Quantum Simulation of TSTU Scalar Field Dynamics: Mapping Aetheron Stability onto Dipolar Quantum Droplets

Revision v1.1: Technical Refinement and Physical Mapping.

This version establishes a reinforced formal mapping between the scalar field potential of the Unified Tensor-Scalar Theory (TSTU) and the Gross-Pitaevskii dynamics of dipolar Bose-Einstein condensates.

Key updates in v1.1 include:

1. Symmetry Convergence: Explicit quantification of the U(1) \to \mathbb{Z}_2 symmetry reduction in the strong-coupling limit, including error bounds of order (\delta\mu/\hbar\Omega)^2.
2. Three-Body Dominance: Derivation of the physical criteria for g_3 dominance over Lee-Huang-Yang (LHY) quantum fluctuations, utilizing Efimov-enhanced interactions near Feshbach resonances.
3. Physical Scale Mapping: Conversion of the dimensionless charge Q into actual atom numbers (N \sim 10^9 - 10^{10}), revealing that Aetheron analogues in ^{164}\text{Dy} manifest as spatially extended phase-contrast structures rather than compact droplets.
4. Stability Analysis: Refined Phase Map distinguishing between laboratory robustness (\alpha_{BEC}) and the cosmological stability zone (\alpha \in [3, 9]).

This work provides a controlled laboratory analogue to probe dark sector-inspired scalar dynamics, offering a falsifiable benchmark for the internal consistency of the TSTU scalar sector ahead of the Euclid Data Release 1.