R-layer Mode Theory (RLMT) XLI‑P: CUP Non-existence in 4D and Higher-dimensional Projections from Mini-universe Time, Sgr A Wind, and Quantum Spin Liquids*

This volume XLI‑P of the R-layer Mode Theory (RLMT) investigates the fundamental statement that the CUP mode cannot exist as a stable, extended configuration in emergent four-dimensional spacetime. Although confined to the higher-dimensional R-layer at (TR, XR) = (0,0), the CUP structure leaves observable projections in 4D through its influence on internal time, tension gradients, and quantum geometry. We analyze three recent developments as higher-dimensional projections of the CUP structure: (1) entropy-based internal time in a cold-atom mini-universe, (2) a long-lived wind from Sgr A*, and (3) ultra-pure quantum spin-liquid crystals. We further show that quantum spin liquids provide a material analogue for AUP-based Quantum Information Tunneling Computing (QITC).