On the nature of Mersenne fluctuations
U. Merkel
TL;DR
The paper builds a comprehensive pregeometric framework in which crotons act as boundary labels and volume fluctuations driven by Mersenne fluctuations, organized into qphyla and bound into volume via time-like and space-like refinements.Continued fractions (CFRs) organize refinement pathways, producing structured Mersenne fluctuations whose boundary realizability is constrained by Catalan numbers and interordinal rules, linking holographic boundary data to volume behavior and to kissing-number patterns.The work develops a detailed intraworldly architecture (crotons of the first and second kind, organizers) and demonstrates speculative connections to subatomic physics, beta decay, neutrino phenomenology, and the fine structure constant via interordinal bounds and CBC-like constructions, suggesting a unified, albeit highly conjectural, pregeometric path to fundamental constants and particle structure.Overall, the framework offers a mathematically rich language to connect pregeometric refinements, boundary–volume holography, and subatomic phenomena, proposing concrete, CFR-guided mechanisms for particle creation and interaction within a pregeometric world.
Abstract
In Part I, crotons are introduced, multifaceted pre-geometric objects that occur both as labels encoded on the boundary of a "volume" and as complementary aspects of geometric fluctuations within that volume. If you think of crotons as linear combinations, then the scalars used are croton base numbers. Croton base numbers can be combined to form the amplitudes and phases of Mersenne fluctuations which, in turn, form qphyla. Volume normally requires space or space-time as a prerequisite; in a pregeometric setting, however, "volume" is represented by a qphyletic assembly. Various stages of pre-geometric refinement, expressed through the aspects crotonic amplitude or phase, combine to eventually form and/or dissolve sphere-packed chunks of Euclidean space. A time-like crotonic refinement is a rough analog of temporal resolution in tenacious time, whereas space-like crotonic refinement is analogous to spatial resolution in sustained space. The analogy suggests a conceptual link between the ever-expanding scope of Mersenne fluctuations and the creation and lifetime patterns of massive elementary particles. A three-stage process of ideation, organization and intraworldly action is introduced to back this up. In Part II, the intrawordly aspect is analyzed first, including our preon model of subnuclear structure, and the organizer aspect thereafter, based on three types of Mersenne numbers, $M_{\textrm{reg}}$, $M_{5/8}$, $M_{9/8}$, and two formal principles: juxtaposition $x$ vs. $\! x\!\pm\!1(2)$ and the interordinal application of functional $1\!\divideontimes(f^{(a)}\!\circ(f^{(b)}\!\divideontimes f^{(c)}))$.