Gauge Invariance, Topodynamic Phase Holonomies, and Optical Confinement in High-Luminosity Colliders: Resolution of Signal Annihilation via Decoupled Waist Rematching in the HL-LHC Inner Triplet (IR1 / ATLAS)

We systematically evaluate the physical and operational implications of a geometric, non-integrable phase perturbation (topodynamic gauge holonomy) of magnitude Δϕ ≈ -10.7110°, localized within the interaction region IP1 (ATLAS detector) of the High-Luminosity Large Hadron Collider (HL-LHC, √s = 14 TeV, β* = 15 cm). Using the official CERN lattice model (acc-models-lhc, sequence lhcb1, cycle cycle_round_v0, optics opt_150) implemented in MAD-X, we demonstrate that standard Achromatic Telescopic Squeezing (ATS) matching algorithms erroneously interpret this holonomy as a conventional continuous quadrupolar gradient defect. By enforcing rigid local phase closure across the insertion, the ATS protocol completely annihilates the observable physical signal between adjacent beam position monitors (4L1 → 4R1), causing discovery significance to collapse from Z = -56.8σ to Z ≈ -0.28σ while driving a severe betatronic beta-beating standing wave of up to 29.45% along the ring. To resolve this fundamental incompatibility, we formulate and implement the Decoupled Waist Confinement Regime. We demonstrate analytically and numerically that by restricting insertion quadrupoles (Q4–Q6) strictly to waist invariance (α* = 0, β* = 14.8 cm) and transferring residual betatron tune compensation to the regular main arcs, peak β-beating is suppressed to 6.75%, guaranteeing machine dynamic aperture compliance while preserving an unambiguous discovery signature of Z = -18.24σ. Associated Production Datasets: This record includes the complete, compressed standard TFS transport table twiss_topodynamic_production.tfs.gz generated via CPymad/MAD-X. It consolidates all Twiss parameters, phase advances, and betatron functions across the entire 26.7 km lattice to enable direct and independent numerical replication.