A theoretical framework proposing Born Rule Fusion (BRF) for combining large language model ensemble outputs using quantum-inspired interference. BRF introduces bilinear cross-terms modulated by phase cosines — a structural operation absent from all surveyed ensemble methods. Three potentially fatal problems are presented with equal rigour. The framework is falsifiable: a concrete phase coherence test using the Rayleigh statistic is specified. All conceptual contributions are the sole responsibility of the author.