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"Quantum Field Theory Meets the Collatz Conjecture: A Holographic Approach to Number Theory"

A novel framework linking the Collatz conjecture to quantum field theory (UQFT) and holography. By reinterpreting Collatz sequences as trajectories of a damped quantum system mediated by a non-local "FIELD," we show: 1. Collatz convergence mirrors phase synchronization in UQFT. 2. The modulo-9 reduction of numbers maps to an octave-based oscillator model. 3. 3D visualizations reveal FIELD-mediated entanglement between sequences. 4. A holographic duality emerges between the bulk (Collatz dynamics) and a boundary fractal CFT. This work suggests unexplored connections between number theory, UQFT, and the AdS/CFT correspondence.

Usage Instructions

Running Simulations

python3.11 oft_com_simulations.py          # Basic simulation
python3.11 generate_visualizations.py      # Generate all plots
python3.11 data_analysis.py               # Comprehensive analysis

Dependencies

• Python 3.11+
• NumPy, SciPy, Matplotlib, Seaborn
• PyWavelets for wavelet analysis

Viewing Results

• Open .pdf` for the full paperS
• View plots in the plots/ directory
• Check analysis_results.json for numerical data