QFunity: Quantum Fractal Unity – A Scale-Dependent Unified Theory of Everything (Version 1.3)

QFunity (Quantum Fractal Unity) is a scale-dependent unified framework emerging from an eternal Emergent Pre-Temporal (EPT) fractal substrate with Hausdorff dimension d_H > 4.

The theory is built on three foundational pillars:
1. Everything is rotation (encoded by the dimensionless torsion operator B̂_ε)
2. Zero does not exist (enforced by the regularization ‖Ψ‖² + ε²)
3. Everything depends on the size of the observer (via the resolution parameter ε)

These pillars are unified by the stabilized master commutator equation (verified in collaboration with DeepSeek and Grok):

lim_{ε→0^±} [B̂_ε V̂_ε - V̂_ε B̂_ε²] Ψ = Λ E_P · Ψ / (‖Ψ‖² + ε²)

The EPT substrate replaces classical singularities with finite critical-radius interfaces r_c ∼ ℓ_P (M/m_P)^{1/3} and naturally resolves major cosmological tensions (Hubble constant, JWST early galaxies, core-cusp problem, dark energy equation of state).

This record is the full preprint corresponding exactly to the main page: https://qfunity.com/index.html (Version 1, May 2026).

The work results from a unique Human-AI collaboration.