The Neutrino and the Self-Organizing Vacuum: From Amphichiral Topology to Cosmic Equilibrium

This paper develops a unified, topological account of the neutrino within the V–j–Aj generative framework, identifying the neutrino as a torsional soliton of the vacuum weave. By modeling the neutrino as the amphichiral figure-eight knot, the simplest hyperbolic knot with zero writhe, the work explains its defining properties, namely Majorana nature, spin-½ behavior, and observed left-handedness, as necessary consequences of this single topological identity.

The analysis shows that:

• Majorana behavior arises from the figure-eight knot’s amphichirality, making the neutrino topologically identical to its antiparticle (Sec. 3.1).

• Spin-½ emerges from the intrinsic torsion holonomy of the knot: a single loop yields a 2π phase reversal, requiring a full 4π rotation to return to identity, the hallmark of a spinorial excitation (Sec. 3.2).

• Left-handed weak interactions follow from relational chirality: the neutrino’s amphichiral core becomes left-handed only through its coupling to the chiral SU(2) environment of the weak force (Sec. 3.3).

The paper then extends this microscopic picture to the cosmological scale. The vacuum is modeled as a self-organizing torsion–curvature weave engaged in a dynamic equilibrium (“vacuum respiration”) between expansive curvature and contractive torsion (Sec. 5.1). Within this framework:

• The cosmological constant arises from a small, persistent imbalance in this curvature–torsion respiration (Sec. 5.2).

• The Cosmic Neutrino Background (CNB) is interpreted as the thermal shadow of this same process, the dynamic, low-energy torsional activity of the vacuum (Sec. 5.3).

This dual interpretation reveals the neutrino as a bridge between quantum-scale torsional excitations and cosmic-scale vacuum dynamics. The paper presents quantitative links between neutrino torsion modes, the mass splittings Δm², the CNB temperature, and the cosmological constant, forming a unified and predictive framework that connects particle physics, cosmology, and vacuum structure (Secs. 5.3–E).

Part of the Generative Wholeness series: building on “A Pre-Geometric Origin for Quantum Dynamics,” “A Topological Origin for SU(3) Symmetry,” “A Topological Origin for SU(2)×U(1),” and “A Derivation of the Fundamental Constants from the Vacuum.”

Keywords: neutrino, Majorana fermion, torsion soliton, figure-eight knot, topological vacuum, cosmological constant, cosmic neutrino background, torsion–curvature equilibrium, generative wholeness, SU(2) sector.