Assembly Theory of Binary Messages

Szymon Łukaszyk; Wawrzyniec Bieniawski

doi:10.20944/preprints202401.1113.v10

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preprints.org > physical sciences > mathematical physics > doi: 10.20944/preprints202401.1113.v10 (registering DOI)

Preprint Article Version 10 This version is not peer-reviewed

Assembly Theory of Binary Messages

Szymon Łukaszyk

^* and

Wawrzyniec Bieniawski

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)

How to cite: Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages. Preprints 2024, 2024011113. https://doi.org/10.20944/preprints202401.1113.v10 Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages. Preprints 2024, 2024011113. https://doi.org/10.20944/preprints202401.1113.v10

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MDPI and ACS Style

Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages. Preprints 2024, 2024011113. https://doi.org/10.20944/preprints202401.1113.v10

APA Style

Łukaszyk, S., & Bieniawski, W. (2024). Assembly Theory of Binary Messages. Preprints. https://doi.org/10.20944/preprints202401.1113.v10

Chicago/Turabian Style

Łukaszyk, S. and Wawrzyniec Bieniawski. 2024 "Assembly Theory of Binary Messages" Preprints. https://doi.org/10.20944/preprints202401.1113.v10

Abstract

Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show that the bitstring assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it has regularities that can be used to determine the length of the shortest addition chain for N. We show that a bitstring with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this bitstring is expressible as a product of Fibonacci numbers. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the bitstring so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite bitstring.

Keywords

assembly theory; emergent dimensionality; shortest addition chains; P versus NP problem; mathematical physics

Subject

Physical Sciences, Mathematical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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