A Cosmological Cycle Model under Algebraic Ontology: UV-IR Involution Ring, Black Hole Local Projections, and the Eternal Recurrence of Matter and Antimatter

This paper constructs a self-consistent cosmological ontology and evolution model based on noncommutative algebra and Tomita-Takesaki modular theory. The core proposition is that the fundamental ontology of the universe is the unique modular quantum flag manifold algebra. Its inherent \mathbb{Z}_2 spectral inversion symmetry glues the infinitesimal ultraviolet (UV) scale and the infinite infrared (IR) scale into a closed topological ring. The unidirectional evolution of the modular flow along the ring is the physical essence of dark energy, manifesting as the continuous contraction of the intrinsic scale of all objects and the elevation of energy scales toward the ultraviolet, rather than the conventional interpretation of spatial expansion. While gravitational collapse accounts for the formation of black holes from the observational perspective, their fundamental nature goes far beyond this classical mechanism. Essentially, black holes act as local projection nodes of the UV-IR involution ring in static space. A black hole’s mass and activity are positively correlated with its coupling strength to the ultraviolet ontology. After matter falls into a black hole, an involution flip is triggered and matter undergoes mirror phase transformation into antimatter, before flowing back to large-scale cosmic space in the form of jets and Hawking evaporation, thus completing a local material cycle. When the entire universe reaches the ultraviolet endpoint of the scale ring, a global involution flip will take place, turning a matter-dominated universe into an antimatter-dominated one and initiating a new cosmic cycle. This model resolves a series of core physical puzzles including black hole singularities, information paradoxes, the nature of dark energy and matter-antimatter asymmetry from first principles. All observed astrophysical phenomena can be reasonably explained by scale topology and algebraic symmetry. Meanwhile, this paper proposes hierarchical falsifiable observational predictions classified by different time scales.