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Abstract The formation of magma‐poor continental rifts is an enigmatic process, as the weakening mechanism(s) for cratonic lithosphere remains uncertain in the absence of elevated lithospheric temperature. One view links weakening to melts hidden at depth, while another ascribes it to pre‐existing weaknesses. Long‐term extensional rates also influence lithospheric strength and rift evolution. We target the Linfen Basin (LB) in the magma‐poor Shanxi Rift System (SRS) in the North China Craton to understand these components. We apply cosmogenic²⁶Al/¹⁰Be burial dating on 14 core samples at different depths from three deep boreholes in the basin and obtain six valid burial ages ranging from 2.37^{+1.18/−1.21}to 5.86^+inf/−1.37 Ma. We further re‐interpret a seismic reflection profile and quantify the geometry and amount of extension by forward structural modeling with multiple constraints based on extensional fault‐bend folding theory. The timing of the basal sedimentation is estimated to be ∼6.1 and ∼4.2 Ma in the southern and northern portions, respectively, indicating diachronous, northward‐propagating rifting. The amount and mean rate of extension are ∼3.6 km and ∼0.9 km/Myr, respectively. The basin depths increasing northward indicates the clockwise rotation of the basin. We propose a basin‐scale non‐rigid transtensional bookshelf faulting model to explain the rotation patterns of the circum‐Ordos basins. We argue that the inherited structures weaken the cratonic lithosphere of the SRS, and the low extension rate contributes to its magma‐poor nature. We propose a lithospheric‐scale evolution model for the LB, invoking the inherited crustal weakness, low extension rate, and lower lithosphere counterflow. 

In this article, we tackle the estimation and inference problem of analyzing distributed streaming data that is collected continuously over multiple data sites. We propose an online two‐way approach via linear mixed‐effects models. We explicitly model the site‐specific effects as random‐effect terms, and tackle both between‐site heterogeneity and within‐site correlation. We develop an online updating procedure that does not need to re‐access the previous data and can efficiently update the parameter estimate, when either new data sites, or new streams of sample observations of the existing data sites, become available. We derive the non‐asymptotic error bound for our proposed online estimator, and show that it is asymptotically equivalent to the offline counterpart based on all the raw data. We compare with some key alternative solutions both analytically and numerically, and demonstrate the advantages of our proposal. We further illustrate our method with two data applications.