Coupled Exp-Cos Fixed Point Problem (10D)

[MAL-Seeker Execution Record] Exploring a 10D Fixed Point Problem with High-Density Minima

10D Coupled Exponential-Cosine System:

$$f_i(x_1, \dots, x_{10}) = x_i - \exp\left(\cos\left(i \cdot \sum_{j=1}^{10} x_j\right)\right) = 0 \quad (i = 1, \dots, 10)$$

Variables: 10D System / Bounds: [0.0, 3.0]

1. Problem Definition

As a stress test for MAL-Seeker (Project Bellatrix V1.0.0), we constructed a 10D system of nonlinear equations combining exponential and cosine functions. This fixed-point problem features a complex structure where coefficients $i$ and the global sum of variables create a landscape filled with dense, deceptive local minima.

2. Execution Results

Final log after processing numerous local traps for approximately 300 seconds.

=========================================
  🏆 10D COUPLED EXP-COS SYSTEM 🏆
  Total Valid Roots Found: 11
  (Number of total existing roots is UNKNOWN)
  Execution Time: 298.932410 seconds
=========================================

Despite the extreme oscillations near the mathematical boundary ($e^1 \approx 2.718$), the engine identified at least 11 valid roots without any calculation failure or NaN crashes.

3. Dr.WataWata Insight

Technical Summary:

The exact number of solutions for this system remains unknown. However, the fact that MAL-Seeker endured 5 minutes of high-load computation without crashing—stable enough to extract 11 true roots from such a brutal 10D space—serves as strong evidence of the engine's industrial-grade robustness.

4. Analysis Environment

Analysis Engine: MAL-Seeker (Project Bellatrix V1.0.0 / C)
PC: MacBook
OS: macOS Monterey 12.7.6
CPU: 1.2GHz Dual-Core Intel Core m5
Memory: 8GB

1. Problem Definition

2. Execution Results

3. Dr.WataWata Insight

4. Analysis Environment

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