The general idea of Infinite Compression is extremely simple:
1.All files are converted to integers, integer X in this case.
2.Arbitrary precision floating point numbers A and B that are
X and X+1 respectively(interval X.0 <->(x+1).0) are generated.
3.The numbers A&B(and effectively the interval between them) is multiplied by 2^n(n can be adjusted later to search more space).
4.The resulting (x*2^n)<->((x+1)*2^n) interval is set as target area for specific formulas.(e.g. a very short polynomial).
5.The variables of polynomial formula are tried to match a result inside the interval in #4, if its not found the number 'n' is changed and process repeats as in #3.
6.When the search find a set of variables which result in the some number that is within interval the variables,n(in 2^n) and file size are recorded into a 'hash-like' link.
7.If the search fails for all reasonable n' values the file is appended with "dummy values"(since real size is recorded) and search is run again on the 'file+dummyarea'.
There is also a way to pre-emptively search 'file+dummydata' as in interval arithmethic(think dummydata with any multiplier), discarding the 'dummydata' later:
any effective multiplier can be used instead of 2^n, granted its easily generated by formula.
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>>2
It was copied from tinychan.
There are also ways to make files less entropic(Gray code):
applying repeatedly x^(x>>1) on the file integer representation, will produce a form with has least 1's vs 0's.
This form can be back-transformed to x, by recovering the pre-xor bits of each step(as it represents change of old bit to next bit).
https://en.wikipedia.org/wiki/Gray_code#Converting_to_and_from_Gray_code