Preprint Article Version 5 Preserved in Portico This version is not peer-reviewed

Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)

Version 1 : Received: 13 January 2024 / Approved: 15 January 2024 / Online: 15 January 2024 (07:39:14 CET)
Version 2 : Received: 23 February 2024 / Approved: 27 February 2024 / Online: 27 February 2024 (08:02:17 CET)
Version 3 : Received: 4 March 2024 / Approved: 5 March 2024 / Online: 5 March 2024 (06:39:56 CET)
Version 4 : Received: 7 March 2024 / Approved: 8 March 2024 / Online: 8 March 2024 (11:02:28 CET)
Version 5 : Received: 13 March 2024 / Approved: 14 March 2024 / Online: 14 March 2024 (10:02:52 CET)
Version 6 : Received: 18 March 2024 / Approved: 19 March 2024 / Online: 20 March 2024 (04:38:20 CET)
Version 7 : Received: 4 April 2024 / Approved: 5 April 2024 / Online: 7 April 2024 (05:34:12 CEST)
Version 8 : Received: 12 April 2024 / Approved: 12 April 2024 / Online: 15 April 2024 (04:22:22 CEST)
Version 9 : Received: 17 April 2024 / Approved: 18 April 2024 / Online: 19 April 2024 (10:20:42 CEST)
Version 10 : Received: 29 April 2024 / Approved: 30 April 2024 / Online: 30 April 2024 (11:56:33 CEST)
Version 11 : Received: 14 May 2024 / Approved: 14 May 2024 / Online: 15 May 2024 (04:02:32 CEST)

A peer-reviewed article of this Preprint also exists.

Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages. Mathematics 2024, 12, 1600, doi:10.3390/math12101600. Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages. Mathematics 2024, 12, 1600, doi:10.3390/math12101600.

Abstract

Using assembly theory, we investigate the assembly pathways of fixed-length binary strings formed by joining the individual bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below and above, and we conjecture about the form of the upper bound. We show that a string having the smallest assembly index can be assembled by an elegant trivial program of length equal to this index, if the length of the string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index that could assemble this string. We conjecture that a black hole surface is defined by a balanced distinct string that satisfies the upper bound of a distinct string assembly index. The results confirm that four Planck areas provide a minimum information capacity that provides a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that the problem of determining the assembly index of a given binary string is NP-complete, while the problem of creating the string so that it would have a predetermined maximum assembly index is NP-hard. Therefore, once the new information is assembled by a dissipative structure or by a human, increasing the information entropy according to the second law of infodynamics, it is subject to the second law of thermodynamics, and nature seeks to optimize its assembly pathway.

Keywords

assembly theory; emergent dimensionality; holographic principle; black holes; complexity measures; P versus NP problem; Gödel's incompleteness theorems; halting problem; elegant program; Fibonacci sequence; Collatz conjecture; addition chains; quantum orthogonalization interval theorems; second law of infodynamics; mathematical physics; binputation

Subject

Physical Sciences, Mathematical Physics

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