If you don't trust crypto, then you cannot trust this whole procedure ; if you can't trust your wallet having done this correctly, then you don't know anything about the legitimity of any transaction.
Have you ever heard of scientific controls ?
In this case, the independent variable is the balance in the destination address and the dependent variables are just about every aspect of the blockchain mechanics that you cite in last previous post.
Do you know the most common error in scientific controls ? The false sense of security, when the scientific control you think is "independent" is in fact totally correlated with your original.
And this is an example of it.
After all, what are we looking at ?
We are looking at the VALIDITY OF A SINGLE TRANSACTION.
Now, that transaction will essentially be something like:
{input: transaction X with address A ; output address B (10 bitcoin)}
Now you THINK that you have TWO INDEPENDENT ways of verifying that transaction:
namely that address A has now 10 bitcoin less, and address B has now 10 bitcoin more.
You think that the verification of the diminishing of 10 coins in A is a kind of INDEPENDENT verification of the increase of 10 coins in address B, which would bring "credibility to the validity of the above transaction". You THINK that you do a scientific control.
There's nothing about it.
What happens when a wallet calculates the CONTENT OF address A ?
It looks at all transactions that have an UNSPEND OUTPUT at address A. How does the wallet do that ? It looks at all the transactions that have address A as output, and LEAVES OUT THOSE THAT HAVE THEM SOMEWHERE AS AN INPUT. (to keep only the unspend)
So what happens when your wallet calculates the content of B, before and after the transaction ?
Well, before the transaction it makes the sum of all unspend outputs containing address B. After the transaction, it finds ONE MORE such output, namely 10 bitcoin. Why ? Because of the above transaction !
What happens now when your wallet calculates the content of A, before and after the transaction ?
Well, before the transaction it makes the sum of all unspend outputs containing address A. After the transaction, it has to leave out one output, of 10 bitcoin (plus fee). Why ? *** because of the above transaction ***
So your "scientific control" involves TWICE the same transaction of which you want to verify the veracity. You thought that by verifying that the balance of A diminishes while the one of B increases, you have a kind of double check on the validity of the transaction. But this is not true: the increase of B and the diminishing of A are BOTH calculated using one and the same transaction: the one you wanted to verify ! So checking that A diminished, didn't ADD any "independent control" at all ! You checked twice the same thing !
This is a common mistake in "scientific control": depending on the same element, and thinking one has done an independent verification.
And now we come to the essence that kills all your arguments: the BALANCE of addresses FOLLOWS from the VALIDITY of transactions, and not the other way around. The whole idea of crypto currencies is NOT to have "bank accounts", but is to have VALID TRANSACTIONS. The atomic component of a crypto currency is not a balance, but is a transaction. And the essence of a monetary asset is the "right/power to spend", that is, the CAPABILITY OF PROVIDING A VALID TRANSACTION, not of 'changing balances'. That is a consequence of it, it is not the cause.
Your "double check" in bitcoin balances was nothing else but using twice the same valid transaction. If the transaction is invalid and you didn't see it, your "double check" would work just as well, and you would be wrong. Your whole check stands or falls with the validity or not of that transaction, and nothing else. And as I pointed out, checking the validity of a transaction in bitcoin (which is the essential function of the whole bitcoin thing !) is complex, uses a lot of cryptography, and can only be done with software.
IF the transaction is deemed valid, your balances will check, but the balance of A will not check anything more than the balance of B, because it uses exactly the same information you validated.
The validity of a transaction in bitcoin is checked by verifying that:
1) the block chain is all right
2) that the inputs of the transaction exist as former outputs of other transactions and are unspend
3) that the transaction is correctly cryptographically signed
the inclusion of the transaction in the block chain will make the former outputs now "spend".
In Monero, it is not much different. The only thing that changes is the WAY 2) is verified. In bitcoin, there is an explicit indication of which transaction had which output. In monero too, but there are OTHER transaction outputs in the list which have nothing to do with this transaction. However, the cryptographic signature used CAN ONLY BE USED ONCE for a given output. When that signature is used, we know that this output is "spent", because nobody will be able to produce a SECOND signature on the block chain using the same output, without it being seen. So directly checking, or using this signature, comes down to the same effect: the impossibility of spending an output twice.