Horizon Monism: A Unified Relational Framework for Emergent Time, Quantum Structure, and Spacetime Geometry

Horizon Monism proposes a unified theoretical framework in which quantum structure, operational time, and spacetime geometry emerge from finite reference horizons embedded within a single, scale-free relational–interaction totality. Rather than treating spacetime, fundamental time, and quantum probabilities as primitive, the framework investigates their possible reconstruction through finite distinguishability, relational compression, and effective projection structures. The paper establishes a strict mathematical hierarchy of finite-horizon resolutions, deriving monotonic distinction deficits and a directed fine-to-coarse order as a candidate foundation for operational time. This construction is extended to multiple reference horizons through order-preserving transport and conditional shared-blindness theorems. Within a conditionally constructed complex groupoid algebra, the minimal noncommutative effective structure is identified as M₂(ℂ). Projection compression is shown to generate noncommuting effective operators, while smoothly varying projections induce connection curvature. Under specified geometric conditions, this curvature reconstructs the Levi-Civita curvature of an emergent Lorentzian spacetime. Explicit de Sitter and nonlinear Green-spectral constructions provide conditional examples of Einstein geometry and stable nonvanishing projected curvature. A further reconstruction of quantum probability establishes that normalized, context-independent, coarse-graining-consistent effect assignments admit a unique density-matrix representation, recovering the Born rule for pure states. The Principle of Minimal Sufficient Realization is additionally applied to a restricted class of Standard-Model-type representations, yielding conditional minimality results for color, fermion generations, and Higgs structure. The framework distinguishes exact mathematical theorems from conditional physical realizations. Its principal unresolved questions concern the microscopic origin of quantum probability consistency, physical state selection, continuum dynamics, and experimentally distinguishable predictions. Horizon Monism is presented as a mathematical and theoretical research program toward the possible co-emergence of quantum physics and gravitation.