Relational Reality under Global Zero Constraint : A Unified Interpretative Framework for Conundrums in Cosmology and Quantum Mechanics

Building upon the theory of 'Relational Differentiation under Global Zero Constraint ($\sum U_i = 0$)' proposed in the previous research series (Paper I–III), this paper presents a unified interpretative framework for macroscopic (cosmology) and microscopic (quantum mechanics) conundrums in modern physics. Specifically, we reinterpret the Horizon Problem, Flatness Problem, Hubble Tension, and the quantum measurement problem from a graph-geometric perspective. We redefine the universe not as a set of particles on a spacetime background, but as a Spectral Boundary of a stabilized relational graph satisfying a global constraint. From this perspective, the Big Bang is described not as an explosion of spacetime, but as a Geometric Percolation process in the pre-temporal phase, from which the homogeneity and flatness of the early universe are naturally derived. Furthermore, by introducing a coefficient $\alpha$ representing the validity of the time dimension, we elucidate the mechanism by which time becomes undefined at black hole singularities and in the early universe. This study provides a new phenomenological map that identifies the Structural Origin of why physical phenomena take their specific forms and values, explicitly acknowledging that it offers a meta-interpretation rather than calculating specific standard model parameters. Key Highlights Ontological Foundation: Proposes the 'Global Zero Constraint' as a minimal mathematical condition for observability in a closed system. Cosmological Reinterpretation: Inflation: Modeled as a Percolation Phase Transition where the giant connected component forms. Dark Energy: Reinterpreted as Boundary Tension scaling with the expansion of the relational network, offering a solution to the Hubble Tension. Dark Matter: Explained as Spectral Decoupling (Geometric Shadows) due to inactive subgraphs, analogous to Anderson Localization. Quantum Mechanical Reinterpretation (Expanded in v1.1): Superposition: Defined as Topological Isolation where the interaction term with the environment effectively vanishes. Measurement: Defined as Topological Surgery (Gluing) that alters the graph topology, triggering Spectral Alignment (wavefunction collapse). Born Rule: Derived as the Geometric Consistency Cost (Pythagorean cost) to maintain the global zero constraint. Entanglement: Interpreted as subsystems sharing a Private Zero Constraint, enabling non-local correlations via Bulk Connectivity without violating relativity. Classical Reality: Emerges inevitably from the state of Perpetual Gluing in macroscopic objects, which suppresses superposition. Particle Generations: Linked to the topological invariants (Genus $g=3$) of the microscopic graph structure. Nature of Time: Introduces the effective dimension coefficient $\alpha$. Time is defined as a semigroup trace of information accumulation, which vanishes ($\alpha \to 0$) at singularities, strictly forbidding physical time travel. Notes This paper serves as the final integration (Paper IV) of the research series, synthesizing the mathematical derivations from Papers I, II, and III into a comprehensive physical interpretation.