[STCT-VOL.13] Cosmology & Origin: Fundamental Evolution of the Pure Algebraic State Pre-Big Bang

This paper redefines the pre-Big Bang singularity, where Einstein’s field equations break down, as a ‘Pure Algebraic Space’ based on the Seonggil Theory of Composite Torsion (STCT), Rough Operator Algebra (ROA), and infinite-dimensional Hypertensor mechanics. Criticizing the arbitrary initial conditions of existing quantum tunneling cosmologies, this study demonstrates through ‘Algebraic Causality’ how the residual Weyl tensor topological entropy from the collapse of the previous universe acts as the engine for new expansion. By introducing continuous dynamic rank integration and the non-associative G_2 gauge associator, we mathematically prove that the Big Bang is not a random fluctuation, but a deterministic geometric repulsion driven by the failure of associativity at the maximum compaction limit, perfectly synchronized with the golden ratio resonance attractor.