Yes, money is any item or verifiable record...but record of ownership
Nope. Not verifiable record
of ownership.
Any verifiable record
that is generally accepted as payment for goods and services and repayment of debts, in a particular socio-economic context.
everyone is free to view them as money and trade their property for them, but that's irrational as they are worthless.
It isn't worthless if it is
generally accepted as payment for goods and services and repayment of debts. All commodities (such as gold) or anything else that has "ownership" are also worthless if nobody is willing to accept them as payment for goods and services and repayment of debts. Value is an intrinsically human concept. If humans desire something (membership, ownership, or something else entirely) then it has value. If humans do not desire it, then it does not have value.
Regardless, A Bitcoin private key is proof of "ownership" and not "membership". It is possible to "own" rights to value, which is what a private key provides.
Verifiable means capable of being proven as true or real.
A record is a series of characters.
The following sentence: "The Earth is round", is a series of characters capable of being proven true. But is not money.
Money is a thing (ownership) which is represented with a record. It is something outside the record.
Finally, human concepts can be extremely irrational. If membership in the community of Bitcoin holders has "value" to someone he/she is free to investment his/her entire savings into it. But he/she won't be able to benefit until a new member enters the community. And this is exactly how all fraudulent schemes operate. And that's why they all eventually collapse.
Money is something that doesn't require the addition of a new member to be able to provide benefit to its holder. That is because the benefit comes from the entitlement or utility that is behind money.