Horizon Monism: A Unified Relational Framework for Emergent Quantum Noncommutativity, Spacetime Curvature, Operational Time, and Minimal Physical Realization

Horizon Monism is a relational approach to foundational physics in which a single scale-free, relation-complete totality and a family of finite, referentially non-interchangeable horizons constitute the minimal ontological inputs. Quantum noncommutativity, operational time, spacetime geometry, and matter representations are investigated as effective structures arising from horizon-dependent relational descriptions rather than as independent fundamental substances. This paper consolidates the foundational framework and its mathematical extensions into a unified theoretical treatment. Its central mathematical result identifies a common projection mechanism underlying compression-induced operator noncommutativity and projected-connection curvature. Two exact identities demonstrate how both structures can be expressed through antisymmetrized couplings between accessible and complementary relational sectors. Under additional geometric assumptions, projected curvature admits a Lorentzian Levi-Civita interpretation, while a four-dimensional de Sitter construction provides an explicit nonflat Einstein-space realization. Complementary results establish conditional representations of effective temporal continuity and demonstrate the persistence of nonvanishing weak projected curvature under nonlinear variational stabilization in a specified Green-spectral model. The framework further introduces the Principle of Minimal Sufficient Realization (PMSR), which selects physically admissible models with minimal irreducible structure relative to explicitly specified operational equivalences and consistency requirements. Within a restricted Standard-Model-type chiral representation class, anomaly consistency, non-Abelian mixing, observable CKM-type CP violation, and renormalizable Yukawa mass generation yield the conditional joint minimum of three color degrees of freedom, three fermion generations, and one complex Higgs doublet with hypercharge +1/2. The resulting framework provides exact projection identities, constructive mathematical models, and conditional classification theorems connecting algebraic, geometric, temporal, and particle-physics descriptions. It does not establish a unique derivation of the observed universe, a complete quantum-gravitational dynamics, or independently verified experimental predictions. Horizon Monism is therefore presented as a mathematically developed but physically incomplete research program whose central proposal is that quantum noncommutativity and spacetime curvature may represent distinct effective manifestations of a shared underlying relational structure.