The Neutrino CP Phase from Geometry: Charge-Locked Charged-Lepton Corrections in an E8-Derived E6 Model
Authors/Creators
Description
In the TTOE framework the flavor sector is described by a w0-based ansatz within an E6 grand-unified cascade whose structural value for the leptonic CP phase is δ_PMNS = 180° (CP conservation), while global oscillation data prefer δ_PMNS ~ 197°; the joint T2K+NOvA analysis still permits CP conservation at present precision, so the ~17° displacement is a tension, not an exclusion — but it is the sector's only one, and this paper asks whether the framework can produce it. The setting is the geometric layer that the framework acquired with the flag-manifold resolution of the three-generation problem: three 27's whose U(1)² charges are the weights of the internal 3, six E6-singlet "flavons" whose charges are the six roots (a Froggatt–Nielsen chart with no chosen charges), and a single renormalizable inter-family trilinear. Three no-go theorems are proved first: (i) the trilinear alone forces hollow symmetric Yukawa textures, whose singular values obey σ₂ ≥ σ₁/2 — excluded by the observed hierarchies by factors 135/26/8 in the up/down/lepton sectors; (ii) no combination of the three geometric Higgs doublets escapes the bound; (iii) Kaluza–Klein doublet admixture cannot rescue it, since every geometric–KK mixing requires a vev by U(1)² charge conservation, leaving the light doublet geometric to one part in 10⁴. The geometric layer therefore cannot replace the flavor ansatz; it can only perturb it — and that perturbation is precisely what the CP tension needs. A charged-lepton correction with derived 1–2 dominance (the mass denominators m_μ/m_τ do the work) of size one flavon insertion, θ^e_12 ≈ 3° with near-maximal phase, moves δ from 180° to 196.8° with all three mixing angles within 1σ — succeeding exactly where a pre-registered Majorana-phase route had failed by destroying θ₁₂. Two locks are then tested. The Cabibbo lock: applying the sibling correction to the down sector of the reconstructed CKM benchmark of the framework (reproduced digit-exact from its repository) shows that any sibling strength above one tenth of the leptonic one is excluded at every phase. The charge-arithmetic lock then explains why the required suppression is structural rather than tuned: enumerating the E6 cubic invariant by SU(5)×U(1)_χ×U(1)_ψ charges yields exactly four terms, and the only vertex that rotates chiral fermions at first order in GUT vevs is ⟨ν^c⟩·5̄(16)·5(10): it rotates the lepton doublets (PMNS-active) and the right-handed downs (CKM-blind), and it cannot touch the quark doublets or e^c because the required 1·10·X term admits no charge solution. The mechanism is lopsided by arithmetic; its mediators are the classic E6 exotics with mass λ⟨θ⟩, and the geometric coupling cancels between vertex and mediator, leaving θ^e ~ ⟨ν^c⟩/⟨θ⟩ ≈ 0.05. Three falsifiable consequences follow: with δ confirmed in [196°, 213°] the mixing angles must remain frozen at the ansatz fit within stated bands (JUNO decides); no induced CKM or first-row unitarity anomaly may accompany the phase; and δ outside [~142°, 218°] kills the mechanism outright. What is derived, what is conditional (the near-maximal phase; the vev ordering ⟨ν^c⟩/⟨θ⟩), and what is not claimed (a first-principles value of 197°) are tabulated explicitly.
Notes (English)
This work is a modest contribution from an independent researcher. It does not claim to constitute a Theory of Everything. Each result is classified by its epistemic status — derived, conditional, or open — and should be regarded as a hypothesis requiring independent verification. No result should be treated as established physics until it has been independently checked by the scientific community.
If any researcher discovers results — experimental, theoretical, or computational — that relate to this work or the broader TTOE framework, whether confirming or refuting any part of it, I would be grateful to be informed.
Computational materials (Python scripts, JSON outputs, analysis notebooks) are not included in this deposit but are available upon request. Researchers who wish to inspect, reproduce, or challenge any result may contact me at:
https://orcid.org/0009-0004-8792-9396 foksus@proton.me
I wish to express my gratitude to all the scientists, mathematicians, physicists, biologists, philosophers, and thinkers — past and present — whose discoveries, ideas, and tireless pursuit of truth have built the edifice of knowledge upon which this work rests. No single contribution can emerge in isolation; even the solitary researcher draws from a collective intellectual heritage that spans centuries. Any errors or shortcomings are entirely my own.
E.U.O.