The Weinberg angle, PMNS mixing angle, and Koide ratio fall out of eigenmode counting on S². Paper with JUNO prediction at 0.17σ from first data.

Hi everyone. This is my first time posting here. I have been working on a framework that derives Standard Model quantities from the eigenmode spectrum of S² and S³, the state space and symmetry group of a single qubit, connected by the Hopf fibration.

Although Im a non-physicist (perhaps an immediate red flag for some of you), I have tried to make the framework as rigorous as possible, reporting honestly (including failures), after multiple rounds of review and rebuttal with an LLM. Please find the details and files below:

Starting point: Two inputs only.

1. Observables form a complex *-algebra with probabilistic outcomes
2. Binary observations are complete (both outcomes of any yes/no measurement fully determine the state)

These force N = 2, giving S², S³, and the Hopf fibration. The eigenmode spectra of these spaces are fixed by the spectral theorem. No free parameters anywhere.

What falls out (all from eigenmode counting):

* The gauge group SU(3) x SU(2) x U(1) and 12 gauge bosons

* The Weinberg angle sin²θ_W = 3/8 at the GUT scale (same value as Georgi-Glashow, new derivation route)

* The PMNS solar mixing angle sin²θ₁₂ = 4/13 via the Hopf pullback mechanism

* The Koide lepton mass ratio Q = 2/3 from the first eigenvalue

* 4D Minkowski spacetime with Lorentzian signature from algebraic positivity

* The Born rule from conjugation symmetry via GNS

* Yang-Mills dynamics from topology + quantization + derived constraints

What does NOT fall out (reported in the paper):

* Fine structure constant (1/137)

* Individual fermion masses

* Strong coupling

* PMNS angles θ₂₃ and θ₁₃

* CKM quark mixing angles

* CP violation

* Cosmological constant

* Higgs mechanism

The pattern of failures is informative: the framework produces mixing angles (ratios of representation dimensions) but not coupling constants (which require dynamics beyond Yang-Mills). It produces first-sector mixing only. These limitations are discussed in detail.

Predictions under active experimental test:

* sin²θ₁₂ = 4/13 = 0.30769. JUNO first data (Nov 2025): 0.3092 ± 0.0087. Deviation: 0.17σ. Full precision (~0.003) expected by ~2030. Kill zone: central value outside [0.302, 0.314].

* Tau mass from Koide: 1776.97 MeV. Current measurement: 1776.93 ± 0.09 MeV. Belle II will tighten this.

The JUNO prediction was computed before the measurement. If it holds at full precision, I think it deserves attention. If it fails, the prediction is dead and I will say so.

Included files:

* Full paper (Latex, PDF and Markdown versions included). Sorry, the paper is a bit long!

* A verification notebook (Python/Jupyter, 116 computational tests covering all positive results and all negative results)

Google Drive link: https://drive.google.com/drive/folders/1xGHE9MlhcrL0qk_70xmIxEfZEMYIjiiD?usp=sharing

Kindly share your honest feedback. The paper has been through multiple rounds of review. The remaining criticisms that survived review are all acknowledged in the paper itself.

P.S: I am not claiming this is a complete theory of physics. But perhaps opening up a direction of investigation. Also, as I mentioned, Im from a non-physics background, and much of these are over my head. Ive taken the time to learn them as far as possible, but for any answers for your questions, I will have to depend heavily on LLMs.