Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture
Abstract
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 -Lipschitz in 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.
Cite
@article{arxiv.2508.09693,
title = {Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture},
author = {Faruk Alpay and Bugra Kilictas and Hamdi Alakkad},
journal= {arXiv preprint arXiv:2508.09693},
year = {2025}
}
Comments
16 pages, 2 figures, 2 tables