The Compressed Map in the Future Direction: From Filtering to Topological Fracture

This paper extends the companion work (The Compressed Map as Holonomy of the Spin Connection, Zenodo 2026) to the future direction. When a compressed map is transported forward in time rather than backward, the formal structure changes qualitatively: instead of colliding with established historical structures, the map propagates silently through ordinary interactions and restricts the trajectory space of future observers without producing any detectable anomaly. Four new geometric objects are introduced: the compatibility field C(x,t), the metric fracture, the liminal worldline, and the consistency fixed point of the configuration space. A causal hierarchy among four singularity types is established and the induction condition for metric fracture is derived. The central result is a structural asymmetry theorem: the past direction generates coherence problems with detectable traces; the future direction generates invisible constraints on the possibilities of others.