By randomly pinning particles in fluidized states and finding the local energy minima, we form static packings of mono-disperse disks that resemble random close packing, when only n c = 2.6% of the particles are pinned. The packings are isostatic and exhibit typical critical scalings of the jamming transition. The non-triviality of n c is manifested mainly in two aspects. First, n c acts as a critical point, leading to bifurcated critical scalings in its vicinity. The criticality of n c is also demonstrated in the packings of weakly polydisperse disks. Second, n c sets a length scale in agreement with the characteristic length of random close packing. With robust evidence, we show that this agreement is generally true for both mono- and poly-disperse particles and in both two and three dimensions. The randomness inherited from fluidized states by random pinning thus interprets the randomness of random close packing from a unique perspective.
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