Canadian 6 months in USA

[Peter Smith]

I am a Canadian citizen and I intend to stay for six months in the
United States. I don't plan to work there, and I have adequate
financial support to live there essentially indefinitely (yes, I'm
rich). I would be there under the six month tourist undocumented
category.

What should I tell the border protection officer when he asks me "how
long do you plan to stay in USA" ? Is it safe to tell him the truth,
will he accept that I plan to stay in America for half a year and not
look for a job, or is he likely to be suspicious?

Do CBP actually record each date of arrival and departure for
undocumented aliens, if method of transport is by train or car? If I
were to give a short period of time as my intended stay, would they
record that and cause me more trouble for a future visit?

I would prefer to tell the border officer the truth, but Americans are
completely paranoid about people coming into their country, so would
it be better to tactically lie and hope they don't bother to disprove?