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Context. Historically, due to instrumental limitations and a lack of disk detections, the structure of the transition from the envelope to the rotationally supported disk has been poorly studied. This is now possible with ALMA through observations of CO isotopologues and tracers of freezeout. Class 0 sources are ideal for such studies given their almost intact envelope and young disk. Aims. The structure of the disk-envelope interface of the prototypical Class 0 source, VLA1623A, which has a confirmed Keplerian disk, is constrained through modeling and analysis of ALMA observations of DCO+ (3-2) and C18O (2-1) rotational lines. Methods. The physical structure of VLA1623 is obtained from the large-scale spectral energy distribution (SED) and continuum radiative transfer. An analytic model using a simple network coupled with radial density and temperature profiles is used as input for a 2D line radiative transfer calculation for comparison with the ALMA Cycle 0 12-m array and Cycle 2 ACA observations of VLA1623. Results. The DCO+ emission shows a clumpy structure bordering VLA1623A's Keplerian disk. This suggests a cold ring-like structure at the disk-envelope interface. The radial position of the observed DCO+ peak is reproduced in our model only if the region's temperature is between 11 K and 16 K, lower than expected from models constrained by continuum data and source SED. Altering the density profile has little e ect on the DCO+ peak position, but increased density is needed to reproduce the observed C18O tracing the disk. Conclusions. The observed DCO+ (3-2) emission around VLA1623A is the product of shadowing of the envelope by the disk observed in C18O. Disk-shadowing causes a drop in the gas temperature outside of the disk on >200 AU scales, encouraging the production of deuterated molecules. This indicates that the physical structure of the disk-envelope interface differs from the rest of the envelope, highlighting the drastic impact that the disk has on the envelope and temperature structure. The results presented here show that DCO+ is an excellent cold temperature tracer. [ABSTRACT FROM AUTHOR]