CO(7-6) and C I (2-1) survey in z>6 quasars

High-redshift (z emission, the physical condition and molecular gas content of their interstellar medium (ISM) remain uncertain. We present sensitive Atacama Large Millimeter/submillimeter Array Band 3 observations of the redshifted CO (7--6) and quasars are signposts of the earliest supermassive black holes and intense star formation, offering key laboratories for black hole--galaxy evolution at cosmic dawn. While far-infrared studies have revealed large dust reservoirs and strong C, ii C, i (2--1) emission lines and the underlying dust continuum in a sample of 18 quasars at z ∼ 6. We detected CO (7--6) in 15/18, C, i (2--1) in 6/18, and continuum in 13/18 sources. Line luminosities and continuum fluxes were used to estimate molecular gas masses from CO, C, i, and dust, and a hierarchical Bayesian cross-calibration of all four tracers yielded consistent per-source M_̊m H₂ estimates and global conversion factors. Comparison with photodissociation region (PDR) and X-ray dominated region model grids using the L_ ̊m CII /L_ ̊m CI and L_ ̊m CO (7 6) -- /L_ ̊m TIR ratios suggests gas densities of n > 10⁴ cm -3 and radiation fields of G₀ ∼ 10³–10⁴ for the subset of sources consistent with PDR solutions, while many quasars fall outside the model parameter space. Additional diagnostics based on the L'_ ̊m CO (7-6) /L'_ ̊m CI (2-1) ratio indicate that a large fraction of the molecular gas resides in a warm and highly excited phase. Together these results suggest that classical PDR heating alone cannot explain the observed line ratios and that additional volumetric processes such as X-ray irradiation, turbulence and shocks, or enhanced cosmic-ray heating likely influence the excitation of the cold ISM. These results demonstrate the power of multi-line diagnostics in revealing the excitation and structure of the cold ISM in early quasar host galaxies and highlight the need for a joint analysis of CO, C, i, C, ii, and dust emission to fully characterize star formation and heating driven by active galactic nuclei at cosmic dawn.