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      "statement": "# Xie et al.: doubly-stochastic constrained hyper-connections\n\nConstrained multi-stream residual mixing through Sinkhorn-normalized nonnegative matrices and integrated fused kernels, recomputation and communication overlap to make expanded residual connections more stable at scale.\n\n## Scientific scope\n\nHyper-Connections and Sinkhorn-Knopp are inherited. Doubly stochastic mixing is not an exact identity map or a proof of full nonlinear network stability. Twenty practical normalization iterations only approximate the limiting constraint; norm contraction does not guarantee avoidance of collapse.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nZhenda Xie; Yixuan Wei; Huanqi Cao; Chenggang Zhao; Chengqi Deng; Jiashi Li; Damai Dai; Huazuo Gao; Jiang Chang; Liang Zhao; Shangyan Zhou; Zhean Xu; Zhengyan Zhang; Wangding Zeng; Shengding Hu; Yuqing Wang; Jingyang Yuan; Lean Wang; Wenfeng Liang\n\nSource-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.\n\n\n\n## Original sources\n\n- [mHC: Manifold-Constrained Hyper-Connections](https://arxiv.org/abs/2512.24880v1)\n",
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