Z_7 Defect Cosmology: Domain Walls, Phase Transitions, and the Zero-Relic Prediction

As the early universe cooled, it underwent phase transitions — just like water freezing into ice. When different regions of space independently chose their low-energy configuration, boundaries called domain walls formed between them. These topological defects are potentially catastrophic for the universe's development. This tutorial explains how the Z_7 symmetry of the GTE polynomial gives rise to a specific defect cosmology: what kinds of defects form, why the seven-fold degeneracy of the GTE vacuum predicts a zero relic abundance of dangerous monopoles and textures, and how the discrete arithmetic structure of the substrate controls the cosmological phase-transition history.