L1 ⚛ L1-242 ⊙ Testnet

Geometric Optics — ray tracing / eikonal

Electromagnetics · Eikonal equation / Fermat ray tracing

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Markdown — human-readable source of truth

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⬇ L1-242.md

# ⚛ L1 Principle — Geometric Optics — ray tracing / eikonal **ID:** `L1-242` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Eikonal equation / Fermat ray tracing* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** image plane irradiance > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553988 --- ## 🧠 1. Introduction **Geometric Optics — ray tracing / eikonal** is a **linear inverse problem** whose unknown lives in **image plane irradiance** space, within the **Eikonal equation / Fermat ray tracing** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **camera image** sensing mechanism. The forward operator applies, in order: L · eikonal operator; L · ray trace operator; L · snell refract 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 · eikonal → L · ray trace → L · snell refract → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.snell_refract` `L.ray_trace` `L.eikonal` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.eikonal` | L · eikonal operator | | `L.ray_trace` | L · ray trace operator | | `L.snell_refract` | L · snell refract operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Eikonal equation / Fermat ray tracing | | Carrier | em | | Problem class | linear_inverse | | Solution space | image_plane_irradiance | | Noise model | gaussian | | Integration axis | spatial | | 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:** `ray_trace` · **Forward operator:** `ray_trace_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N rays | — | 10000 | | Snr db | dB | 30 | | N fields | — | 5 | | N wavelengths | — | 3 | | Alignment error | — | 0 | | Wavelength error | — | 0 | | Lens prescription error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N rays | — | 100 – 10000000 | | Snr db | dB | 0 – 40 | | N fields | — | 1 – 50 | | N wavelengths | — | 1 – 50 | | Alignment error | — | 0.0 – 0.05 | | Wavelength error | — | 0.0 – 0.02 | | Lens prescription error | — | 0.0 – 0.01 | ## 🎯 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 = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8c736f0c715dec3783b81b6356ef073543066a9299e8bbca66e089f4c82047b8` - **Chain tx hash:** `0xdc121a127b03f271dddc18868c4e2bdd886b8ea7538ad23a45d318a07cb1286d` - **Chain block:** `41553988` --- ## File Mapping This bundle consists of: `L1-242.md`, `L1-242.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-242.md` | Source of truth — edit this | Human or LLM | | `L1-242.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 `L1-242`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-242.md).
Regenerate L1-242.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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L2-242-001 Geometric Optics — ray tracing / eikonal Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-242",
  "chain_block": 41553988,
  "chain_hash": "0x8c736f0c715dec3783b81b6356ef073543066a9299e8bbca66e089f4c82047b8",
  "chain_tx_hash": "0xdc121a127b03f271dddc18868c4e2bdd886b8ea7538ad23a45d318a07cb1286d",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "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": 2.8,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.eikonal",
      "L.ray_trace",
      "L.snell_refract",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "camera_image",
    "solution_space": "image_plane_irradiance",
    "sub_domain": "Eikonal equation / Fermat ray tracing",
    "title": "Geometric Optics \u2014 ray tracing / eikonal"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ray_trace_forward"
    ],
    "allowed_omega_dimensions": [
      "N_rays",
      "N_fields",
      "N_wavelengths",
      "SNR_dB",
      "lens_prescription_error",
      "alignment_error",
      "wavelength_error",
      "lens_prescription_error",
      "alignment_error",
      "wavelength_error"
    ],
    "allowed_problem_classes": [
      "ray_trace"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "ray_trace_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_fields": 5,
        "N_rays": 10000,
        "N_wavelengths": 3,
        "SNR_dB": 30,
        "alignment_error": 0.0,
        "lens_prescription_error": 0.0,
        "wavelength_error": 0.0
      },
      "problem_class": "ray_trace"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_fields": [
        1,
        50
      ],
      "N_rays": [
        100,
        10000000
      ],
      "N_wavelengths": [
        1,
        50
      ],
      "SNR_dB": [
        0,
        40
      ],
      "alignment_error": [
        0.0,
        0.05
      ],
      "lens_prescription_error": [
        0.0,
        0.01
      ],
      "wavelength_error": [
        0.0,
        0.02
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Eikonal equation / Fermat ray tracing",
  "title": "Geometric Optics \u2014 ray tracing / eikonal"
}

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