The Standard Model says neutrinos are massless. They are not.
For decades, the Standard Model treated neutrinos as massless. Then oscillation experiments — neutrinos changing flavor as they travel — proved they have mass. Mass differences between the three species were measured. But the absolute scale — the actual mass of the lightest neutrino — remains experimentally uncertain. KATRIN gives an upper bound of 0.8 eV. The true value lies somewhere below that.
The Standard Model has no mechanism to predict it. The neutrino masses are free parameters, inserted by hand. There are also no Standard Model explanations for the two mass splittings — why the atmospheric splitting is so much larger than the solar splitting, or why those specific ratios hold.
In Cosmic Egg Theory, all three are derived. Each from a different geometric source. Each from a structure already present in the framework — the cascade depth, the octahedron, and the Hypatia emission window. No new elements introduced.
Cascade depth sets the floor
n_ν = 76.77
(from Q_ν = 0 geometry)
m_ν,1 = E_P / (√2+1)^76.77
= 0.050 eV
KATRIN bound: <0.8 eV ✓
The cascade depth n_ν = 76.77 was determined in the Q_ν = 0 derivation — the neutrino sits at the bilateral crossing axis. Inverting the cascade formula gives the absolute mass. No experimental input.
Octahedron circumradius to midradius
Interior octahedron:
R (circumradius) = a√2/2
ρ (midradius) = a/2
→ R/ρ = √2
Δm²_atm = m₁² · (√2² − 1) = 2.500×10⁻³ eV²
Observed: 2.513×10⁻³ eV² · 0.52%
The octahedron's circumradius-to-midradius ratio is exactly √2. This ratio gives the m₃/m₁ mass ratio. The atmospheric splitting follows without additional input.
The Hypatia emission window
Hypatia window: steps [67, 69]
ΔN = 2 (integer width)
m₂/m₁ = √(69/67)
Δm²_sol = m₁² · (69/67 − 1) = 7.46×10⁻⁵ eV²
Observed: 7.49×10⁻⁵ eV² · 0.36%
The same Hypatia emission window [67, 69] that sets the SGWB frequency at 93 mHz also encodes the solar mass splitting. One mechanism — two physical sectors.
The same numbers write gravitational waves and neutrino masses
The SGWB signal at 93 mHz is constrained by the Hypatia emission window — the cascade steps [67, 69] at which the Sophia Formation's gravitational wave emission is strongest. The same window, with the same integer width ΔN=2, determines the ratio m₂/m₁ for neutrino masses. These are not the same measurement. They are the same geometric structure operating in two completely different physical sectors — one cosmological, one sub-eV particle physics.
This is the Hypatia Co-Deformation principle: a single geometric mechanism leaving its fingerprint across four distinct physical domains. The solar neutrino splitting is ZFP 38 — the final result sealed in CET v22.
The Isis Alternation Principle
The three CKM mixing angles do not draw from the same quark sector. The SU(2) weak force — a bilateral gap structure — couples to quarks alternately across the isospin doublet: the up type and down type alternate at each generation. This alternating pattern was formally derived in the quark sector work and named the Isis Alternation Principle.
Isis in the Egyptian tradition is the one who gathers, restores, and completes — the bilateral oscillation between presence and absence that re-assembles what was scattered. The weak force alternation is precisely that: the gauge structure that moves across the bilateral gap, coupling to each face in turn. The name was not decorative.
Neutrino sector — all derivations
| ZFP | Quantity | CET Derived | Observed / Bound | Residual |
|---|---|---|---|---|
| 36 | Lightest neutrino m_ν,1 | 0.050 eV | KATRIN: <0.8 eV | Consistent |
| 37 | Atmospheric splitting Δm²_atm | 2.500×10⁻³ eV² | 2.513×10⁻³ eV² | 0.52% |
| 38 | Solar splitting Δm²_sol | 7.46×10⁻⁵ eV² | 7.49×10⁻⁵ eV² | 0.36% |
| 25 | Neutrino EM charge Q_ν | 0 (exact) | <10⁻²¹ e | Exact |
| — | Mass ordering | Normal (m₁ < m₂ < m₃) | NuFIT: normal preferred | Direction |
| — | Sum of masses Σm_ν | ≈ 0.171 eV | Planck: <0.12–0.26 eV | Consistent |
ZFPs 36–38 complete the CET v22 result set, bringing the total to 38 zero-free-parameter derivations. The neutrino sector is now fully closed. Q_ν = 0 (ZFP 25) was derived earlier and set the cascade depth that ZFP 36 uses. The three results form a self-consistent chain.