Modal Typal Theory: A New Paradigm for Quantum Gravity

We present a radical new paradigm for quantum gravity: Modal Typal Theory. Founded on a revolutionary core principle---the relativity of physical reality itself---the theory asserts that existence, facts, and even physical laws acquire definite meaning only within specific ``universe type'' frameworks. Distinct observer frameworks (e.g., external vs. infalling near a black hole) are equally valid and self-consistent; transitions between them entail fundamental changes in physical content. We construct the paradigm's robust mathematical backbone: Modal Type Theory. This is a rigorous framework synthesizing category theory, homological algebra, and topology, wherein ``information'' is globally described and strictly conserved via derived functors. The apparent information paradox---most notably the black hole information problem that has perplexed physicists for half a century---finds its complete and elegant resolution here. Information is never lost; it is merely redistributed through typal projections.