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Abstract We present new Atacama Large Millimeter/submillimeter Array (ALMA) continuum and NH₂D, N₂D⁺, and H₂D⁺line emission at matched, ∼100 au resolution toward the dense star-forming cores SM1N and N6 within the Ophiuchus molecular cloud. We determine the density and temperature structure of SM1N based on radiative transfer modeling and simulated observations of the multiwavelength continuum emission at 0.8, 2, and 3 mm. We show that SM1N is best fit by either a broken power-law or Plummer-like density profile with high central densities (n∼ 10⁸cm⁻³), and an inner transition radius of only ∼80–300 au. The free-fall time of the inner region is only a few ×10³yr. The continuum modeling rules out the presence of an embedded first hydrostatic core (FHSC) or protostar. SM1N is therefore a dynamically unstable but still starless core. We find that NH₂D is likely depleted at high densities within SM1N. The nonthermal velocity dispersions increase from NH₂D to N₂H⁺and H₂D⁺, possibly tracing increasing (but still subsonic) infall speeds at higher densities as predicted by some models of starless core contraction. Toward N6, we confirm the previous ALMA detection of a faint, embedded point source (N6-mm) in 0.8 mm continuum emission. NH₂D and N₂D⁺avoid N6-mm within ∼100 au, while H₂D⁺is not strongly detected toward N6. The distribution of these tracers is consistent with heating by a young, warm object. N6-mm thus remains one of the best candidate FHSCs detected so far, although its observed (sub)millimeter luminosity remains below predictions for FHSCs.