L1 ⚛ L1-242 ⊙ Testnet

Geometric Optics — ray tracing / eikonal

Electromagnetics · Eikonal equation / Fermat ray tracing

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-242

⬇ L1-242.md ⬇ L1-242.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-242 (Geometric Optics — ray tracing / eikonal) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-242.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-242.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.snell_refract` `L.ray_trace` `L.eikonal` x + n,    n ~ 𝒩(0, σ²)

world state x (image plane irradiance)

→

L · eikonal `L.eikonal`

→

L · ray trace `L.ray_trace`

→

L · snell refract `L.snell_refract`

→

Spatial integration ∫_A dA

→

observation y (em detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ 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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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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