Infinity Algebra and the Rejection of Closed Timelike Curves: Disproofs of Incomplete Frameworks in Relativity

Closed timelike curves (CTCs) have long presented paradoxes and logical challenges within the context of general relativity. Proposed constructs such as Gödel's rotating universe, the Tipler cylinder, traversable wormholes, and the inner regions of Kerr black holes all theoretically allow CTCs-but only under unphysical assumptions such as infinite mass, negative energy, or cosmological rotation. This paper introduces Infinity Algebra as a symbolic and structural framework that replaces such pathological geometries with a consistent algebraic encoding of time, causality, and recurrence. We demonstrate that CTCs do not emerge under Infinity Algebra, not by constraint, but by coherent symbolic substitution. The analysis shows how CTCs are artifacts of incomplete frameworks and idealized conditions-disproved in physical reality by cosmological observations and thermodynamic consistency. Infinity Algebra thus offers a causally consistent, infinite-dimensional alternative to curved-loop solutions.