Stars like our Sun form in self-gravitating dense and cold structures within interstellar clouds, called pre-stellar cores. Although much is known about the physical structure of dense clouds just before and soon after the switch-on of a protostar, the central few thousand astronomical units (au) of pre-stellar cores are unexplored. It is within these central regions that stellar systems assemble and fragmentation may take place, with the consequent formation of binaries and multiple systems. We present ALMA Band 6 observations (ACA and 12m array) of the dust continuum emission of the 8 Msun pre-stellar core L1544, with angular resolution of 2 x 1.6 (linear resolution 270 au x 216 au). Within the primary beam, a compact region of 0.1 Msun, which we call a kernel, has been unveiled. The kernel is elongated, with a central flat zone with radius Rker ~ 10 (~ 1400 au). The average number density within Rker is ~1 x 10^6 cm^{-3}, with possible local density enhancements. The region within Rker appears to have fragmented, but detailed analysis shows that similar substructure can be reproduced by synthetic interferometric observations of a smooth centrally concentrated dense core with a similar central flat zone. The presence of a smooth kernel within a dense core is in agreement with non-ideal magneto-hydro-dynamical simulations of a contracting cloud core with a peak number density of 1 x 10^7 cm^{-3}. Dense cores with lower central densities are completely filtered out when simulated 12m-array observations are carried out. These observations demonstrate that the kernel of dynamically evolved dense cores can be investigated at high angular resolution with ALMA.
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