The article discusses a solution to the cosmological tensions, namely the phantom matter (PM) scenario within the framework of the running vacuum model (RVM). The authors propose a simplified version of the AXCDM model, known as the $w$XCDM model, which incorporates PM behavior. This model includes two dark energy (DE) components: one is the running vacuum energy density $\rho_{\text{vac}}(H)$, and the other is a component $X$ that behaves as PM, characterized by positive pressure and negative energy density. The PM component is supported by theoretical scenarios in stringy RVM, where it appears as a transient "phantom vacuum" tunneling into the late universe before transitioning to a new de Sitter era. Using a combination of cosmological data sets, including Planck 2018 CMB data, SNIa, cosmic chronometers, transverse BAO, and large-scale structure (LSS) data, the authors find that the $w$XCDM model significantly reduces the Hubble tension and the LSS growth tension. The model is also supported by statistical information criteria, which indicate strong evidence in favor of the PM solution. The $w$XCDM model is shown to provide a better fit to the data than the standard $\Lambda$CDM model, with the PM component dominating at high redshifts and the quintessence-like component dominating at lower redshifts. The analysis reveals that the $w$XCDM model is strongly preferred over the $\Lambda_s$CDM model, with a significant difference in the information criteria. The results are consistent with recent DESI measurements and suggest that the $w$XCDM model provides a more accurate description of the universe's evolution. The study highlights the importance of considering composite dark energy models in addressing the cosmological tensions and suggests that the PM scenario offers a promising solution to these issues.The article discusses a solution to the cosmological tensions, namely the phantom matter (PM) scenario within the framework of the running vacuum model (RVM). The authors propose a simplified version of the AXCDM model, known as the $w$XCDM model, which incorporates PM behavior. This model includes two dark energy (DE) components: one is the running vacuum energy density $\rho_{\text{vac}}(H)$, and the other is a component $X$ that behaves as PM, characterized by positive pressure and negative energy density. The PM component is supported by theoretical scenarios in stringy RVM, where it appears as a transient "phantom vacuum" tunneling into the late universe before transitioning to a new de Sitter era. Using a combination of cosmological data sets, including Planck 2018 CMB data, SNIa, cosmic chronometers, transverse BAO, and large-scale structure (LSS) data, the authors find that the $w$XCDM model significantly reduces the Hubble tension and the LSS growth tension. The model is also supported by statistical information criteria, which indicate strong evidence in favor of the PM solution. The $w$XCDM model is shown to provide a better fit to the data than the standard $\Lambda$CDM model, with the PM component dominating at high redshifts and the quintessence-like component dominating at lower redshifts. The analysis reveals that the $w$XCDM model is strongly preferred over the $\Lambda_s$CDM model, with a significant difference in the information criteria. The results are consistent with recent DESI measurements and suggest that the $w$XCDM model provides a more accurate description of the universe's evolution. The study highlights the importance of considering composite dark energy models in addressing the cosmological tensions and suggests that the PM scenario offers a promising solution to these issues.