{"abstract":"Capacity checks reject payloads that would still fit, forcing a larger symbol version.","category":"Barcode symbology encoding","checks":8,"contract":"Compute the length in bits of one QR segment: 4-bit mode indicator, a character count indicator whose width depends on mode and version band (1-9, 10-26, 27-40): numeric 10/12/14, alphanumeric 9/11/13, byte 8/16/16, and the data bits: numeric 10 bits per 3 digits plus 4 or 7 for a remainder of 1 or 2, alphanumeric 11 bits per pair plus 6 for a single, byte 8 bits per UTF-8 byte. Alphanumeric allows 0-9 A-Z space $ % * + - . / :. A count that does not fit the indicator is too-long. Errors: version, charset, mode, too-long.","evaluation_group":"w2-barcode-symbology-encoding-qr-segment-bits","failed_approach":"Three bits cannot represent a single digit 0-9.","family":"w2-barcode-symbology-encoding-qr-segment-bits-numeric-remainder","id":"FA-79636","implementations":{"attempt":{"sha256":"bcd70cef8101a3650b43c707ee309fae12aeeef33ee4755dfa90afc2dafa2e6f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(mode, data, version):\n    if not 1 <= version <= 40:\n        return {'error': 'version'}\n    band = 0 if version <= 9 else (1 if version <= 26 else 2)\n    ALNUM = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:'\n    if mode == 'numeric':\n        if not all(c in '0123456789' for c in data):\n            return {'error': 'charset'}\n        count = len(data)\n        bits = 10 * (count // 3) + [0, 3, 7][count % 3]\n        cci = [10, 12, 14][band]\n    elif mode == 'alnum':\n        if not all(c in ALNUM for c in data):\n            return {'error': 'charset'}\n        count = len(data)\n        bits = 11 * (count // 2) + 6 * (count % 2)\n        cci = [9, 11, 13][band]\n    elif mode == 'byte':\n        count = len(data.encode('utf-8'))\n        bits = 8 * count\n        cci = [8, 16, 16][band]\n    else:\n        return {'error': 'mode'}\n    if count >= 1 << cci:\n        return {'error': 'too-long'}\n    return 4 + cci + bits\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[('numeric', '51951717', 40), 45], [('numeric', '1322507885', 27), 52], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('alnum', '-', 1), 19], [('alnum', '%', 1), 19], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('numeric', '97888196275', 27), 55]], [[('numeric', '41605446623', 10), 53], [('numeric', '7840130886', 40), 52], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('numeric', '51', 40), 25]], [[('numeric', '53', 26), 23], [('numeric', '6256737', 1), 38], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('byte', '', 26), 20], [('alnum', '%/2*+% $', 0), {'error': 'version'}], [('numeric', '37219', 5), 31]], [[('numeric', '86667136', 5), 41], [('numeric', '9736438869', 15), 50], [('byte', 'abbbaaa', 26), 76], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', 'A:*éZA', 40), {'error': 'charset'}], [('numeric', '82758', 27), 35]], [[('numeric', '30390', 26), 33], [('numeric', '5', 1), 18], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('byte', 'a€', 26), 52], [('alnum', '.', 5), 19], [('byte', '€é1', 27), 68], [('numeric', '14974', 9), 31]]]\nlabels = [\"regression: numeric remainder bits\", \"repair trap\", \"combined fault\", \"control\", \"control\", \"boundary\", \"boundary\", \"control\"]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (labels[i % len(labels)], i), 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":"c0464f219e09703cfaa3c5488ddb64cc7936a5aaa5b8646354c29f65663b5dc4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(mode, data, version):\n    if not 1 <= version <= 40:\n        return {'error': 'version'}\n    band = 0 if version <= 9 else (1 if version <= 26 else 2)\n    ALNUM = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:'\n    if mode == 'numeric':\n        if not all(c in '0123456789' for c in data):\n            return {'error': 'charset'}\n        count = len(data)\n        bits = 10 * (count // 3) + [0, 4, 8][count % 3]\n        cci = [10, 12, 14][band]\n    elif mode == 'alnum':\n        if not all(c in ALNUM for c in data):\n            return {'error': 'charset'}\n        count = len(data)\n        bits = 11 * (count // 2) + 6 * (count % 2)\n        cci = [9, 11, 13][band]\n    elif mode == 'byte':\n        count = len(data.encode('utf-8'))\n        bits = 8 * count\n        cci = [8, 16, 16][band]\n    else:\n        return {'error': 'mode'}\n    if count >= 1 << cci:\n        return {'error': 'too-long'}\n    return 4 + cci + bits\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[('numeric', '51951717', 40), 45], [('numeric', '1322507885', 27), 52], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('alnum', '-', 1), 19], [('alnum', '%', 1), 19], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('numeric', '97888196275', 27), 55]], [[('numeric', '41605446623', 10), 53], [('numeric', '7840130886', 40), 52], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('numeric', '51', 40), 25]], [[('numeric', '53', 26), 23], [('numeric', '6256737', 1), 38], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('byte', '', 26), 20], [('alnum', '%/2*+% $', 0), {'error': 'version'}], [('numeric', '37219', 5), 31]], [[('numeric', '86667136', 5), 41], [('numeric', '9736438869', 15), 50], [('byte', 'abbbaaa', 26), 76], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', 'A:*éZA', 40), {'error': 'charset'}], [('numeric', '82758', 27), 35]], [[('numeric', '30390', 26), 33], [('numeric', '5', 1), 18], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('byte', 'a€', 26), 52], [('alnum', '.', 5), 19], [('byte', '€é1', 27), 68], [('numeric', '14974', 9), 31]]]\nlabels = [\"regression: numeric remainder bits\", \"repair trap\", \"combined fault\", \"control\", \"control\", \"boundary\", \"boundary\", \"control\"]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (labels[i % len(labels)], i), 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"},"fixed":{"sha256":"3459bf022428adc50b75b65b46c98603eaa2b5999583a3bde3f979bdc19d3c67","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(mode, data, version):\n    if not 1 <= version <= 40:\n        return {'error': 'version'}\n    band = 0 if version <= 9 else (1 if version <= 26 else 2)\n    ALNUM = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:'\n    if mode == 'numeric':\n        if not all(c in '0123456789' for c in data):\n            return {'error': 'charset'}\n        count = len(data)\n        bits = 10 * (count // 3) + [0, 4, 7][count % 3]\n        cci = [10, 12, 14][band]\n    elif mode == 'alnum':\n        if not all(c in ALNUM for c in data):\n            return {'error': 'charset'}\n        count = len(data)\n        bits = 11 * (count // 2) + 6 * (count % 2)\n        cci = [9, 11, 13][band]\n    elif mode == 'byte':\n        count = len(data.encode('utf-8'))\n        bits = 8 * count\n        cci = [8, 16, 16][band]\n    else:\n        return {'error': 'mode'}\n    if count >= 1 << cci:\n        return {'error': 'too-long'}\n    return 4 + cci + bits\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[('numeric', '51951717', 40), 45], [('numeric', '1322507885', 27), 52], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('alnum', '-', 1), 19], [('alnum', '%', 1), 19], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('numeric', '97888196275', 27), 55]], [[('numeric', '41605446623', 10), 53], [('numeric', '7840130886', 40), 52], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('numeric', '51', 40), 25]], [[('numeric', '53', 26), 23], [('numeric', '6256737', 1), 38], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('byte', '', 26), 20], [('alnum', '%/2*+% $', 0), {'error': 'version'}], [('numeric', '37219', 5), 31]], [[('numeric', '86667136', 5), 41], [('numeric', '9736438869', 15), 50], [('byte', 'abbbaaa', 26), 76], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', 'A:*éZA', 40), {'error': 'charset'}], [('numeric', '82758', 27), 35]], [[('numeric', '30390', 26), 33], [('numeric', '5', 1), 18], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('byte', 'a€', 26), 52], [('alnum', '.', 5), 19], [('byte', '€é1', 27), 68], [('numeric', '14974', 9), 31]]]\nlabels = [\"regression: numeric remainder bits\", \"repair trap\", \"combined fault\", \"control\", \"control\", \"boundary\", \"boundary\", \"control\"]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (labels[i % len(labels)], i), 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 with a stipulated contract; it makes no claim of conformance to any published specification. 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-barcode-symbology-encoding-qr-segment-bits-numeric-remainder","generated_at":"2026-09-29T14:49:46.342213+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Retail, logistics, pharmacy and document workflows depend on encoders that produce exactly the module pattern, code-set switches, separators and quiet zones scanners expect; one misplaced module or separator makes a label unreadable or, worse, scan as different data.","repair":"Use 4 bits for one remaining digit and 7 bits for two.","root_cause":"A two-digit numeric remainder is counted as 4 bits per digit instead of 7 bits.","sha256":"ba73557b8f98b0652c386c4ebebc07b6a5c19616086791c78c94e430a6cca995","title":"QR numeric remainder of two digits is sized as 8 bits · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.939,"exit_code":1,"observations":[{"actual":45,"check":"regression: numeric remainder bits 0","expected":45,"passed":true},{"actual":51,"check":"repair trap 1","expected":52,"passed":false},{"actual":{"error":"version"},"check":"combined fault 2","expected":{"error":"version"},"passed":true},{"actual":19,"check":"control 3","expected":19,"passed":true},{"actual":19,"check":"control 4","expected":19,"passed":true},{"actual":108,"check":"boundary 5","expected":108,"passed":true},{"actual":{"error":"charset"},"check":"boundary 6","expected":{"error":"charset"},"passed":true},{"actual":55,"check":"control 7","expected":55,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: numeric remainder bits 0\", \"actual\": 45, \"expected\": 45, \"passed\": true}, {\"check\": \"repair trap 1\", \"actual\": 51, \"expected\": 52, \"passed\": false}, {\"check\": \"combined fault 2\", \"actual\": {\"error\": \"version\"}, \"expected\": {\"error\": \"version\"}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": 19, \"expected\": 19, \"passed\": true}, {\"check\": \"control 4\", \"actual\": 19, \"expected\": 19, \"passed\": true}, {\"check\": \"boundary 5\", \"actual\": 108, \"expected\": 108, \"passed\": true}, {\"check\": \"boundary 6\", \"actual\": {\"error\": \"charset\"}, \"expected\": {\"error\": \"charset\"}, \"passed\": true}, {\"check\": \"control 7\", \"actual\": 55, \"expected\": 55, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.505,"exit_code":1,"observations":[{"actual":46,"check":"regression: numeric remainder bits 0","expected":45,"passed":false},{"actual":52,"check":"repair trap 1","expected":52,"passed":true},{"actual":{"error":"version"},"check":"combined fault 2","expected":{"error":"version"},"passed":true},{"actual":19,"check":"control 3","expected":19,"passed":true},{"actual":19,"check":"control 4","expected":19,"passed":true},{"actual":108,"check":"boundary 5","expected":108,"passed":true},{"actual":{"error":"charset"},"check":"boundary 6","expected":{"error":"charset"},"passed":true},{"actual":56,"check":"control 7","expected":55,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: numeric remainder bits 0\", \"actual\": 46, \"expected\": 45, \"passed\": false}, {\"check\": \"repair trap 1\", \"actual\": 52, \"expected\": 52, \"passed\": true}, {\"check\": \"combined fault 2\", \"actual\": {\"error\": \"version\"}, \"expected\": {\"error\": \"version\"}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": 19, \"expected\": 19, \"passed\": true}, {\"check\": \"control 4\", \"actual\": 19, \"expected\": 19, \"passed\": true}, {\"check\": \"boundary 5\", \"actual\": 108, \"expected\": 108, \"passed\": true}, {\"check\": \"boundary 6\", \"actual\": {\"error\": \"charset\"}, \"expected\": {\"error\": \"charset\"}, \"passed\": true}, {\"check\": \"control 7\", \"actual\": 56, \"expected\": 55, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.978,"exit_code":0,"observations":[{"actual":45,"check":"regression: numeric remainder bits 0","expected":45,"passed":true},{"actual":52,"check":"repair trap 1","expected":52,"passed":true},{"actual":{"error":"version"},"check":"combined fault 2","expected":{"error":"version"},"passed":true},{"actual":19,"check":"control 3","expected":19,"passed":true},{"actual":19,"check":"control 4","expected":19,"passed":true},{"actual":108,"check":"boundary 5","expected":108,"passed":true},{"actual":{"error":"charset"},"check":"boundary 6","expected":{"error":"charset"},"passed":true},{"actual":55,"check":"control 7","expected":55,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: numeric remainder bits 0\", \"actual\": 45, \"expected\": 45, \"passed\": true}, {\"check\": \"repair trap 1\", \"actual\": 52, \"expected\": 52, \"passed\": true}, {\"check\": \"combined fault 2\", \"actual\": {\"error\": \"version\"}, \"expected\": {\"error\": \"version\"}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": 19, \"expected\": 19, \"passed\": true}, {\"check\": \"control 4\", \"actual\": 19, \"expected\": 19, \"passed\": true}, {\"check\": \"boundary 5\", \"actual\": 108, \"expected\": 108, \"passed\": true}, {\"check\": \"boundary 6\", \"actual\": {\"error\": \"charset\"}, \"expected\": {\"error\": \"charset\"}, \"passed\": true}, {\"check\": \"control 7\", \"actual\": 55, \"expected\": 55, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}