Articles of Colonization
From Battlestar Wiki, the free, open content Battlestar Galactica encyclopedia and episode guide
This event was apparently in response to the Cylon War to unite against a common enemy . Before the Articles, each colony was a sovereign nation, and there was open fighting between the colonies at times.
Chief Tyrol invokes the 23rd Article to avoid testifying against himself during the investigation into how Aaron Doral got aboard Galactica and accessed the munitions stores. While Sergeant Hadrian attempts to use this as evidence of his guilt, Commander Adama later points out to President Roslin that there is no legal precedent for doing so (Litmus).
Although the above details the only named articles mentioned in the Re-imagined Series, there are further hints as to protected rights included.
The right to a trial with representation before a jury seems to be guaranteed. When disapproving of the decision of then-President Tom Zarek to form the Circle, a form of war crimes tribunal, Laura Roslin states that everyone has the right to a trial before a jury of one's peers. In a separate statement Roslin refers to the right to representation at a trial (Collaborators). The right to a jury trial is also claimed by Gaius Baltar (Taking a Break From All Your Worries). Whether these are two separate rights quoted from the Articles or just natural extensions of a more general right to a fair trial as in the sixth Amendment to the U.S. Constitution is unknown.
Baltar's trial shows other levels of jurisprudence. Instead of a jury, a five-member tribunal is used as judge and jury. Numerous legal maneuvers are parallels to modern American practices (Crossroads, Part I & II).