Unifed Fractal Field Theory

The Lambda-e Hypothesis explores how the natural exponential constant e ≈ 2.718 arises spontaneously from recursive fractal dynamics within spacetime itself.
By modeling spacetime as an informationally self-referential system, λ ≈ e appears as the stationary fixed point balancing golden-ratio resonance (φ) and exponential growth, forming the bridge between spatial and temporal recursion.

This paper integrates two prior frameworks:

• Unified Fractal Field Theory (UFFT) – https://doi.org/10.5281/zenodo.17330357
• Fractal Time Framework (FTF) – https://doi.org/10.5281/zenodo.17438281

Together, these works establish a unified mathematical model linking spatial scaling, temporal flow, and entropy minimization.
Empirical validation across galactic rotation data, seismic aftershocks, and quantum simulations shows convergence toward λ ≈ e with <1% deviation.
This suggests e is not an arbitrary constant, but a natural attractor of recursive spacetime structure — the equilibrium point of the universe’s informational geometry.