Mass as an Emergent Topological Property

Abstract The origin of elementary particle masses and their generational hierarchies remain parameterized phenomenological features within the Standard Model. This theoretical preprint proposes an underlying information-theoretic manifold where mass emerges not as a fundamental dimension, but as a macroscopic topological resistance stemming from quantum entanglement. By utilizing the information coupling constant (μ = ħ/2c), we demonstrate that fundamental information topology is inherently one-dimensional (self-referential 1D loops). Defining information density as a strict 1D spatial gradient and substituting the reduced Compton wavelength as the minimal topological bounding radius, the mass variable algebraically collapses. This deterministically proves that an elementary spin-1/2 fermion constitutes exactly two irreducible logical bits, mirroring the foundational two-component Weyl spinors. Furthermore, we expand this limit by modeling higher lepton generations (such as the muon and tau) as folded topological resonances, governed by knot invariants. This framework theoretically derives a strict upper bound for particle generations: a fourth generation is topologically forbidden, as its required spatial compression would force the local manifold tension to exceed the holographic limit (S > 1), resulting in an immediate metric collapse. Key Contributions of this Paper: The Two-Bit Fermionic Limit: An algebraic proof that fundamental spin-1/2 particles are localized 2-bit topological correlations. Mass as Topological Resistance: A geometric redefinition of mass scaling inversely with the topological bounding radius (m ∝ 1/r). Demystification of Particle Decay: Explaining the decay of higher generations as the thermodynamic relaxation of highly tensioned topological knots into the unknotted ground state (the electron). The Three-Generation Bound: A deterministic, holographic constraint explaining the absence of a fourth lepton generation. Note: This preprint builds upon the foundational framework introduced in "The Information-Theoretic Spacetime Manifold: Gravity and Inertia as Emergent Topological Phenomena", https://doi.org/10.5281/zenodo.20030220