Archive Trap

• WWizards of the Coast2009-10-01
  Official Ruling
  A spell or ability causes a player to search their library only if it specifically contains the word “search” in its text. For example, if a spell or ability lets a player look at the top four cards of their library and do something with one of those cards, that’s not a search.
• WWizards of the Coast2009-10-01
  Official Ruling
  Archive Trap checks only whether an opponent searched their library. It doesn’t matter whether that player found a card during the search.
• WWizards of the Coast2009-10-01
  Official Ruling
  You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.
• WWizards of the Coast2009-10-01
  Official Ruling
  Casting a Trap by paying its alternative cost doesn’t change its mana cost or mana value. The only difference is the cost you actually pay.
• WWizards of the Coast2009-10-01
  Official Ruling
  Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.
• WWizards of the Coast2009-10-01
  Official Ruling
  If the targeted opponent has fewer than thirteen cards in their library, that player puts their entire library into their graveyard.
• WWizards of the Coast2009-10-01
  Official Ruling
  If a search effect is affected by Aven Mindcensor’s ability (which causes a player to search the top four cards of their library instead), that still counts as searching that library.
• WWizards of the Coast2009-10-01
  Official Ruling
  The opponent you target doesn’t have to be the opponent who searched their library.

Rulings via Scryfall