Shiftless Collatz Model: Binary Interference in the 3n+LSB Trajectory

This work introduces the Shiftless Collatz model, a reformulation of the classical Collatz mapping that completely removes the right-shift operation (n/2). Instead of discarding the least significant bit (LSB), the model injects its full binary weight (2^v) into the system.
The Shiftless Collatz model preserves all bit-level information, enabling the entire trajectory to be visualized as a 2D binary canvas. This study analyzes the mathematical and visual structure of the Shiftless Collatz trajectory and demonstrates:

• Full equivalence to the standard Collatz model (odd-part synchronization, step-count equivalence)
• Carry avalanches and Sierpiński-gasket-like fractal structures
• A two-phase internal structure: Reach (3n) and Fill (3n+LSB)
• Synchronized comparison of 3n / 3n+1 / 3n+LSB
• Linear decomposition of the trajectory into geometric expansion and cumulative LSB contributions, revealing moiré-like interference patterns
  This repository includes the full research report (JP/EN), Python implementations, and all visualizations.