I'm probably thinking about this too much.

Here's the play.

Game clock displays tenths. It shows .3, .2, or .1, whichever. Therefore, you can't catch and shoot. However, can a player catch and be fouled?

Thanks in advance. Hope everyone's Holiday Tournaments are going well.

Reasoning from first principles
 

Reasoning from first principles, I'll say (but not prove) you can be fouled in all the ways a player can be fouled while the ball is alive EXCEPT that the foulee cannot be considered to be in the act of shooting.

You can't have a catch and a shooting foul, but...

*5.2.5 SITUATION C: With three-tenths of a second or less left in a tied game, each team is in the bonus. Team A has a throw-in on the end line near their basket. A1 throws the ball to A5 on the near block who catches the ball and quickly shoots. A5 is fouled by B3 just prior to the period ending horn. The ball goes through A's basket. RULING: Since A5 may not control the ball and attempt a try with three-tenths of a second or less, A5 cannot score a goal and is not considered in the act of shooting. However, B3's foul cannot be ignored and is considered a common foul. A5 is awarded a one-and-one bonus free-throw situation with the lane cleared. A5's free throw attempts will determine if the game is over or if an overtime period is necessary. (4-41-6)

Hmm... Interesting. Can a "tap-per" get fouled? If it's during the tap, is it the act of shooting, even though she's tapping not shooting?

Yes a tapper may be fouled and it is considered in the act of shooting.

5.2.5 SITUATION B: With three-tenths of a second or less left in the first half, Team B has been charged with only four team fouls. A1 is at the free throw line for one free throw. A1's shot hits the rim and bounds off. A2 legally taps the ball toward the basket and is fouled by B3. The ball had left A2's hand and the foul occurred before the period-ending horn sounded. The tap is unsuccessful. RULING: B3's foul is considered in the "act of tapping" and will result in two free throws for A2. The lane will be cleared and the period ends after A2's free throw attempts. (4-41-1,5,6,7)

Taking a trick out of Ref Daddy's bag?

Blame Tony he sent me the file.:D

Thanks for the case reference. I knew it was probably in there, just didn't want to go searching! Thanks again.