Personal Property cost unknown

Unfortunately, if you have no documentation it will be very difficult to establish basis.  In this case, if your wife inherited the Stradivarius, you can use the stepped up basis.  The step-up in basis provision adjusts the value, or “cost basis,” of an inherited asset when it is passed on, after death.  (This gets you closer in time.)  You may wan to see if you can get appraisals for when it was inherited and use that as your basis.

Hopefully, you already have such an appraisal. Getting it appraised after it was already sold at auction will be rather difficult, and more than likely impossible since you no longer have possession of it.