L1 ⚛ L1-253 ⊙ Testnet

Ray Tracing (EM) — wireless propagation model

Electromagnetics · Urban propagation ray tracing (5G/6G)

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Layer template

⬇ principle.md ⬇ principle.json

Fork L1-253

⬇ L1-253.md ⬇ L1-253.json

Prompt — copy into your LLM

You are helping me submit a MODIFICATION of L1-253 (Ray Tracing (EM) — wireless propagation model) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-253.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-253.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.gather_paths` `L.reflect_diffract` δ_source x + n,    n ~ 𝒩(0, σ²)

world state x (signal strength map)

→

Source emission δ_source

→

L · reflect diffract `L.reflect_diffract`

→

L · gather paths `L.gather_paths`

→

Spatial integration ∫_A dA

→

observation y (em detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-253.md

# ⚛ L1 Principle — Ray Tracing (EM) — wireless propagation model **ID:** `L1-253` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Urban propagation ray tracing (5G/6G)* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** signal strength map > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554001 --- ## 🧠 1. Introduction **Ray Tracing (EM) — wireless propagation model** is a **linear inverse problem** whose unknown lives in **signal strength map** space, within the **Urban propagation ray tracing (5G/6G)** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **rx power map** sensing mechanism. The forward operator applies, in order: isotropic point-source emission model; L · reflect diffract operator; L · gather paths 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** → Source emission → L · reflect diffract → L · gather paths → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.gather_paths` `L.reflect_diffract` δ_source x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.source_emit` | Isotropic point-source emission model | | `L.reflect_diffract` | L · reflect diffract operator | | `L.gather_paths` | L · gather paths operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Urban propagation ray tracing (5G/6G) | | Carrier | em | | Problem class | linear_inverse | | Solution space | signal_strength_map | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | RSSI_error_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `ray_tracing_em` · **Forward operator:** `ray_tracing_em_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N rx | — | 64 | | N rays | — | 100000 | | Snr db | dB | 30 | | N walls | — | 1000 | | Freq ghz | GHz | 3.5 | | Geometry error | — | 0 | | Material eps error | — | 0 | | Antenna pattern error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N rx | — | 1 – 10000 | | N rays | — | 1000 – 100000000 | | Snr db | dB | 0 – 40 | | N walls | — | 1 – 100000 | | Freq ghz | GHz | 0.1 – 300 | | Geometry error | — | 0.0 – 0.1 | | Material eps error | — | 0.0 – 0.3 | | Antenna pattern error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 3.0 | Metric | Range | |---|---| | Rssi db | 0.5 – 20.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **RSSI_error_dB**, with κ = `360` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2b80902bf2d6782d0d99478ed531b8b769ff810669e7d7cf69b8d96afd5cf23b` - **Chain tx hash:** `0xcc15c77e404ff48d63f9bcf9cfa621aeb3922cbe82ed7190eef7fc9a87fd25b2` - **Chain block:** `41554001` --- ## File Mapping This bundle consists of: `L1-253.md`, `L1-253.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-253.md` | Source of truth — edit this | Human or LLM | | `L1-253.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 `L1-253`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-253-001 Ray Tracing (EM) — wireless propagation model Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-253",
  "chain_block": 41554001,
  "chain_hash": "0x2b80902bf2d6782d0d99478ed531b8b769ff810669e7d7cf69b8d96afd5cf23b",
  "chain_tx_hash": "0xcc15c77e404ff48d63f9bcf9cfa621aeb3922cbe82ed7190eef7fc9a87fd25b2",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 360,
    "metric": "RSSI_error_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "RSSI_error_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.source_emit",
      "L.reflect_diffract",
      "L.gather_paths",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "rx_power_map",
    "solution_space": "signal_strength_map",
    "sub_domain": "Urban propagation ray tracing (5G/6G)",
    "title": "Ray Tracing (EM) \u2014 wireless propagation model"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ray_tracing_em_forward"
    ],
    "allowed_omega_dimensions": [
      "N_rays",
      "N_walls",
      "N_rx",
      "freq_GHz",
      "SNR_dB",
      "material_eps_error",
      "geometry_error",
      "antenna_pattern_error",
      "material_eps_error",
      "geometry_error",
      "antenna_pattern_error"
    ],
    "allowed_problem_classes": [
      "ray_tracing_em"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0",
      "forward_operator": "ray_tracing_em_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_rays": 100000,
        "N_rx": 64,
        "N_walls": 1000,
        "SNR_dB": 30,
        "antenna_pattern_error": 0.0,
        "freq_GHz": 3.5,
        "geometry_error": 0.0,
        "material_eps_error": 0.0
      },
      "problem_class": "ray_tracing_em"
    },
    "epsilon_bounds": {
      "RSSI_dB": [
        0.5,
        20.0
      ]
    },
    "omega_bounds": {
      "N_rays": [
        1000,
        100000000
      ],
      "N_rx": [
        1,
        10000
      ],
      "N_walls": [
        1,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "antenna_pattern_error": [
        0.0,
        0.3
      ],
      "freq_GHz": [
        0.1,
        300
      ],
      "geometry_error": [
        0.0,
        0.1
      ],
      "material_eps_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Urban propagation ray tracing (5G/6G)",
  "title": "Ray Tracing (EM) \u2014 wireless propagation model"
}

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