1. Catherine is sleeping so late because she's up all night doing mathematical research and constructing a proof. She doesn't even tell her dad that she's doing this.
2. She is AWAKENED by Hal. The scene with her father is a dream. Sane people often work out anxieties and negative feelings in dreams.
3. Catherine knows that what her father left behind is his legacy. She also knows that there is a notebook upstairs that contains a very valuable proof. She is not paranoid to express a protectiveness towards something she values.
4. Alone=grief? inability to get along with her sister? Being 25 and never having lived by herself? Wishing to be alone is not necessarily insane in a house where you've been living 24/7 with a lunatic.
5. The call to the police is passive agressive behavior to be sure, but isn't necessarily insanity.
6. Sleeping for an entire week may be crazy.
There are many assumptions the author wishes you to make that are turned topsy turvy. He wants you to believe that Catherine's lazy so that you are surprised to find out she's working on math. He wants you to believe that Hal is dishonest so that you can be surprised when he reaches out to Catherine in a vulnerable way. He wants you to believe that Robert is alive in the first scene so that you can be astounded that it's a "vision" and he's dead. He wants you to assume that Dad had a period of lucidity that produced that proof so that you'll suspect that Catherine is lying about having written the proof. He wants you to see Claire as a manipulative brat so that when you find out that she actually paid for all of Catherine's expenses at school, paid off the home and SUPPORTED her for the last 5 years so that she is now unskilled, unemployed, and at a loss as to how to live her own life, you feel a bit of compassion towards her.
Claire wants others to accept her on faith. To just assume her value. The author brings this out by letting the audience make several assumptions that turn out to be wrong. Namely...that Claire might be insane...
Proof of Catherine's illness can be found in several places
1. (line)85 - "Kid ..You sleep til noon, you eat junk food, you don't work, the dishes pile up in the sink....Some days you don't get up, you don't get out of bed."
2. Beginning - she thinks she is having drinks with her father who has passed away.
3. (line 300) paranoia about Hal taking her dad's notebook
4.( line 332_-I want to be alone
She is easily agigitated. Doesn't want to eat
(line 170) calls the police and then becomes abusive and agigitated with them. Did not really want the police.
ACT 2 Scene 3 /Scene 5 (line 73)
Catherine sleeps for an entire week