What question did this study set out to answer?

This work aims to derive various observables from the cubic polynomial equation with no free parameters.

April 17, 2026Open Access

Cascade Framework: Deriving Standard Model Observables from x³ = x² + 1

Puntos clave

This work aims to derive various observables from the cubic polynomial equation with no free parameters.
Developed a framework overview and complete scorecard for Standard Model predictions.
Predicted dark energy and provided forecasts for validation through DESI/Euclid.
Used cascade arithmetic to determine fermion mass ratios.
Analyzed electroweak sector, CKM matrix, and neutrino masses.
Derived 27 total observables with 19 achieving sub-0.1% accuracy.
Predicted dark energy density Ω_Λ = 0.6823.
Validated 8/8 predictions in electroweak sector and 5/5 in CKM matrix.
Proven fourteen exact algebraic theorems supporting the framework.

Resumen

A theoretical framework deriving 27 Standard Model and cosmological observables from the single cubic polynomial x³ = x² + 1 with zero free parameters. The four papers cover: (1) framework overview and complete scorecard (19/27 sub-0. 1%), (2) dark energy prediction Ω_Λ = 0. 6823 with falsifiable DESI/Euclid forecasts, (3) fermion mass ratios via cascade arithmetic, and (4) electroweak sector (8/8 sub-0. 1%), CKM matrix (5/5 sub-0. 1%), and neutrino masses. Fourteen exact algebraic theorems are proven. The sub-leading correction structure classifies into geometric, algebraic, and hybrid branches.

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