(I) We construct instantaneous counterexamples to Penrose's "cosmic censorship conjecture" (CCC) in Einstein's vacuum field equations (EVFEs) in general relativity (GR).

(II) We also construct ones that persist for a positive timespan (e.g. 1012 years). More precisely, II demonstrates either (1) the existence of a solution of EVFEs — note, no matter is involved — for 1012 years, throughout which there are any desired arbitrary number (including infinities as "numbers") of "naked" point-singularities, or (2) Einstein solutions suddenly stop existing, or (3) solutions of Einstein that ought to be well described by Newton-law dynamics, are not, or (4) "stability" of Newton law solutions is much worse than everybody had thought based both on many experiments and KAM/Nekhoroshev mathematical theory. Consequently, if Penrose's CCC is physically valid, then the reason is not Einstein gravity alone — some other physics must play a crucial role. The construction for II shows as corollaries that GR can have everywhere non-analytic metrical solutions, maximally-refuting an unfortunately-widely-believed myth; and also indicates that naked singularities arise from generic initial data — at least with some people's notions of the word "generic" (but possibly not yours).

(III) We sketch a proof of the "Turing unsimulability" of EVFEs. More precisely, either (1) the metric of spacetime time-evolves during a finite timespan (e.g. 1 year) in a manner which no Turing machine can simulate to within arbitrary user-specified accuracy bound in any finite timespan, or (cases 2 & 3 basically same as in II), or (4) "chaos lifetime" in Newtonian 3-body scenarios is much shorter than everybody had thought based on extensive experiments. It might be possible to get rid of case (4) via a different, chaos-avoiding, proof technique based on more-explicitly defined motions with perturbation bounds devised with computer aid — I sketch how but do not actually do this. The argument also suggests that unsimulability happens with generic initial data, at least with some people's notions of the word "generic" (but possibly not yours). All these scenarios I, II, III involve finite and bounded total mass-energy, initially localized with arbitrarily near 100% of it lying entirely within a ball in 3-space.

(Truncated by viXra Admin to < 400 words)