提出嵌入空间中时间锚定的理论框架，解析事件触发下的投影与收敛机制。
Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture
- 构建漂移-事件块-仿射投影的递归架构，实现时间锚定
- 证明漂移-投影收敛性及带均匀间隙边界，支持稳定计算
- 内建手稿计算机模型，可精确模拟注意力层的收缩行为
本文构建了嵌入空间中时间锚定的算子理论框架，模型由交替的漂移映射与事件索引块组成，最终通过仿射投影收束。我们完整证明了可变块收缩引理（利普希茨因子乘积）、带显式均匀间隙包络的漂移-投影收敛定理，以及在嵌套仿射锚点下的本体论收敛性与鲁棒性变体。形式化定义了一个内部手稿计算机（MC），其运算完全由这些算子定义，并证明了严格有限运行等价性（含扰动界）。针对注意力层，给出软最大函数在ℓ₂范数下为1/2-利普希茨的自包含证明，并推导出层收缩的充分条件（正交/非正交头）。所有浮点数均按原文位置放置；手稿仅使用文中伪代码与附录图示。
原文摘要 · Abstract (English)
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.
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