@astner (sorry i don't do the split-quote thing, so bear with me)
fallacious reasoning. first off, any valid theory require some form of supporting evidence-or in the case of mathematics, valid reasoning. you can't just say "the universe came from a unicorn's butthole", put the burden of proof on the doubter to prove it wrong, and then kick back and celebrate your victory. secondly, since goldbach's conjecture cannot be proven, it cannot be asserted as mathematical fact. thats the whole point of calling something 'theoretical'. so i don't see how that's even relevant.
...and if the pawn shop is selling something claimed to be authentic, it is also up to them to provide proof. neither party is required to prove a lack of authenticity. pawn shops will of course take up that burden regardless, in order to not miss out on a good purchase.
no it does not indicate motive. all it does is leave room for suspicion, which doesn't hold up when the goal is assigning any guilt, let alone "beyond reasonable doubt".
nah, that's just pure supposition. pleading the 5th cannot be used as supporting evidence of guilt. there's no way to explain around that.