# 🏆 Milestone: Pure Physical 1/R⁴ & Zero-Tilt Symmetry

**Date:** 2026-04-08  
**Iteration Range:** 20 — 26  
**Status:** **LOCKED-IN BASELINE**

---

## 🏗️ 1. The Physics Breakthrough: 1/R⁴ Power Law

Prior to this milestone, the C-Shenron engine used various "normalization" workarounds (like Iteration 16's `DENSITY_REF = 1000`) to prevent distant buildings from overwhelming the scene. However, these were artificial and lacked dynamic fidelity.

### The Problem:
- Distant buildings (massive surface area) were integrated with the same weight as near cars.
- Because distance-based attenuation was "neutralized" in the code, the building's magnitude (1600) was higher than a near car (1400).
- This made ADAS algorithm testing impossible as the SNR profiles were physically incorrect.

### The Solution:
We have stripped all artificial normalizations and returned to **Pure Free-Space Physics**:
1.  **Transmitter Power ($P_{inc} \propto 1/R^2$)**: Each LiDAR point's incident power now follows the inverse square law.
2.  **Receiver Voltage ($V_{adc} \propto 1/R^2$)**: The final ADC signal is attenuated by the return path ($1/R^1 \text{ voltage} \implies 1/R^2 \text{ power}$).
3.  **Result**: The total power follows the **$1/R^4$ Radar Range Equation**. A distant building is now physically $ \sim 50,000\times$ weaker in power than a near car, making the car the natural dominant peak.

---

## 📐 2. The Geometric Breakthrough: Zero-Tilt Symmetry

The Range-Azimuth "Fan" plot in earlier iterations appeared slightly tilted (sheared) toward the left.

### The Problem:
- **Index Asymmetry:** Standard FFT indexing `np.arange(-N/2, N/2)` results in an asymmetric range (e.g., $-32 \to +31$ for 64 points).
- **Angular Mapping:** This created a ~15° mismatch between the left and right boundaries of the Field of View.

### The Solution:
- **Symmetry-Lock:** We updated `radar_processor.py` to use perfectly centered index linear spaces: `np.linspace(-N/2 + 0.5, N/2 - 0.5, N)`.
- **Result:** The 120° FOV fan is now perfectly symmetric around the boresight. This is critical for ADAS verification where lateral accuracy is paramount.

---

## 🖼️ 3. Visual Standard: "Radar Blue"

We have standardized the diagnostic visualization suite for all future automated MCAP sessions:
- **Colormap:** `viridis` (Professional high-contrast blue/green/yellow).
- **Normalization:** **Global Frame Normalization**. No per-range-bin stretching is allowed, as it obscures the physical $1/R^2$ amplitude decay.
- **Dynamic Range:** Diagnostic heatmaps now preserve the "Energy Difference" between targets, ensuring human and AI agents can accurately judge target priority.

---
*Generated by Antigravity | Fox CARLA ADAS Pipeline Calibration Milestone | 2026-04-08*