We present details of the CARMA Large Area Star Formation Survey (CLASSy), while focusing on observations of Barnard 1. CLASSy is a CARMA Key Project that spectrally imaged N2H+, HCO+, and HCN (J=1-0 transitions) across over 800 square arcminutes of the Perseus and Serpens Molecular Clouds. The observations have angular resolution near 7 and spectral resolution near 0.16 km/s. We imaged ~150 square arcminutes of Barnard 1, focusing on the main core, and the B1 Ridge and clumps to its southwest. N2H+ shows the strongest emission, with morphology similar to cool dust in the region, while HCO+ and HCN trace several molecular outflows from a collection of protostars in the main core. We identify a range of kinematic complexity, with N2H+ velocity dispersions ranging from ~0.05-0.50 km/s across the field. Simultaneous continuum mapping at 3 mm reveals six compact object detections, three of which are new detections. A new non-binary dendrogram algorithm is used to analyze dense gas structures in the N2H+ position-position-velocity (PPV) cube. The projected sizes of dendrogram-identified structures range from about 0.01-0.34 pc. Size-linewidth relations using those structures show that non-thermal line-of-sight velocity dispersion varies weakly with projected size, while rms variation in the centroid velocity rises steeply with projected size. Comparing these relations, we propose that all dense gas structures in Barnard 1 have comparable depths into the sky, around 0.1-0.2 pc; this suggests that over-dense, parsec-scale regions within molecular clouds are better described as flattened structures rather than spherical collections of gas. Science-ready PPV cubes for Barnard 1 molecular emission are available for download.
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