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We study synchronization transitions in financial markets via persistent homology applied to time-varying correlation networks. Vietoris–Rips filtrations on rolling Mantegna distance matrices (49 Fama–French industry portfolios, 1976–2026) capture one-dimensional homological cycles (H1) that reflect intransitive sectoral triples—configurations where two pairwise correlations are strong but the third is weak. Exact analytical null distributions for the persistence and count of such intransitive precursors in random metric spaces are derived. The data reveal a two-scale topological response: stress amplifies intransitivity among the most strongly correlated industries while dissolving it among weakly and moderately correlated ones. Because static topological summaries are highly collinear with average correlation, we assess the predictive ability of the momentum of topological reorganization for market stress onset. At short horizons (5–20 days) the momentum of average pairwise correlation dominates, but at 80–100 day horizons the standardized rate of change of the persistence-weighted mean cycle birth (dAvgBirth) significantly outperforms both a correlation-only control and the momentum of average correlation itself. Decomposing cycles into sectoral triples maps abstract topology onto interpretable linkages. The findings show that higher-order topological momentum captures a slow, structural component of stress build-up complementary to fast-moving correlation dynamics.