Accurately modeling cross-variate dependencies remains a key challenge in multivariate time series forecasting, particularly in the presence of strong periodic patterns. Many existing approaches rely on attention-based mechanisms that incur quadratic complexity and scale poorly with increasing numbers of variates. Recent attention-free aggregation models address this issue through linear-complexity core-based interactions, but they do not explicitly leverage the global periodic structure present in the data. To overcome this limitation, we propose CARNet, a Cycle-Conditioned Core Aggregation and Redistribution framework that integrates global recurrent cycle information into efficient core based interaction modeling via Multihead Core Aggregation. Extensive experiments on multiple real-world multivariate forecasting benchmarks demonstrate that CARNet consistently outperforms strong transformer and non-attention baselines across diverse prediction horizons while preserving linear-complexity modeling of cross-variate dependencies.