**Is the deterministic AHS-RNG a TRNG ?**

Without any scientifically proven basis, it is repeatedly and reflexively claimed that a computer as a deterministic machine cannot generate true random numbers. The bogus arguments put forward relate exclusively to the typical PRNG structure, i.e. arithmetic procedures for calculating a series of random numbers using algorithms, starting from a seed. The random numbers generated in this way vary from abysmally bad for the older algorithms (partly due to the limited technology of the time) to quite useful newer variants, such as MT19937 and Xoshiro256**.

What they all have in common, however, is the fact that the mathematical function does not make it possible to generate true random numbers. The classic statement by John von Neumann applies here: "Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin." But the statement then goes on: "For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."

Of course, it is in principle impossible to prove directly that the random numbers generated by AHS-RNG are true random numbers, but we can only substantiate the assessment "true random numbers" through very extensive tests, and demonstrate the non-mathematical principle by showing exactly how it works. To paraphrase John von Neumann, the method of generating random numbers used in AHS-RNG must be considered a correct method of generating true random numbers, the underlying principle being the generation of every single bit with a 50/50 chance. The motto we gave the method is: "Born to be wild or tame, or anything between".

In this evaluation, we want to limit ourselves to the deterministic AHS-RNG, which can deliver a minimum number of 281,474 billion bits, corresponding to a file of over 35 terabytes, without additional entropy, using only the loaded parameters BFT, FAAP and LCG. To run a large simulation on 1000 cores, you would therefore need only 17 megabytes of AHS-RNG parameters, compared against up to 35 petabytes of stored random numbers in case of physical RNGs. If the generated AHS-RNG random numbers really have the properties that are essential for true random numbers, this would certainly be a major improvement. We have created a pool of one million variants and we need only 17 gigabytes. For a pool of a billion different parameter tables, the memory requirement would be 17 terabytes. This can be compared with the memory requirement of 35,000,000 petabytes for the same amount of real, physically generated random numbers.

How this large amount of true random numbers can be generated from 17 kilobytes of initial data? Due to the way AHS-RNG works, more than 10exp19800 completely independent variants of random number sequences are possible with the limited initial values, and are thus stored virtually in the initial data. For example, if we create a program for multiplication, there are no results in the program. But by calling the program with the help of two indexes, we can calculate a multiplication table up to 12 digits each, i.e. over 500,000 trillion results. We can therefore justifiably claim that, if our program can calculate results up to 24 digits, then this number of results is virtually available. The deterministic AHS-RNG can be viewed in a similar way. The only decisive question is: Are the virtually available random numbers, which are materialized by the execution of the program, true random numbers? We are convinced that the answer to this question is "yes".