Universal Nanohertz Gravitational Wave Background from Topological Phase Transitions

We present a unified model explaining the nanohertz gravitational wave (GW) background observed by pulsar timing arrays (PTAs). The signal arises fromubiquitous topological phase transitions between spherical (S2) and toroidal (T 2) spacetime configurations mediated by graviton surgeons. Unlike conventional binary black hole mergers, this mechanism produces a characteristic f ^(−1) spectrum through continuous vacuum oscillations and defect dynamics. The model predicts anisotropic correlations with large-scale structure and spectral features testable with next-generation PTAs. Fundamental implications for quantum gravity anddark energy are discussed.