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## Cumulative Distribution Function (CDF) Plot: Rollbacks per Verification Window
### Overview
The image displays a Cumulative Distribution Function (CDF) plot comparing the distribution of "Rollbacks per Verification Window" across four different window sizes. The chart illustrates how the probability of observing a certain number of rollbacks (or fewer) changes as the window size increases.
### Components/Axes
* **Chart Type:** Step-wise Cumulative Distribution Function (CDF) plot.
* **X-Axis:**
* **Label:** "Rollbacks per Verification Window"
* **Scale:** Linear, ranging from 0.0 to approximately 0.9.
* **Major Ticks:** 0.0, 0.2, 0.4, 0.6, 0.8.
* **Y-Axis:**
* **Label:** "CDF" (Cumulative Distribution Function).
* **Scale:** Linear, ranging from 0.0 to 1.0.
* **Major Ticks:** 0.0, 0.2, 0.4, 0.6, 0.8, 1.0.
* **Legend:**
* **Position:** Bottom-right quadrant of the plot area.
* **Content:** Four entries, each associating a colored line with a "Window Size".
* Blue Line: `Window Size=32`
* Orange Line: `Window Size=64`
* Green Line: `Window Size=128`
* Red Line: `Window Size=256`
* **Grid:** Light gray, dashed grid lines are present for both major x and y ticks.
### Detailed Analysis
The plot contains four distinct step-function lines, each representing a different window size. The general trend is that for a given x-value (rollbacks per window), the CDF value is highest for the smallest window size (32) and decreases as the window size increases.
1. **Window Size=32 (Blue Line):**
* **Trend:** Rises most steeply and reaches a CDF of 1.0 (indicating 100% of samples) at the lowest x-value.
* **Key Points (Approximate):**
* At x=0.0, CDF ≈ 0.55.
* At x=0.2, CDF ≈ 0.80.
* At x=0.4, CDF ≈ 0.95.
* Reaches CDF=1.0 at approximately x=0.5.
2. **Window Size=64 (Orange Line):**
* **Trend:** Rises less steeply than the blue line but more steeply than the green and red lines.
* **Key Points (Approximate):**
* At x=0.0, CDF ≈ 0.58.
* At x=0.2, CDF ≈ 0.72.
* At x=0.4, CDF ≈ 0.88.
* Reaches CDF=1.0 at approximately x=0.7.
3. **Window Size=128 (Green Line):**
* **Trend:** Shows a more gradual increase, with a pronounced step around x=0.5.
* **Key Points (Approximate):**
* At x=0.0, CDF ≈ 0.58.
* At x=0.2, CDF ≈ 0.62.
* At x=0.4, CDF ≈ 0.75.
* Has a large vertical step at x≈0.5, jumping from CDF≈0.77 to CDF≈0.90.
* Reaches CDF=1.0 at approximately x=0.8.
4. **Window Size=256 (Red Line):**
* **Trend:** Rises the most slowly, indicating a higher probability of larger rollback values.
* **Key Points (Approximate):**
* At x=0.0, CDF ≈ 0.58.
* At x=0.2, CDF ≈ 0.59.
* At x=0.4, CDF ≈ 0.64.
* Has a large vertical step at x≈0.5, jumping from CDF≈0.64 to CDF≈0.83.
* Reaches CDF=1.0 at approximately x=0.9.
### Key Observations
1. **Initial Value at x=0:** All lines except the blue one (Window Size=32) start at a CDF of approximately 0.58 at x=0. The blue line starts lower, at ~0.55. This indicates that for window sizes 64, 128, and 256, about 58% of verification windows have **zero** rollbacks. For window size 32, only about 55% have zero rollbacks.
2. **Step Function Nature:** The lines are not smooth curves but step functions, indicating the data (rollbacks per window) is discrete.
3. **Convergence Point:** All lines converge to a CDF of 1.0, meaning 100% of the data is captured, but at different x-values (from ~0.5 for size 32 to ~0.9 for size 256).
4. **Major Discontinuity:** A significant, synchronized vertical step occurs for the green (128) and red (256) lines at x ≈ 0.5. The orange (64) line has a smaller step at the same location. This suggests a common event or threshold in the data at approximately 0.5 rollbacks per window that affects larger window sizes more dramatically.
### Interpretation
This CDF plot demonstrates a clear inverse relationship between the verification window size and the system's rollback performance. **Smaller window sizes (e.g., 32) are associated with fewer rollbacks per verification window.**
* **Performance Implication:** The steep rise of the blue line (size 32) shows that the vast majority of its verification windows experience very few rollbacks. In contrast, the slower rise of the red line (size 256) indicates a higher likelihood of encountering windows with a larger number of rollbacks.
* **Trade-off Insight:** The data suggests a potential trade-off. While larger window sizes might offer efficiency gains (verifying more data at once), they come at the cost of increased instability or error rates, manifested as more frequent rollbacks within a single window. The system appears more stable or "safer" when operating with smaller, more frequently verified chunks of data.
* **Anomaly/Threshold:** The pronounced step at x≈0.5 for larger window sizes is a critical feature. It implies that once the rollback rate crosses this approximate threshold (0.5 rollbacks per window), there is a high probability (a jump of 10-20% in the CDF) that the window will contain a significantly higher number of rollbacks. This could point to a systemic bottleneck or a failure mode that triggers more severely under larger window configurations.
