Finite Distinguishability and the Emergence of Quantum and Gravitational Structures

This work introduces and formalizes Horizon Monism, a foundational relational research program built upon minimal ontology. It postulates a timeless, scale-free, geometry-free totality of relations \mathfrak{R}, together with a collection of irreducible first-person referential anchors. All observable physical phenomena emerge from a single core constraint: finite distinguishability. Each referential anchor carries a non-injective information extraction map, which induces reference-dependent equivalence relations. These partition the underlying relational totality into quotient spaces of effectively distinguishable states. Non-commutative algebraic structures (quantumness), effective time and its arrow, Lorentzian spacetime geometry together with gravity, and gauge interactions all arise homologously as effective descriptions for observers confined within finite referential horizons. We rigorously demonstrate that finite equivalence classes equipped with relation groupoids yield non-commutative C^*-algebras. A four-point classical toy model further illustrates that incompatible extraction operations can naturally produce non-commutativity, serving as a mathematical prototype for the horizon-based origin of quantum structures. We clearly separate three tiers of statements: constructively proven mathematical results, hypothetical emergence mechanisms, and low-energy effective phenomenology. The Standard Model gauge group and particle spectra are treated as low-energy emergent features to be derived in future work, rather than fundamental axioms. This framework avoids circular reasoning by not presupposing time, probability, spacetime geometry or quantum states at the ontological level, offering a falsifiable relational pathway toward quantum gravity.