The Origin of Neutrino Masses as Non-Integer Residuals: The Transcendental Number Residual Mechanism of Carrier Dilution in Self-Construction Theory

Abstract

Within the already established framework of carrier generation in Self-Construction Theory (SCT), this paper systematically expounds the origin mechanism of neutrino masses. In SCT, the neutrino is not "another kind of fermion"——it is the non-integer residual of the carrier dilution process.

In the carrier dilution mechanism, when a carrier is定格 at the critical point of the phase transition, its total energy E_total and its mass-charge n (the minimum number of time-points constituting the carrier) are simultaneously determined. The integer part of E_total/m₀, namely (K+n), is determined by combinatorial geometry and is released as m₀ quanta during the dilution process; the small numerical offset δ arises from the cooperative modulation of all the transcendental numbers in the Constant Spectrum (π, e, ϕ, γ, ζ₃, G, δ)——each transcendental number contributing an irreplaceable modulation weight at a different link of the critical dynamics of the phase transition.

When E_total/m₀ = K+n+δ (with 0<δ<1), the carrier, after radiating K quanta, cannot stabilize at (n+δ)m₀. The mass-charge n of a carrier is the number of vertices of its simplest triangulation——this is a topological invariant of the carrier as a three-dimensional closed manifold. After the phase transition, each time-point carries one unit of the information differential m₀, and the total information differential of the carrier is strictly equal to n·m₀. Any energy exceeding n·m₀ implies the existence of "surplus" information differential within the carrier, which cannot be anchored by the n time-points of the carrier——it is topologically unstable and must be released through weak decay. Any energy less than n·m₀ implies that there are incompletely anchored time-points within the carrier——these time-points will absorb energy from the surrounding space-time until the stable state of n·m₀ is reached. This is the physical origin of neutrino production.

The extremely small mass of the neutrino is naturally given by the small transcendental numerical value of δ——the order of magnitude of δ lies between 10⁻⁷ and 10⁻⁶, corresponding to neutrino masses at the sub-eV level. The three generations of neutrinos correspond precisely to the three generations of charged leptons: ν_e, ν_μ, and ν_τ originate respectively from the dilution residuals of electron-type (n=4), muon-type (n=827), and tauon-type (n=13905) carriers. The internal topological structures of the three classes of carriers are different, and each is subject to different weights of transcendental number modulation at the phase transition, hence they possess different δ values. The neutrino is a Dirac particle——it is an independent residual of carrier decay and is not its own antiparticle. Neutrinoless double-beta decay is therefore forbidden in SCT——this is a definite prediction currently being tested by multiple experiments.

Keywords: neutrino mass; non-integer dilution residual; transcendental number modulation; carrier decay; Dirac neutrino; Self-Construction Theory