arXiv:2606.09153v2 Announce Type: replace Abstract: This paper studies the asymptotic behavior of sample canonical directions in a finite-rank spiked high-dimensional canonical correlation analysis model under a Gaussian population assumption. Under the asymptotic regime in which the dimensions of the two data blocks grow proportionally with the sample size, sample canonical directions are generally not consistent estimators of their population counterparts, even when the corresponding sample canonical correlations separate from the bulk spectrum. To quantify directional recovery, we investigate the squared alignment between a sample canonical direction and its associated population direction. For a supercritical simple population spike, we establish an explicit nonzero deterministic limit for the squared alignment. In contrast, for population non-spikes, we show that the alignment with the corresponding population signal directions vanishes asymptotically. Thus, the same phase transition that governs eigenvalue separation also marks a transition in directional recovery. For a supercritical simple spike, we further prove a central limit theorem for its fluctuations around the deterministic limit, with an explicit asymptotic variance expressed through deterministic limits of resolvent trace functionals. To make the theoretical quantities computable from data, we further construct plug-in estimators for both the deterministic alignment limit and the asymptotic variance by inverting the deterministic outlier eigenvalue map, and prove their consistency. Numerical simulations and a real-data illustration support the theoretical results and demonstrate how the proposed estimators assess the recovery quality of sample canonical directions.