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 rigorously define 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 an effective time 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 Inevitability 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, serving as a topological constraint on the allowed space of relational structures. Cosmological Reinterpretation Inflation: Modeled as a Percolation Phase Transition where the giant connected component forms, naturally resolving the Horizon and Flatness problems without fine-tuning. Dark Energy: Reinterpreted as Boundary Tension scaling with the expansion of the relational network. Accelerated expansion is explained as a result of tension saturation, offering a structural solution to the Hubble Tension and the Coincidence Problem. Dark Matter: Explained as 'Topological Shadows' (Ghost Graphs)—inactive subgraphs that are gravitationally coupled via the global constraint but spectrally decoupled from the electromagnetic sector. Observational Predictions: Predicts enhanced local expansion rates in cosmic voids and a cosmological linkage of the Radial Acceleration Relation (RAR). Quantum Mechanical Reinterpretation Superposition: Defined as Topological Isolation where the interaction term with the environment effectively vanishes (Temporary Isolation). Measurement: Defined as Topological Surgery (Gluing) that creates a new edge between the observer and the system, triggering Spectral Alignment (wavefunction collapse). Born Rule: Derived not as an axiom but as the Geometric Consistency Cost (Pythagorean cost) required to maintain the global zero constraint during spectral alignment. Entanglement: Interpreted as subsystems sharing a Private Zero Constraint, enabling non-local correlations via Bulk Connectivity. Classical Reality: Emerges inevitably from the state of Perpetual Gluing in macroscopic objects, which suppresses superposition. Nature of Time & Particles Emergence 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. Particle Generations: Linked to the topological invariants (Genus $g=3$) of the microscopic graph structure, explaining the three generations of fermions. 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. Related Works in this Series: Paper I: Relational Differentiation under Global Zero Constraint (DOI: 10.5281/zenodo.18028564) Paper II: Geometry of the Differentiation Boundary under Global Zero Constraint (DOI: 10.5281/zenodo.18051033) Paper III: Local Observer and the Flow of Time (DOI: 10.5281/zenodo.18058187)