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DHoTT: A Temporal Extension of Homotopy Type Theory for Semantic Drift
Iman Poernomo
https://arxiv.org/abs/2506.09671 https://arxiv.o…

DHoTT: A Temporal Extension of Homotopy Type Theory for Semantic Drift
We introduce Dynamic Homotopy Type Theory (DHoTT), a temporal extension of Homotopy Type Theory (HoTT) designed to reason formally about concepts whose meanings evolve continuously or rupture discontinuously over time. While traditional HoTT captures identity and equivalence within a fixed semantic landscape, DHoTT enriches this framework by explicitly indexing types with a temporal parameter, allowing types themselves to deform, rupture, and reassemble as contexts shift. Formally, we show th…