# Technical Data Extraction: Relative Upper Bound Analysis This document provides a comprehensive extraction of the data and trends presented in the provided image, which consists of two side-by-side line charts comparing "Relative upper bound" against "Relative distance" for different "base" configurations. ## 1. General Metadata * **Image Type:** Two-panel line graph. * **Language:** English. * **Primary Metrics:** * **Y-Axis:** Relative upper bound (Linear scale). * **X-Axis:** Relative distance (Linear scale). * **Common Legend Format:** `base:1eN` (where N is an integer). --- ## 2. Left Chart Analysis (Short Range) ### Component Isolation * **Header/Legend:** Located in the top-right quadrant. * **X-Axis Range:** 0 to 4000. Markers at [0, 2000, 4000]. * **Y-Axis Range:** 2.5 to 15.0. Markers at [2.5, 5.0, 7.5, 10.0, 12.5, 15.0]. ### Data Series & Trends | Series Label | Color | Initial Value (approx.) | Visual Trend Description | Convergence/Steady State | | :--- | :--- | :--- | :--- | :--- | | **base:1e4** | Blue | ~16.0 | Sharp exponential decay from 0 to 1000, then stabilizes into a high-frequency oscillation. | Oscillates between ~4.0 and ~6.0. | | **base:1e2** | Green | ~10.0 | Extremely rapid drop to a floor within the first 100 units of distance. | Oscillates between ~4.0 and ~5.5. | | **base:1e3** | Orange | ~13.0 | Rapid decay, intersecting the green line at distance ~500. Exhibits the highest amplitude oscillations. | Oscillates between ~3.0 and ~6.5. | --- ## 3. Right Chart Analysis (Long Range) ### Component Isolation * **Header/Legend:** Located in the top-right quadrant. * **X-Axis Range:** 0 to 30000+. Markers at [0, 10000, 20000, 30000]. * **Y-Axis Range:** 5 to 15+. Markers at [5, 10, 15]. ### Data Series & Trends | Series Label | Color | Initial Value (approx.) | Visual Trend Description | Convergence/Steady State | | :--- | :--- | :--- | :--- | :--- | | **base:1e4** | Blue | ~18.0 | Rapid decay. In this wider view, it maintains the lowest baseline of the three series. | Oscillates between ~3.5 and ~6.0. | | **base:1e5** | Green | ~15.0 | Moderate decay. Stays consistently between the blue and orange lines. | Oscillates between ~4.0 and ~7.0. | | **base:1e6** | Orange | ~18.0 | Slowest decay relative to the others. Maintains the highest average bound across the distance. | Oscillates between ~5.0 and ~8.0. | --- ## 4. Comparative Summary and Key Findings ### Trend Verification 1. **Initial Penalty:** All configurations start with a high "Relative upper bound" at distance 0, which decays as distance increases. 2. **Base Value Correlation:** * In the **Left Chart** (lower base values), the `base:1e4` (highest in that set) has the slowest decay and highest initial bound. * In the **Right Chart** (higher base values), the `base:1e6` (highest in that set) has the slowest decay and maintains the highest bound over long distances. * **Conclusion:** Increasing the "base" value generally increases the relative upper bound and slows the rate of decay toward the steady-state oscillation. 3. **Oscillatory Behavior:** All series transition from a smooth decay curve into a "noisy" or oscillatory steady state. The amplitude of these oscillations appears more pronounced in the `base:1e3` (Left) and `base:1e6` (Right) configurations. ### Spatial Grounding of Legends * **Left Plot Legend [x~0.7, y~0.8]:** Correctly identifies Blue (1e4), Green (1e2), and Orange (1e3). * **Right Plot Legend [x~0.7, y~0.8]:** Correctly identifies Blue (1e4), Green (1e5), and Orange (1e6). Note that Blue (1e4) is the common reference point between both charts.

# Technical Document Extraction ## Image Description The image contains two side-by-side line charts comparing "Relative upper bound" values across varying "Relative distance" for different base values. Both charts use color-coded lines to represent distinct base magnitudes, with legends positioned on the right side of each chart. --- ## Chart 1: Base Values 1e2, 1e3, 1e4 ### Axes - **X-axis**: Relative distance (0 to 4000) - **Y-axis**: Relative upper bound (2.5 to 15.0) ### Legend - **Blue**: base:1e4 - **Green**: base:1e2 - **Orange**: base:1e3 ### Line Trends 1. **Blue (1e4)**: - Starts at ~15.0 at x=0 - Drops sharply to ~5.0 by x=1000 - Stabilizes with minor oscillations (~5.0–7.5) between x=1000–4000 2. **Green (1e2)**: - Starts at ~12.5 at x=0 - Drops sharply to ~5.0 by x=1000 - Stabilizes with oscillations (~5.0–7.5) between x=1000–4000 3. **Orange (1e3)**: - Starts at ~10.0 at x=0 - Drops sharply to ~5.0 by x=1000 - Stabilizes with oscillations (~5.0–7.5) between x=1000–4000 ### Key Observations - All lines exhibit a steep initial decline followed by stabilization. - The 1e4 (blue) line has the highest initial value and slowest decline. - Oscillations increase in amplitude for all lines as relative distance increases. --- ## Chart 2: Base Values 1e4, 1e5, 1e6 ### Axes - **X-axis**: Relative distance (0 to 30,000) - **Y-axis**: Relative upper bound (5.0 to 15.0) ### Legend - **Blue**: base:1e4 - **Green**: base:1e5 - **Orange**: base:1e6 ### Line Trends 1. **Blue (1e4)**: - Starts at ~15.0 at x=0 - Drops sharply to ~5.0 by x=1000 - Stabilizes with oscillations (~5.0–10.0) between x=1000–30,000 2. **Green (1e5)**: - Starts at ~10.0 at x=0 - Drops sharply to ~5.0 by x=1000 - Stabilizes with oscillations (~5.0–10.0) between x=1000–30,000 3. **Orange (1e6)**: - Starts at ~15.0 at x=0 - Drops sharply to ~5.0 by x=1000 - Stabilizes with oscillations (~5.0–10.0) between x=1000–30,000 ### Key Observations - All lines show a similar sharp decline pattern but with extended oscillations. - The 1e6 (orange) line has the most pronounced oscillations. - The 1e5 (green) line starts lower than the others but stabilizes similarly. --- ## Cross-Chart Comparison | Base Value | Initial Y-Value | Stabilization Range | Oscillation Amplitude | |------------|------------------|----------------------|------------------------| | 1e2 (Chart 1) | ~12.5 | 5.0–7.5 | Low | | 1e3 (Chart 1) | ~10.0 | 5.0–7.5 | Moderate | | 1e4 (Chart 1) | ~15.0 | 5.0–7.5 | Moderate | | 1e4 (Chart 2) | ~15.0 | 5.0–10.0 | High | | 1e5 (Chart 2) | ~10.0 | 5.0–10.0 | High | | 1e6 (Chart 2) | ~15.0 | 5.0–10.0 | Very High | --- ## Notes - All data points are in English; no non-English text detected. - No embedded tables or diagrams beyond the two line charts. - Spatial grounding confirms legends are consistently placed on the right for both charts. - Trends align with legend labels: higher base values correlate with higher initial Y-values and more pronounced oscillations.