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Context.For the analysis of highly resolved solar spectra the simultaneous observation and interpretation (inversion) of only a few (often only one) spectral lines is still the norm. With modern instruments spatially highly resolved spectropolarimetric data covering many lines are available. Aims.For the first time we combine the information from 85 simultaneously observed absorption lines in spatially highly resolved data to test a proposed solar many-line inversion strategy. Methods.We inverted full Stokes spectra recorded with the FISS spectro-polarimeter (FISS-SP) at the 1.6-m Goode Solar Telescope in California, using the SPINOR code. We contrasted two different setups: one following the traditional approach of using a line doublet, and a new method inverting many-lines simultaneously. Results.Compared to results from an inversion using two lines of a line doublet, we discovered more fine-structure and better constrained values using the many-line technique. An average quiet Sun spectrum was successfully reproduced using a model atmosphere, but when inverting spatially resolved data, uncertainties in line parameters and blend configurations did not average out. Thus, a deliberate selection process of lines and line blends was required, in order to make the many-line case converge to a physically expected and coherent atmosphere. We successfully developed and tested such a selection method. Conclusions.Our results highlight that the many-line inversions method delivers more coherent results with superior line of sight (LOS) resolution of the atmospheric structure. Moreover, it effectively detects and utilizes even weak polarimetric signals in noisy data and thereby partly circumvents low noise requirements. It reveals uncertainties in atomic parameters of individual spectral lines and models, as the degree of freedom to compensate for these uncertainties by compromising the inferred atmospheric parameters is considerably reduced. It is thereby pointing to a need for improved atomic data, including log(gf) values, of many lines in the solar spectrum. The many-line method presents significant potential for solar physics and may become the preferred option for future observations with upcoming spectrographs. 

Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict overlap restricts global discrepancies between the covariate distributions in the treated and control populations. Exploiting results from information theory, we derive explicit bounds on the average imbalance in covariate means under strict overlap and show that these bounds become more restrictive as the dimension grows large. We discuss how these implications interact with assumptions and procedures commonly deployed in observational causal inference, including sparsity and trimming.