Mimblewimble
What?!...
Bitcoin is the first widely used financial system for which all the necessary
data to validate the system status can be cryptographically verified by anyone.
However, it accomplishes this feat by storing all transactions in a public
database called "the blockchain" and someone who genuinely wishes to check
this state must download the whole thing and basically replay each transaction,
check each one as they go. Meanwhile, most of these transactions have not
affected the actual final state (they create outputs that are destroyed
a transaction later).
(...)-- https://download.wpsoftware.net/bitcoin/wizardry/mimblewimble.txt
.......
The key insight of our dear Voldemort is that the blinding factors can be re-purposed as an authentication mechanism (like we currently have digital signatures based on knowledge of private keys). In CT, the blinding factors
(see: hiding and binding, the key properties of a commitment scheme, the 'hiding' property is achieved by attaching a random number to what you commit to, often called a 'blinding factor'. In the Pedersen commitments of CT, the idea is that the totals add up even though the amounts are hidden, ie the sum of all the input and output commitments is zero; to achieve that, the whole set of blinding factors have to add up to zero just as the amounts do)
... are secret to the (sender, receiver), and the network only needs to know that their sum is zero. In MW you add a tweak - restrict knowledge of the receiver's blinding factors to the receiver only, by allowing him to have the total set of blinding factors not add up to zero, but rather add up to some non-zero amount, call it k, then that k is something like a private key - he can sign with its public key kG. It doesn't matter what he signs - can be an empty string. Nobody else can attach that signature, nobody else knows k, only kG (and others do know kG, 'cos its the arithmetic difference of the commitments). It's pretty genius actually.
-- source
you cannot skip verifying a transaction that is spend later, since the Bitcoin might have been lost causing an ambiguity as to where a certain coin originated from.