Lineal Tiles are a concept that I have always enjoyed as a fan of combat sports. The idea started in boxing as a way to keep track of the "real" champion even if he chose to vacate the title for one of the many promotions in boxing. After all, just because a title is "stripped" or "vacated" does not mean that the champion was ever truly defeated.
The easiest way to think about a lineal champion is "the man who beat the man." Below is a table showing the various "Lineal" champions across all of the major MMA promotions: