I am sure even even if i cut off 20-30% of 1 of my pages google will not change rank for its keyword
That might well be the case - because on-page factors are not the whole algo by a long shot. However, I'll bet that if you removed a given secondary word from a new page, then your page would not rank as well for any phrases that include that word.
Here's the way I understand Google rankings. A page does not actually start out with "its" keywords attached some how. In fact, a page can rank for any combination of words on the page itself or in its backlinked pages. Sometimes a page can rank for semantically related phrases that don't even appear at all.
Google's back end calculations do not usually "assign" a SERP position for any particular query. That approach would require Google to calculate every possible query ahead of time. Since they see a large percent of queries every day that are brand new, that approach wouldn't be very practical. It just wouldn't scale.
So instead, Google calculates RELATIVE numbers - numbers that are then compared to other candidate URLs. The candidates being compared are in a preliminary result set of under 1,000 URLs that are most relevant to the query.
Every page is assigned all kinds of meta-data on Google's back end. That meta-data is quantified and those various numbers are then combined in complex calculations. That calculation generates the relative values that are then compared,ending up with an ordered list.
If the meta-data for the URLs in that result set has not changed much, then the URLs might not show any shift in position. But that doesn't mean they are fixed or set.
One of the big purposes for the Caffeine infrastructure was to allow that meta-data to be recalculated in very small batches, rather than having to wait for a long period before recalculating a big batch, all at once.
As I see it, the process I sketched out above is the most common case - by far. But Google does have the capacity to assign a fixed ranking. They showed us that with the old Minus Thirty Penalty
[webmasterworld.com] four years ago. But that was a pretty crude ranking approach compared to what they do today, and it was reserved for harsh penalties - penalties that were assigned on top of a regular ranking.
Two years ago I saw a few cases where a URL would pop back and forth at different times of day, going from position 4 to a varying position on page two. Again this was very rare, but Google did have the ability to assign position 4 directly.
Also Google clearly uses Universal Search results that can be blended into the SERP at a given spot. But these Universal results (News, Video, etc) do not actually "use up" one of the ten organic positions.
So what you are reporting would be a bit of a mystery. I like the idea for some kind of a test. Maybe goodroi's blank page idea, or maybe your own suggestion of removing chunks of content. If you do that and report back, we may all learn something.