Check Digits

Given digits with the final check digit omitted, return the one that completes them. US healthcare NPIs and securities ISINs use the Luhn formula. Use it to build valid test fixtures, to recover a last digit that was lost or illegible, or to check an implementation against a reference. To test a number you already have in full, use validate_identifier instead. Input must reduce to digits only once spaces and dashes are stripped; anything else is an error. Payment cards also use Luhn, and are deliberately out of scope here: do not pass card digits, partial or complete. This constructs a well-formed number and nothing more: it does not create, reserve or verify a real provider or security.

Identify a bare number whose type was never recorded. Tests it against every supported format and reports which ones its check digit satisfies. Use it for an unlabeled spreadsheet column, a value pulled out of a log line or a scanned document, or any number handed over without being named. Reports every format that matches rather than choosing between them. Several matches is normal and does not mean the answer is unclear: some formats are subsets of others, so every ISBN-13 is also a valid EAN-13, and a short value can satisfy two unrelated formats by chance. Read one match as strong evidence and several as a set to narrow from context. As with validation, a match means the arithmetic is consistent, not that the identifier is registered or real.

Verify a number when you already know what it is supposed to be. Use this whenever someone gives you a product barcode (GTIN, UPC or EAN), a book number (ISBN-10 or ISBN-13), a vehicle VIN, a US healthcare provider NPI, a security ISIN, or a legal entity LEI, and acting on a wrong one would cost something: a bounced claim, a rejected listing, a record that quietly corrupts a dataset. Every supported format is a public identifier. Bank accounts, IBANs, routing numbers and payment cards are not supported and must not be sent. Returns whether the checksum passes and, when it fails, the specific reason. If you do not already know the format, call identify_format first rather than guessing a `kind`, since a valid identifier checked against the wrong format comes back invalid. A passing checksum proves only that the digits are internally consistent: it does not mean the book, product, vehicle or provider exists, is active, or belongs to any particular person.