The Protocols of Linearity were the most important and widely-discussed of the Protocols of the Great Houses. They made it illegal (and therefore impossible) for Homeworlders to travel into the past of the Homeworld.
A consequence was that if an agent of the Great Houses were to leave the Homeworld for five years, though they could theoretically return moments after they left, upon their return they would inevitably find that five years had passed there as well. In effect, whenever an agent entered an area of time outside the Homeworld, their relative histories would be temporarily linked so that their "present"s would be indistinguishable, despite being aeons apart. (PROSE: Protocols of Linearity)
This rule applied to other time-active powers as well, including Faction Paradox. Because they signed the Gregorian Compact with George II in 1752, agents of the Faction and the Great Houses alike found it difficult to penetrate Earth's causality for the next seventy years. Observing this period would, in effect, be too much like looking into their own future. (PROSE: Earth)
During the War, both the Great Houses and the enemy obeyed the Protocols of Linearity. Many theorised that this was due to the Houses' inability to revoke the Protcols, an agreement between the two parties, or both parties' fear of the consequences of non-linearity. (PROSE: Protocols of Linearity)
When the Remote left Faction Paradox, they became divorced from linearity. This explains Compassion's life, for instance, since she was born during the War but traveled with an old-fashioned timeship in the pre-War era before becoming the first 102-form. (PROSE: Timeships)
The Violent Unknown Event at Zo la Domini broke linearity and allowed agents of the Great Houses' pre-War Order of the Weal, including Chatelaine Thessalia, to interact with War era agents of Faction Paradox. This led Thessalia to believe that the Faction was the enemy, and shortly after the event she disappeared in another VUE on the frontier of time. (PROSE: Zo la Domini)