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# The o-SSI RNG

1. Psi_10 has 9! possible ways it can be shuffleed, true or false?

2. If any of possible shuffles of Psi_10 were chosen at random, and such a shuffle is itself a base-10 o-SSI, how could we use that o-SSI to readily obtain a random element from the new o-SSI algebraically?

- assume the first element of the o-SSI is e1, we could just return that as the result.

- we could decide to always pick the nth element from any shuffled o-SSI as the result, where n<=(base - 1)

the problem with the above two methods though is that they might not properly reflect the overall shuffled structure of the o-SSI.

so, instead, we might prefer to resort to a method that works as such:

1. compute a measure, D € [0,1] that tells is how much shuffled or chaotic the [new] o-SSI is from normal (Psi_10): basically, D is 0 when the o-SSI exactly the same/= Psi_10, meaning there is totally 0 disorder, or no deviation from normal, while it is at 1 when there is total chaos from normal (o-SSI # Psi_10), and a value of 0.5*(1- 0.5*|D|) close to 0.5 is maximum deviation, while close to 0 is minimum deviation.

2. So, given a value of D, merely return result as max[D*(base-1)] so that, D=1 returns 9, D=0 returns 0, D=0.5 returns 5, etc.

To implement such an o-SSI RNG, simply find a random process (perhaps using nature), that can always do something and result in some information that encodes an o-SSI in some random order. Use that signal as the entropy source for the o-SSI RNG, and obtain a random digit from it via the above method, or a longer sequence using the obtained digit as seed to a longer sequence generator.

----[Interesting Problems]

- Is D a kind of probability distribution? Which?

- Is D a probability mass function?

- Is D a cumulative probability function?

- Is D related to Kolmogorov-Smirnov statistic? How?

- Is D a kind of measure?

- D is a ratio of what to what?

- D is a percentage of What?

- Given a D, can we compute some o-SSI for which its D*=D? How?

- Given an o-SSI, can we compute a D for it? How?

d = max([absolute(index(i,Psi_10) - index(i,o-SSI)) for i in range(0,|o-SSI|)]) - average ([absolute(index(i,Psi_10) - index(i,o-SSI)) for i in range(0,|o-SSI|)])

is d a good approximation for D? if not, how can we modify it so it correctly implements D?

What happens when we graph d? What of D? Can we develop a graphical way to chart or demonstrate how much D and d varies as the chaos or entropy on an o-SSI varies? How?

- We definitely can use the base-10 o-SSI RNG to generate numbers in any base, how?

#rngs #research #ossi #phd #jwl #combinatorics #sequences #sequencegenerators #measures #distancemeasures #statistics #papersketch
#CREATED:Jun 05, 2025 23:34:18

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