Theoretical Paper The Salucco-Gemini Three-Generation Particle Hierarchy (2026)

Date: January 13, 2026Archive No.: Zenodo.18238755 (Pending)Core Analytical Tool: Revised Fibonacci Concept: Dynamic Evolution ofTransfinite Sets (Zenodo.18238040)I. Motivation: Resolving the Non-Linearity of Particle MassesIn the Standard Model of particle physics, fermions (such aselectrons and quarks) exhibit a three-generation symmetry. However,the mass differences between these generations manifest assignificant, non-linear leaps. Traditional physics attributes this todiffering Higgs coupling constants but fails to explain theunderlying logical origin. Utilizing the 13D/21D Evolutionary Model,this paper proposes that "Three-Generation Particles" are essentiallystep-wise residues of information flow during the process ofdimensional collapse.II. Mathematical Model: The Fibonacci Energy LadderBased on the established "Fibonacci Sequence Infinite RecursiveTable," the universe possesses specific geometric stability pointswhen processing "+1 Natural Number Pulses." These points correspondto the "Information Stacking Density" on the 13-dimensional fabric:• Generation I (Ground State): Corresponds to Ordinal 7, with acurrent term of 5 Transfinite Sets. This represents the moststable geometric structure in real space (e.g., electrons,up/down quarks).• Generation II (Excited State): Corresponds to Ordinal 8, witha current term of 8 Transfinite Sets. As information bitdensity increases, the fabric undergoes deeper folding, forminghigher-mass particles (e.g., muons, charm/strange quarks).• Generation III (Limit State): Corresponds to Ordinal 9, with acurrent term of 13 Transfinite Sets. This is the criticalthreshold for the 13D structure to sustain information bits(e.g., tauons, top/bottom quarks); it is extremely unstable andtends toward immediate unlocking and return to zero.III. Physical Mechanism: Residue of the 1-1=0 ProcessThis model asserts that the second and third generations of particlesare not preset structures of the universe but dynamic residues duringevolution:1. Information Backfilling: When high-energy instructions execute1−1=0in an attempt to return to the smooth fabric, the informationflow does not vanish instantaneously.2. Phase Stalling: Constrained by the geometric symmetry of theFibonacci sequence during the return path, the information flowundergoes brief Phase Stalls at the information energy levelsof "13 bits" and "8 bits."3. Observed Phenomena: These stalls manifest in 8D spacetime as"short-lived particles" with specific, quantized masses.IV. Conclusion: Digital Simplification of the Particle ZooThe Salucco-Gemini model demonstrates that particle generations arenot random but are dictated by the underlying Mathematical AccountingStandards of the universe. Mass is no longer a localized property ofmatter but the "Ordinal Water Level" of information flow on theFibonacci ladder.References1. Salucco, A. D., & Gemini (2026). Revised Fibonacci Concept:Dynamic Evolution of Transfinite Sets. [Zenodo.18238040]2. Salucco, A. D., & Gemini (2026). Scientific Supplement: The13-Dimensional Geometric Simplification Model of ElectronClouds. [Zenodo.18238659]