c0450a3` - **Chain tx hash:** `0x400affcdc98972afee3a3617b38912e3d4e9ebff2a355d392f5c059b51da9e51` - **Chain block:** `41553988` --- ## File Mapping This bundle consists of: `L1-241.md`, `L1-241.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-241.md` | Source of truth — edit this | Human or LLM | | `L1-241.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 `L1-241`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-241-001 Fresnel Diffraction — paraxial wave propagation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-241",
  "chain_block": 41553988,
  "chain_hash": "0x962286a8a0878837f180eb1ef49a26fe3456eebd93ac875ffe3719696c0450a3",
  "chain_tx_hash": "0x400affcdc98972afee3a3617b38912e3d4e9ebff2a355d392f5c059b51da9e51",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "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": 3.0,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.paraxial_propagate",
      "L.fresnel_convolve",
      "L.intensity_capture",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "intensity_camera",
    "solution_space": "complex_2D_field",
    "sub_domain": "Paraxial (Fresnel) diffraction integral",
    "title": "Fresnel Diffraction \u2014 paraxial wave propagation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fresnel_forward"
    ],
    "allowed_omega_dimensions": [
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      "W",
      "lambda_nm",
      "z_m",
      "SNR_dB",
      "z_dist_error",
      "aperture_error",
      "wavelength_error",
      "z_dist_error",
      "aperture_error",
      "wavelength_error"
    ],
    "allowed_problem_classes": [
      "fresnel"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "fresnel_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "SNR_dB": 30,
        "W": 512,
        "aperture_error": 0.0,
        "lambda_nm": 633,
        "wavelength_error": 0.0,
        "z_dist_error": 0.0,
        "z_m": 1.0
      },
      "problem_class": "fresnel"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        4096
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        4096
      ],
      "aperture_error": [
        0.0,
        0.1
      ],
      "lambda_nm": [
        1,
        10000
      ],
      "wavelength_error": [
        0.0,
        0.02
      ],
      "z_dist_error": [
        0.0,
        0.05
      ],
      "z_m": [
        0.001,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Paraxial (Fresnel) diffraction integral",
  "title": "Fresnel Diffraction \u2014 paraxial wave propagation"
}

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