标题： 时间锚定在深化嵌入空间中：事件索引投影、漂移、收敛和内部计算架构 显示英文标题

标题： Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture

摘要： 我们开发了一个算子理论框架，用于嵌入空间中的时间锚定，该框架被建模为交替的漂移映射和事件索引块，最终导致仿射投影。 我们提供了可变块收缩引理（乘积的Lipschitz因子）的完整证明，一个带有显式统一间隙包络的漂移-投影收敛定理，以及在嵌套仿射锚点下的本体论收敛性及其鲁棒性变体。 我们形式化了一个内部手稿计算机（MC），其计算仅由这些算子定义，并证明了一个严格的有限运行等价定理（带有扰动界）。 对于注意力层，我们给出了一个自包含的证明，表明softmax在$\ell_2$中是$1/2$-Lipschitz，并推导出足够的层收缩条件（正交/非正交头）。 所有浮点数都精确地放置在原处；手稿仅使用论文中的伪代码和附录图。 显示英文摘要

摘要： We develop an operator-theoretic framework for temporal anchoring in embedding spaces, modeled as drift maps interleaved with event-indexed blocks culminating in affine projections. We provide complete proofs for a variable-block contraction lemma (products of Lipschitz factors), a drift--projection convergence theorem with explicit uniform-gap envelopes, and ontological convergence under nested affine anchors with a robustness variant. We formalize an internal Manuscript Computer (MC) whose computations are defined purely by these operators and prove a rigorous finite-run equivalence theorem (with perturbation bounds). For attention layers, we give a self-contained proof that softmax is $1/2$-Lipschitz in $\ell_2$ and derive sufficient layer-contraction conditions (orthogonal/non-orthogonal heads). All floats are placed exactly where written; the manuscript uses only in-paper pseudocode and appendix figures.