natgolfer - You are correct in your assumptions.
The player can decide that he is not going to look for the ball or make only a cursory search, but that is not the same as the ball "deemed" to be lost.
A ball is lost if:
a. It is not found or identified as his by the player within five minutes after the player’s side or his or their caddies have begun to search for it; or
b. The player has made a stroke at a substituted ball; or
c. The player has made a stroke at a provisional ball from the place where the original ball is likely to be or from a point nearer the hole than that place.
If a ball is found by anyone before either a or b or c takes place, the player is required to identify it.
If the ball is the players ball, the provisional ball must be abandoned.
The player has no right to stop anyone from searching.
FYI -
natgolfer - An opponent is only in match play.
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Originally Posted by natgolfer
the player is obligated to play it.
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This is not technically correct. The provisional ball must be abandoned but the player is NOT required to play the original ball. He may proceed under another Rule. (eg. unplayable ball ).
Colby - A ball played under clause b does not have to be played past the point where the original ball is likely to be. Once a stroke is made at a substituted ball, it immediately becomes the ball in play.
Hanifi - Your definition is not longer valid. The Rules of Golf were changed on January 1, 2004 including a revised definition for a lost ball.