Horizon Monism: A Finite-Horizon Relational Framework for Emergent Quantum Gravity

Horizon Monism is a relational and pre-spatiotemporal framework for emergent quantum gravity based on a minimal ontology consisting of a scale-free relational totality and a family of finite first-person reference horizons. The fundamental relational structure is assumed to contain no primitive spacetime, metric, temporal order, probability, quantum state, or gauge group. Physical structure instead arises from the finite distinguishability and relational compression associated with horizon-relative extraction. Finite relational equivalence classes and reversible relational composition lead, under complex-linear effective representation, to finite groupoid C*-algebras and effective noncommutativity. Under relational atomicity and minimal noncommutative realization, the elementary effective algebra is M_2( C), whose traceless self-adjoint sector is three-dimensional and provides a candidate origin for three spatial directions. Time is treated separately as an operational, horizon-relative local orientation: finite non-equivariance supplies the underlying asymmetry, while order-coherence and compatibility between comparable horizons allow local temporal orders to glue into an effective time-orientable structure. Combining the resulting one-dimensional temporal sector with the three-dimensional spatial sector yields an effective 3+1-dimensional Lorentzian structure. Structure-preserving comparison among neighboring horizons generates connection and curvature, with Einstein-type gravity arising conditionally as the leading local, metric-only infrared response. The framework further interprets effective atomicity not as an ontological minimum length but as the ultraviolet endpoint of a finite horizon’s distinguishability window. The corresponding infrared endpoint represents maximal joint relational accessibility. A proposed Horizon UV/IR Closure mechanism relates the two endpoints and yields the conditional scaling> Λeff_P^2> ~> ({_P}{LIR})^2,>giving an order of magnitude of 10⁻¹²² when the effective ultraviolet and infrared limits are identified with the Planck and cosmological scales. This is presented as a structural conjecture rather than a completed derivation of dark energy. Finally, an internal finite-geometry branch explores the emergence of Standard-Model-type gauge structure. Under additional assumptions involving oriented binary modules, pointed-horizon module naturality, chiral splitting, anomaly freedom, minimality, and faithful relational action, the construction selects a threefold non-Abelian multiplicity and leads to the faithful gauge group> [SU(3)_C× SU(2)_L× U(1)_Y]/ Z_6.>The framework is therefore presented as a conditionally closed research program rather than a completed theory of everything. Its principal open problems include the derivation of complex linearity and the Born rule, rigorous horizon-gluing theorems, the origin of three generations, the Higgs/Yukawa sector, the continuum limit, and numerical fundamental constants.