On Saturday, 25 June 2022 at 00:34:27 UTC+8, B.H. wrote:
> On Friday, June 24, 2022 at 12:09:53 PM UTC-4, B.H. wrote:
> > On Monday, March 14, 2022 at 2:40:22 PM UTC-4, B.H. wrote:
> > > On Monday, March 14, 2022 at 11:34:54 AM UTC-4, B.H. wrote:
> > > > On Monday, March 14, 2022 at 5:01:07 AM UTC-4, wij wrote:
> > > > > I pick the data compression algorithm to your challenge (because, I believe more people would know about and be interested in data compression, and algorithm is
> > > > > more difficult to cheat than abstract theories):
> > > > > Excerpt from https://groups.google.com/g/comp.theory/c/vSE_qYBEDf8/m/J3sLILkgAwAJ
> > > > >
> > > > > - Obtain a binary string corresponding to the file.
> > > > > - Treat the binary string as a number and factor it.
> > > > > - Given any large prime factors, write down the number in a sense as m + 1, and factor m .
> > > > > - Keep going until you have only a finite collection of very small prime factors.
> > > > >
> > > > > ------
> > > > > Actually, just by seeing those sketch, I know I don't have to ask more.
> > > > > 1. By advertising PTIME, I would assume you don't understand real program, thus
> > > > > algoritms. (Had anyone heard of a "PTIME sort" algorithm?).
> > > > > 2. From "Obtain a binary string corresponding to the file."
> > > > > I would wonder what kind of system you were thinking?
> > > > > 3. I don't think you can factorize an average 20Mbyte image file in 100 years,
> > > > > let alone the rest stuff and the basic: How can factorization compress data?
> > > > > You just need to express your compression algorithm clearly. My premature
> > > > > stereotype above can be ignored. I just want to know if I made a big mistake about you.
> > > > I have the updated answer fully written out, and am checking it. It looks right. It contains no proofs; you get what you pay for, I just wrote an algorithm that looks right.
> > > >
> > > > I'll check it over some more and post it later today or early tomorrow. I am not checking it over that much, just enough to make sure that it's right and fully error-free.
> > > >
> > > > -Philip White
> > > OK, here is the answer to your challenge. I warn you: Never demand cutting-edge math help from a human trafficking victim or convicted criminal seeking release, even with consent. Guilt or innocence is the standard for securing release, from prison only (since human trafficking is just a crime), not achievement; I submit this merely to bolster my case since I am nowhere near being able to be properly helped by any "justice" system.
> > >
> > > Here is the updated solution:
> > >
> > > - Assume that this test for finding a j-digit base-10 prime number works: http://www.sci.brooklyn.cuny.edu/~yarmish/finding%20large%20primes%208..5x11.pdf
> > > - We are given a very large number (that represents a file), m, to compress. Consider a number larger than 10^((1000)^10), for example.
> > > - We seek a nearby power of a prime power (r^w=q)^k, in the sense that m - q^k is small. (The prime is r, and q = r^w.)
> > > - Let b be the number of bits needed to express m.
> > > - Use a calculator program to compute an approximation, a = 2^(b/9) .
> > > - Round the value of a down to the nearest integer.
> > > - Let d be the number of base-10 digits in a.
> > > - Using the process linked to above, find the smallest-sized (storage-size-wise) prime number r and integer pair w such that r^w = q has (d-1) base-10 digits.
> > > - Find the largest value k such that q^k is the largest possible integer such that this integer is less than m.
> > > - Compute v = m - z * q^k, where z is selected to be the largest possible integer that that yields non-negative v, such that z < q .
> > > - Record the values of the following 3-tuple: (r, w, k)
> > > - Note that v < z * q^k , and thus it is much smaller than m.
> > > - Now, repeat this process on both v and z, and concatenate the ordered 3-tuple from previous repetitions (perhaps written as a tree structure in prefix notation using base-4), that repetition, and all successive repetitions to form a string, S, until m is "very small."
> > > - When you are done, write down the overall string, S, followed by the #-separated number 1 (if this is the first time th process is being run).
> > > - Repeat the entire process above on S, taken as an integer, and increment the value of "1" to "2", "2" to "3", etc., as many times as desired; repeat until the string cannot be made smaller.
> > >
> > > The big-picture version is: We find a very large but not too large “suitable new base” q to express m in. We record q as a prime power, the correct large power k it is raised to, and the value z it is multiplied by when we subtract from m to obtain v, the value that remains after subtracting the first base-q digit from m. We then repeat this process on v repeatedly until we deem that v is “small enough.” Based on careful selection of a in the process, we ensure that the length of m as a binary or base-10 string of bits/digits decreases by about 1/9 every time this process is applied, disregarding for now the size of recorded values of r, w, and k, which are relatively short strings that are recorded as part of the compressed string. By effectively multiplying the length of the string by approximately 8/9 each time we run the process, while writing down much smaller representations of the base q, which equals r^w, as we diminish the size of the original number m, we compress the string to be “much smaller,” vaguely speaking, than it started out being. Again, we can repeat this overall process with a recorded integer signifying the overall integer number of times the process has been run to make the string smaller and smaller, ultimately yielding a compressed string with an integer number of times to unpack it. It is easy to see that the string can be compressed and decompressed in polynomial time, with randomness needed for the primality test in the compression step.
> > >
> > > Extremely succinct summary: Re-write a given large integer with a particular different, succinctly representable base that can be written as a prime power [1], and then recursively compress the leftmost digit of m in that base and the rest of the representation of m without that digit. Repeat this process itself, keeping track of how many times you’ve done it, until you have a string and integer pair that cannot be made any smaller.
> > >
> > > Note: We would not want for the r value to be 2 every time, if we were indeed decreasing the string length by multiplying it by 8/9 each time; we want to decrease the size of the string each time we run the routine, so selecting large primes r will typically be what we want to do. No proof that we can “usually find” a suitably large prime value for r to minimize the size of (r,w) is included, although it seems to be true. Also, I haven’t fully established the exact effectiveness (i.e., worst-case extent of compression) of the algorithm presented, having not spent the time to write any proofs about this updated version of the idea. It looks very good, though.
> > >
> > > [1] Think of writing “3^1000000” as (3,1000000) instead of in binary or base-10.
> > >
> > > (I’m glad I decided to check this; I caught and fixed a few rather minor glitches.)
> > >
> > > - - -
> > >
> > >
> > > Write a response if you have an objection or have found a mistake. Try not to waste my time with fluff; present your argument carefully if you want to present one.
> > >
> > > Of course, any mathematically literate person who gets programming and would give this a little thought would see that it is correct. I didn't write a full proof or check my work too many times over, though; you get what you pay for. Maybe if you present a coherent objection I'll write a proof establishing that you are wrong.
> > >
> > > Don't say it was trivial to you, since you clearly didn't see it yourself.
> > >
> > > How many more times are you going to lie to the world and insist that I am a scammer person and must prove otherwise by sharing math explanations with you? What are the consequences of doing that, even once? Do you insist that every innovator or student go through this process to prove his/her ability to be genuine? What will happen to American STEM because of this, is that your plan? It might work, I see that; who would want to major in STEM given the zero-ethics, zero-accountability culture of it, even in the US? Are you going to ask Grigori Perelman or Terence Tao if they are scammer people, too? Why is it just me, I wonder? What do institutions like Harvard and MIT have to say about this kind of dishonorable conduct, I wonder?
> > >
> > > -Philip White (philip...@yahoo.com)
> > One slight issue to correct on this, since I could at least in theory still patent it (that's probably why more people haven't implemented it yet....it will be a disaster for Facebook next March if I'm not out by then): The digit of the large prime power should be compressed, too. There are three recursive calls within the routine, not 2.
> >
> > -Philip White (philip...@yahoo.com)
> I take it back--the base was selected carefully, I just forgot how my algorithm worked when I started trying to code it just now. The key is the selection of d.
>
> -Philip

Hi dear Big-Head:

Any progress of the compression algorithm? I saw you brought this post up.
But the law has settled and approved: Philip is detained, enslaved and tortured in prison
until a working compression algorithm is presented, life-long effective.

You seem not to really understand this is the 'incentivization' of your work,
I don't see any way around that can better liberate you.