{"abstract":"Numbers containing a doubled 9 are misjudged.","category":"Check-digit algorithms","checks":8,"contract":"Input a card-style number that may contain spaces or hyphens as group separators. After removing them the text must be 2..19 ASCII digits, otherwise \"malformed\". Doubling applies to every second digit counting from the rightmost (check) digit, doubled values above 9 lose 9, and the number is \"valid\" when the sum is a multiple of 10, else \"invalid\".","contract_signature":"s","evaluation_group":"w2-check_digit_algorithms-luhn-validate","failed_approach":"Subtracting 10 drops the carried tens digit and undercounts every doubled digit of 5 or more by one.","family":"w2-check_digit_algorithms-luhn-validate-doubled-digit-reduction","id":"FA-72346","implementations":{"attempt":{"sha256":"8b6cd36d5c91598d19ea0c96c7c4288b1c0e9f68ffd928cf0dee73b78f017929","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(s):\n    t = s.replace(' ', '').replace('-', '')\n    if not t.isascii() or not t.isdigit() or len(t) < 2 or len(t) > 19:\n        return 'malformed'\n    total = 0\n    for i, ch in enumerate(reversed(t)):\n        d = ord(ch) - 48\n        if i % 2 == 1:\n            d *= 2\n            if d > 9:\n                d -= 10\n        total += d\n    return 'valid' if total % 10 == 0 else 'invalid'\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [\"49717735275\"]', ['49717735275'], 'valid'], ['regression [\"7985145013991721\"]', ['7985145013991721'], 'valid'], ['partial-repair [\"59\"]', ['59'], 'valid'], ['partial-repair [\"182\"]', ['182'], 'valid'], ['control [\"52\"]', ['52'], 'invalid'], ['control [\"185\"]', ['185'], 'invalid'], ['control [\"97959\"]', ['97959'], 'invalid'], ['control [\"60866459\"]', ['60866459'], 'invalid']], [['regression [\"1513156399001929628\"]', ['1513156399001929628'], 'valid'], ['regression [\"9505094299844733505\"]', ['9505094299844733505'], 'valid'], ['partial-repair [\"60866456\"]', ['60866456'], 'valid'], ['partial-repair [\"49717735275\"]', ['49717735275'], 'valid'], ['control [\"9207919074166\"]', ['9207919074166'], 'invalid'], ['control [\"2300017738893841\"]', ['2300017738893841'], 'invalid'], ['control [\"4111-1111-1111-1111\"]', ['4111-1111-1111-1111'], 'valid'], ['control [\"4111 1111 1111 1111\"]', ['4111 1111 1111 1111'], 'valid']], [['regression [\"91\"]', ['91'], 'valid'], ['regression [\"992\"]', ['992'], 'valid'], ['partial-repair [\"470663048070284\"]', ['470663048070284'], 'valid'], ['partial-repair [\"2300017738893848\"]', ['2300017738893848'], 'valid'], ['control [\"0\"]', ['0'], 'malformed'], ['control [\"18\"]', ['18'], 'valid'], ['control [\"00\"]', ['00'], 'valid'], ['control [\"4111a1111\"]', ['4111a1111'], 'malformed']], [['regression [\"49717735275\"]', ['49717735275'], 'valid'], ['regression [\"7985145013991721\"]', ['7985145013991721'], 'valid'], ['partial-repair [\"067122965057139178\"]', ['067122965057139178'], 'valid'], ['partial-repair [\"1513156399001929628\"]', ['1513156399001929628'], 'valid'], ['control [\"١٨\"]', ['١٨'], 'malformed'], ['control [\"٣٤٥\"]', ['٣٤٥'], 'malformed'], ['control [\"79927398710\"]', ['79927398710'], 'invalid'], ['control [\"-\"]', ['-'], 'malformed']], [['regression [\"1513156399001929628\"]', ['1513156399001929628'], 'valid'], ['regression [\"9505094299844733505\"]', ['9505094299844733505'], 'valid'], ['partial-repair [\"0906050370970\"]', ['0906050370970'], 'valid'], ['partial-repair [\"3165356977\"]', ['3165356977'], 'valid'], ['control [\"185\"]', ['185'], 'invalid'], ['control [\"97959\"]', ['97959'], 'invalid'], ['control [\"60866459\"]', ['60866459'], 'invalid'], ['control [\"49717735278\"]', ['49717735278'], 'invalid']]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"d4fa204b000d49a1b643e1e0c4224920d15d5e0e43dccb053fd9fc24fe2c4c4c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(s):\n    t = s.replace(' ', '').replace('-', '')\n    if not t.isascii() or not t.isdigit() or len(t) < 2 or len(t) > 19:\n        return 'malformed'\n    total = 0\n    for i, ch in enumerate(reversed(t)):\n        d = ord(ch) - 48\n        if i % 2 == 1:\n            d *= 2\n            if d > 9:\n                d = d % 9\n        total += d\n    return 'valid' if total % 10 == 0 else 'invalid'\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression [\"49717735275\"]', ['49717735275'], 'valid'], ['regression [\"7985145013991721\"]', ['7985145013991721'], 'valid'], ['partial-repair [\"59\"]', ['59'], 'valid'], ['partial-repair [\"182\"]', ['182'], 'valid'], ['control [\"52\"]', ['52'], 'invalid'], ['control [\"185\"]', ['185'], 'invalid'], ['control [\"97959\"]', ['97959'], 'invalid'], ['control [\"60866459\"]', ['60866459'], 'invalid']], [['regression [\"1513156399001929628\"]', ['1513156399001929628'], 'valid'], ['regression [\"9505094299844733505\"]', ['9505094299844733505'], 'valid'], ['partial-repair [\"60866456\"]', ['60866456'], 'valid'], ['partial-repair [\"49717735275\"]', ['49717735275'], 'valid'], ['control [\"9207919074166\"]', ['9207919074166'], 'invalid'], ['control [\"2300017738893841\"]', ['2300017738893841'], 'invalid'], ['control [\"4111-1111-1111-1111\"]', ['4111-1111-1111-1111'], 'valid'], ['control [\"4111 1111 1111 1111\"]', ['4111 1111 1111 1111'], 'valid']], [['regression [\"91\"]', ['91'], 'valid'], ['regression [\"992\"]', ['992'], 'valid'], ['partial-repair [\"470663048070284\"]', ['470663048070284'], 'valid'], ['partial-repair [\"2300017738893848\"]', ['2300017738893848'], 'valid'], ['control [\"0\"]', ['0'], 'malformed'], ['control [\"18\"]', ['18'], 'valid'], ['control [\"00\"]', ['00'], 'valid'], ['control [\"4111a1111\"]', ['4111a1111'], 'malformed']], [['regression [\"49717735275\"]', ['49717735275'], 'valid'], ['regression [\"7985145013991721\"]', ['7985145013991721'], 'valid'], ['partial-repair [\"067122965057139178\"]', ['067122965057139178'], 'valid'], ['partial-repair [\"1513156399001929628\"]', ['1513156399001929628'], 'valid'], ['control [\"١٨\"]', ['١٨'], 'malformed'], ['control [\"٣٤٥\"]', ['٣٤٥'], 'malformed'], ['control [\"79927398710\"]', ['79927398710'], 'invalid'], ['control [\"-\"]', ['-'], 'malformed']], [['regression [\"1513156399001929628\"]', ['1513156399001929628'], 'valid'], ['regression [\"9505094299844733505\"]', ['9505094299844733505'], 'valid'], ['partial-repair [\"0906050370970\"]', ['0906050370970'], 'valid'], ['partial-repair [\"3165356977\"]', ['3165356977'], 'valid'], ['control [\"185\"]', ['185'], 'invalid'], ['control [\"97959\"]', ['97959'], 'invalid'], ['control [\"60866459\"]', ['60866459'], 'invalid'], ['control [\"49717735278\"]', ['49717735278'], 'invalid']]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic, bounded teaching model of the named scheme under the stated contract; not a certified validator. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-check_digit_algorithms-luhn-validate-doubled-digit-reduction","generated_at":"2026-09-29T14:48:37.770761+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Payment-card, loyalty and account numbers are screened with the Luhn mod-10 check before any lookup.","root_cause":"The doubled value is reduced with d % 9, so a doubled 9 (18) contributes 0 instead of 9.","sha256":"380c6d0e716e8296755425847fa8831a022bd025d01141bd0dde450cd8fb57ec","title":"Luhn doubled 9 collapses to zero through modulo nine · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":37.731,"exit_code":1,"observations":[{"actual":"invalid","check":"regression [\"49717735275\"]","expected":"valid","passed":false},{"actual":"invalid","check":"regression [\"7985145013991721\"]","expected":"valid","passed":false},{"actual":"invalid","check":"partial-repair [\"59\"]","expected":"valid","passed":false},{"actual":"invalid","check":"partial-repair [\"182\"]","expected":"valid","passed":false},{"actual":"invalid","check":"control [\"52\"]","expected":"invalid","passed":true},{"actual":"invalid","check":"control [\"185\"]","expected":"invalid","passed":true},{"actual":"invalid","check":"control [\"97959\"]","expected":"invalid","passed":true},{"actual":"invalid","check":"control [\"60866459\"]","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [\\\"49717735275\\\"]\", \"actual\": \"invalid\", \"expected\": \"valid\", \"passed\": false}, {\"check\": \"regression [\\\"7985145013991721\\\"]\", \"actual\": \"invalid\", \"expected\": \"valid\", \"passed\": false}, {\"check\": \"partial-repair [\\\"59\\\"]\", \"actual\": \"invalid\", \"expected\": \"valid\", \"passed\": false}, {\"check\": \"partial-repair [\\\"182\\\"]\", \"actual\": \"invalid\", \"expected\": \"valid\", \"passed\": false}, {\"check\": \"control [\\\"52\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"control [\\\"185\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"control [\\\"97959\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"control [\\\"60866459\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":37.115,"exit_code":1,"observations":[{"actual":"invalid","check":"regression [\"49717735275\"]","expected":"valid","passed":false},{"actual":"invalid","check":"regression [\"7985145013991721\"]","expected":"valid","passed":false},{"actual":"valid","check":"partial-repair [\"59\"]","expected":"valid","passed":true},{"actual":"valid","check":"partial-repair [\"182\"]","expected":"valid","passed":true},{"actual":"invalid","check":"control [\"52\"]","expected":"invalid","passed":true},{"actual":"invalid","check":"control [\"185\"]","expected":"invalid","passed":true},{"actual":"invalid","check":"control [\"97959\"]","expected":"invalid","passed":true},{"actual":"invalid","check":"control [\"60866459\"]","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [\\\"49717735275\\\"]\", \"actual\": \"invalid\", \"expected\": \"valid\", \"passed\": false}, {\"check\": \"regression [\\\"7985145013991721\\\"]\", \"actual\": \"invalid\", \"expected\": \"valid\", \"passed\": false}, {\"check\": \"partial-repair [\\\"59\\\"]\", \"actual\": \"valid\", \"expected\": \"valid\", \"passed\": true}, {\"check\": \"partial-repair [\\\"182\\\"]\", \"actual\": \"valid\", \"expected\": \"valid\", \"passed\": true}, {\"check\": \"control [\\\"52\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"control [\\\"185\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"control [\\\"97959\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"control [\\\"60866459\\\"]\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}