Ab-Initio Prediction of the 1.088 TeV Topological Resonance ($Z'_{geom}$) in the IT³ Spectral-Geometric Framework

The IT³ spectral-geometric framework has recently achieved unprecedented empirical validation, culminating in the exact, blind prior prediction of the reactor neutrino oscillation parameters confirmed by the JUNO collaboration. Transitioning from the post-diction of the Standard Model spectrum to rigorous a-priori predictions of Beyond Standard Model (BSM) physics, we derive the exact mass of the first higher cyclic excitation over the electroweak core: the heavy topological vector resonance $Z'_{geom}$ (the Logvinovich Boson).

By restricting the physical vacuum to the multiquadratic constructible field $\mathbb{K}=\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ and evaluating the topological tension of the Cassini-oval moduli space, we formulate the exact mass operator for this higher-order spectral state. The derivation relies strictly on the fundamental dimension of the topological ensemble ($N_{total}=206$), the geometric holonomy screening, and the bare electroweak core scale ($\mathcal{M}_{bulk}$).

The resulting predicted pole mass is strictly 1088.04 GeV. Furthermore, this 1.088 TeV resonance lies in close proximity to the topological confinement energy barrier ($\sim 0.966$ TeV) previously derived via the Ternary Perez Hourglass fractal, suggesting a deep connection between geometric excitations and hadronic stability. This establishes a definitive, exact kinematic target for the High-Luminosity LHC (HL-LHC) at CERN.

Data Availability: The upload includes the full theoretical manuscript (.tex and .pdf) and the monolithic Python script (Boson_Logvinovich.py) for exact 60-digit precision reproducibility of the BSM mass spectrum.