Universal Flavour Geometry (ERB Framework) Complete Algebraic Closure: Quarks, Bosons, and CKM Mixing
Authors/Creators
Description
The Emergent Resonant Brane (ERB) framework presents a purely geometric derivation of the fundamental parameters of the Standard Model. This work achieves a complete algebraic closure, reducing the 22 free parameters of the flavour sector—including gauge boson and Higgs masses—to a single geometric seed: the hexagonal vacuum attractor ($\xi = 3/2$).
By modeling the vacuum as a collision of two branes ($N_B=2$), we derive the three fermion generations as stationary SO(3) modes within a spherical cavity. Key findings include:
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Mass Derivations: The Top-quark mass is identified as a natural Euler-decay ($m_t = \Lambda/e$) of the energy scale $\Lambda$.
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Gauge Sector: $W, Z,$ and $Higgs$ masses are calculated as torsional responses to vacuum strain, matching experimental data with $>99\%$ accuracy.
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Mixing Dynamics: CKM and PMNS matrices are derived as geometric projections, identifying the CP-violating phase as a hexagonal lock-in ($60^\circ$) shifted by Berry curvature.
The framework is validated via the ERB Diamond Master Engine (v66), a Python-based implementation that reproduces all 13 primary constants without the use of free fit-parameters.