Interference Vacuum: A Mathematical Framework for the Model and a Research Program

This paper presents a mathematical framework for the "Interference Vacuum" concept, where our Universe is a 3-brane embedded in a higher-dimensional bulk, dividing it into two half-spaces. The observed vacuum is interpreted as the interference of projections from processes occurring in these half-spaces. The model provides geometric foundations for quantum fluctuations, treats the false vacuum as a region of enhanced interference, and describes new universe birth as "breakthroughs" of projections. The work does not claim to be a complete theory; instead, it explicitly identifies five fundamental research gaps (nature of the bulk field, projection kernels, breakthrough dynamics, tunneling mechanism, and parameter calibration) that must be filled to develop a predictive theory.