Phase Coherence as a Control Axis in Bipartite Quantum Correlations: A Gate-Formalism Perspective on Entanglement Visibility (Paper I/VII)

Systematic analysis of a parametrized two-qubit system demonstrating that phase coherence functions as a physical resource governing entanglement visibility. The differential correlation Δ⟨σx⊗σx⟩ oscillates with relative phase φ, while Wootters concurrence C = |sin 2γ| remains phase-invariant. Results are framed within the Δ-Gate Formalism, where each measurement constitutes a coherence-dependent transition operator. The parametrization maps directly onto tt̄ spin correlations at the LHC, yielding three falsifiable predictions testable with ATLAS/CMS Run 3 data. Paper I of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).