The Loop-of-Loops Expansion Model (LEM) proposes a bidirectional framework in which the universe expands both outwardly through physical space and inwardly through cognitive observability. Three governing variables are introduced: the Universe Expansion Rate U(t), the Cognitive Expansion Rate C(t), and the Observability Index O(t). The Destiny Invariance Principle holds that the total informational content of the universe is fixed while our capacity to read it expands. Central mechanisms include Angle-Multiplication, a non-binary observational encoding system; seven discrete Waves of Observability marking phase transitions in cognitive reach; Inference Overflow, the condition in which inferential output exceeds verifiable substrate; Sleep Synchronization as a reset mechanism between individual cognitive loops and the universal data layer; and Corrupt-Data Epochs, historical periods of systematic inferential divergence. The framework culminates in the Universal Entanglement Language hypothesis: a non-binary, angle-native symbolic system posited as the necessary language for post-biological cognitive systems operating at full loop resolution.