$\Omega_c(3185)$ as a Compact Pentaquark State: A QCD Sum Rule Analysis

This is the final, fully revised Version 4 manuscript for archive, compiled with bug-free single-column revtex4-2 LaTeX source. All table rendering bugs, redundant appendix logs and placeholder arXiv references have been eliminated, with complete published LHCb 2024 citation added. Core content overview: We present a dimension-13 QCD sum rule calculation for the $J^{P}=1/2^{-}$ compact diquark-diquark-antiquark pentaquark interpretation of the LHCb observed $\Omega_c(3185)$ state with mass $3.18\pm0.09$ GeV, consistent with experimental measurement. We systematically contrast compact pentaquark, $D\Xi$ molecular, and conventional three-quark D-wave baryon frameworks, and propose four measurable LHCb Run 3/4 observables to discriminate these models. The natural $\sim50$ MeV strong decay width of the pentaquark picture stands out compared to molecular state fine-tuning requirements. Supplementary machine-readable numerical datasets containing all Borel stability scan curves, full OPE Wilson coefficient values and mass uncertainty scan data are uploaded alongside the PDF manuscript for full computational reproducibility. No internal revision logs or auxiliary draft materials are attached to maintain clean preprint formatting.