# 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).
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## 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. |
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## 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. |
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## 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.
