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

The $IT^3$ 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.

To facilitate immediate experimental verification by the ATLAS and CMS collaborations, this release includes a formal Monte Carlo sensitivity projection for the dilepton invariant mass channel ($m_{\ell\ell}$). The simulation demonstrates that the $Z'_{geom}$ signal, injected against the exponentially falling Standard Model Drell-Yan background, yields an expected local significance of $10.07\sigma$, definitively crossing the standard $5\sigma$ threshold for formal discovery.

Data Availability & Reproducibility:

This repository contains the complete theoretical framework and all open-source computational scripts required for exact reproducibility:

• Boson_Logvinovich_v2.pdf / Boson_Logvinovich_v2.tex: The comprehensive theoretical manuscript detailing the ab-initio topological derivation.

• Boson_Logvinovich.py: The monolithic Python computational core, utilizing mpmath for 60-digit precision reconstruction of the Standard Model and the $Z'_{geom}$ resonance.

• Z_prime_Expected_Sensitivity.py: The Monte Carlo simulation script generating the HL-LHC Run 3 sensitivity projection and calculating the Asimov profile likelihood ratio.

• Z_prime_Expected_Sensitivity_Annotated.jpg: The publication-ready kinematic plot demonstrating the BSM signal against the Drell-Yan background.