深化嵌入空间中的时间锚定：事件索引投影、漂移、收敛与内部计算架构
Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture
AI总结：
本文提出一个用于嵌入空间时间锚定的算子理论框架，通过漂移映射与事件索引块交织构建模型，并证明了变块收缩引理、漂移-投影收敛定理及有限运行等价定理。
摘要：
我们为嵌入空间中的时间锚定开发了一个算子理论框架，建模为漂移映射与以仿射投影告终的事件索引块交织。我们为变块收缩引理（Lipschitz因子的乘积）、具有显式均匀间隙包络的漂移-投影收敛定理，以及具有鲁棒性变体的嵌套仿射锚下的本体论收敛提供了完整证明。我们形式化了一个内部Manuscript Computer (MC)，其计算完全由这些算子定义，并证明了严格的有限运行等价定理（带扰动界限）。对于注意力层，我们给出了softmax在ℓ2中是1/2-Lipschitz的自包含证明，并推导了充分的层收缩条件（正交/非正交头）。所有浮点数完全按照书写位置放置；手稿仅使用论文内伪代码和附录图。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
