The evolution of modern architecture in Colombia during the mid-20th century was influenced by visionary engineers such as Domenico Parma. This study analyzes the ribbed slab system known as the “Reticular Celulado” developed by Parma, an innovation that facilitated the design of over 1,600 projects, streamlining the construction process. Through the examination of 450 historical layouts of its structural projects—especially from five major hospitals in Bogotá—alongside patents and journals from 1939 to 1970, this work describes the development and implementation of this system for the industrialization of construction in Colombia between 1947 and 1963. The “Reticular Celulado” system enabled rapid and cost-effective construction, with records indicating a progress rate of one floor per week. It was patented in four countries and implemented in nine, gaining recognition as the “Colombian system”. This research highlights how this technical advancement was crucial in the modern architecture style in Bogotá, contributing to the construction of nine-story buildings within 90 working days. Eight slab systems are presented, revealing their evolution towards the prefabricated “Reticular Celulado” slab system. This research underscores the importance of understanding these systems for proper seismic retrofitting. A linear and nonlinear mathematical analysis is included to propose updated reinforcement strategies under current seismic codes in Colombia.