{"abstract":"Paragraphs starting with Arabic letters default to left-to-right.","category":"Bidirectional text layout","checks":8,"contract":"Input [bidi classes, default level]. Scan for the first L (level 0) or R/AL (level 1), skipping characters between an isolate initiator (LRI, RLI, FSI) and its matching PDI (nesting counted; an unmatched PDI is ignored). Embedding codes are not skipped. Return [level, index of deciding character] or [default, None].","evaluation_group":"w2-bidirectional-text-layout-paragraph-direction","failed_approach":"Adding AN instead of AL makes Arabic digits decide the direction.","family":"w2-bidirectional-text-layout-paragraph-direction-arabic-letter-strength","id":"FA-80341","implementations":{"attempt":{"sha256":"8e236c5bef1633e0e180e388e0c3554e1f03c1efef991f5a997d97b8f25d4427","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    classes, default = x\n    depth = 0\n    for i, c in enumerate(classes):\n        if c in ('LRI', 'RLI', 'FSI'):\n            depth += 1\n        elif c == 'PDI':\n            if depth > 0:\n                depth -= 1\n        elif depth == 0:\n            if c == 'L':\n                return [0, i]\n            if c in ('R', 'AN'):\n                return [1, i]\n    return [default, None]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL'], 0], [1, 0]), ('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('partial-repair probe', [['AN', 'R', 'L', 'ON', 'L'], 1], [1, 1]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['WS', 'FSI'], 0], [0, None]), ('control layout', [['EN', 'R'], 0], [1, 1])], [('regression: Arabic letter strength', [['AL', 'ON', 'PDI', 'AL', 'WS'], 1], [1, 0]), ('regression: Arabic letter strength', [['WS', 'WS', 'AL', 'AN', 'WS', 'PDI'], 0], [1, 2]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('partial-repair probe', [['AN', 'ES', 'L', 'L', 'WS', 'L', 'AL', 'R'], 0], [0, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['PDI', 'FSI', 'L', 'NSM', 'ON', 'R'], 1], [1, None]), ('control layout', [['R', 'WS', 'ON', 'AN', 'RLI', 'RLI'], 0], [1, 0])], [('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('regression: Arabic letter strength', [['ON', 'AL', 'FSI'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL', 'L', 'WS'], 0], [1, 0]), ('partial-repair probe', [['LRE', 'AN', 'L', 'AN'], 1], [0, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('control layout', [['RLI', 'PDI', 'RLI', 'EN'], 1], [1, None])], [('regression: Arabic letter strength', [['EN', 'LRE', 'AL', 'FSI'], 1], [1, 2]), ('regression: Arabic letter strength', [['ON', 'AL', 'ES', 'L', 'PDI', 'AN', 'NSM', 'LRI', 'ON'], 0], [1, 1]), ('partial-repair probe', [['ON', 'AN', 'RLI', 'RLI', 'R', 'R', 'EN', 'EN', 'L'], 1], [1, None]), ('regression: Arabic letter strength', [['AL', 'R', 'ON', 'AN', 'AL', 'EN', 'L', 'PDI', 'PDI', 'L'], 0], [1, 0]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['L', 'R', 'R', 'NSM', 'L', 'PDI', 'PDI', 'EN'], 1], [0, 0]), ('control layout', [['LRI', 'ES'], 0], [0, None])], [('regression: Arabic letter strength', [['AL', 'PDI'], 1], [1, 0]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('regression: Arabic letter strength', [['NSM', 'AL', 'PDI', 'ON', 'AN', 'WS'], 0], [1, 1]), ('regression: Arabic letter strength', [['ON', 'AL'], 1], [1, 1]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS'], 0], [0, None]), ('control layout', [['EN'], 0], [0, None])]]\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":"47c6474a5317fab57e5e2f26110aa16bf901dd55915304e5563e716f62e3ff5e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    classes, default = x\n    depth = 0\n    for i, c in enumerate(classes):\n        if c in ('LRI', 'RLI', 'FSI'):\n            depth += 1\n        elif c == 'PDI':\n            if depth > 0:\n                depth -= 1\n        elif depth == 0:\n            if c == 'L':\n                return [0, i]\n            if c == 'R':\n                return [1, i]\n    return [default, None]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL'], 0], [1, 0]), ('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('partial-repair probe', [['AN', 'R', 'L', 'ON', 'L'], 1], [1, 1]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['WS', 'FSI'], 0], [0, None]), ('control layout', [['EN', 'R'], 0], [1, 1])], [('regression: Arabic letter strength', [['AL', 'ON', 'PDI', 'AL', 'WS'], 1], [1, 0]), ('regression: Arabic letter strength', [['WS', 'WS', 'AL', 'AN', 'WS', 'PDI'], 0], [1, 2]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('partial-repair probe', [['AN', 'ES', 'L', 'L', 'WS', 'L', 'AL', 'R'], 0], [0, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['PDI', 'FSI', 'L', 'NSM', 'ON', 'R'], 1], [1, None]), ('control layout', [['R', 'WS', 'ON', 'AN', 'RLI', 'RLI'], 0], [1, 0])], [('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('regression: Arabic letter strength', [['ON', 'AL', 'FSI'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL', 'L', 'WS'], 0], [1, 0]), ('partial-repair probe', [['LRE', 'AN', 'L', 'AN'], 1], [0, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('control layout', [['RLI', 'PDI', 'RLI', 'EN'], 1], [1, None])], [('regression: Arabic letter strength', [['EN', 'LRE', 'AL', 'FSI'], 1], [1, 2]), ('regression: Arabic letter strength', [['ON', 'AL', 'ES', 'L', 'PDI', 'AN', 'NSM', 'LRI', 'ON'], 0], [1, 1]), ('partial-repair probe', [['ON', 'AN', 'RLI', 'RLI', 'R', 'R', 'EN', 'EN', 'L'], 1], [1, None]), ('regression: Arabic letter strength', [['AL', 'R', 'ON', 'AN', 'AL', 'EN', 'L', 'PDI', 'PDI', 'L'], 0], [1, 0]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['L', 'R', 'R', 'NSM', 'L', 'PDI', 'PDI', 'EN'], 1], [0, 0]), ('control layout', [['LRI', 'ES'], 0], [0, None])], [('regression: Arabic letter strength', [['AL', 'PDI'], 1], [1, 0]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('regression: Arabic letter strength', [['NSM', 'AL', 'PDI', 'ON', 'AN', 'WS'], 0], [1, 1]), ('regression: Arabic letter strength', [['ON', 'AL'], 1], [1, 1]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS'], 0], [0, None]), ('control layout', [['EN'], 0], [0, None])]]\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"},"fixed":{"sha256":"2db669c004c99f1ae0200880b5e2a283cdb2dc136f24634611584908016866e3","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    classes, default = x\n    depth = 0\n    for i, c in enumerate(classes):\n        if c in ('LRI', 'RLI', 'FSI'):\n            depth += 1\n        elif c == 'PDI':\n            if depth > 0:\n                depth -= 1\n        elif depth == 0:\n            if c == 'L':\n                return [0, i]\n            if c in ('R', 'AL'):\n                return [1, i]\n    return [default, None]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('Arabic letter decides', [['ON', 'AL', 'L'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL'], 0], [1, 0]), ('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('partial-repair probe', [['AN', 'R', 'L', 'ON', 'L'], 1], [1, 1]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['WS', 'FSI'], 0], [0, None]), ('control layout', [['EN', 'R'], 0], [1, 1])], [('regression: Arabic letter strength', [['AL', 'ON', 'PDI', 'AL', 'WS'], 1], [1, 0]), ('regression: Arabic letter strength', [['WS', 'WS', 'AL', 'AN', 'WS', 'PDI'], 0], [1, 2]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('partial-repair probe', [['AN', 'ES', 'L', 'L', 'WS', 'L', 'AL', 'R'], 0], [0, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['PDI', 'FSI', 'L', 'NSM', 'ON', 'R'], 1], [1, None]), ('control layout', [['R', 'WS', 'ON', 'AN', 'RLI', 'RLI'], 0], [1, 0])], [('regression: Arabic letter strength', [['AL', 'EN'], 1], [1, 0]), ('regression: Arabic letter strength', [['ON', 'AL', 'FSI'], 0], [1, 1]), ('regression: Arabic letter strength', [['AL', 'L', 'WS'], 0], [1, 0]), ('partial-repair probe', [['LRE', 'AN', 'L', 'AN'], 1], [0, 2]), ('nested isolates', [['LRI', 'RLI', 'R', 'PDI', 'L', 'PDI', 'R'], 0], [1, 6]), ('stray PDI before isolate', [['PDI', 'RLI', 'L', 'PDI', 'R'], 0], [1, 4]), ('control layout', [['EN', 'PDI', 'L', 'EN', 'FSI'], 1], [0, 2]), ('control layout', [['RLI', 'PDI', 'RLI', 'EN'], 1], [1, None])], [('regression: Arabic letter strength', [['EN', 'LRE', 'AL', 'FSI'], 1], [1, 2]), ('regression: Arabic letter strength', [['ON', 'AL', 'ES', 'L', 'PDI', 'AN', 'NSM', 'LRI', 'ON'], 0], [1, 1]), ('partial-repair probe', [['ON', 'AN', 'RLI', 'RLI', 'R', 'R', 'EN', 'EN', 'L'], 1], [1, None]), ('regression: Arabic letter strength', [['AL', 'R', 'ON', 'AN', 'AL', 'EN', 'L', 'PDI', 'PDI', 'L'], 0], [1, 0]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['L', 'R', 'R', 'NSM', 'L', 'PDI', 'PDI', 'EN'], 1], [0, 0]), ('control layout', [['LRI', 'ES'], 0], [0, None])], [('regression: Arabic letter strength', [['AL', 'PDI'], 1], [1, 0]), ('regression: Arabic letter strength', [['AL', 'RLI', 'PDI', 'WS', 'FSI', 'ON', 'L'], 1], [1, 0]), ('regression: Arabic letter strength', [['NSM', 'AL', 'PDI', 'ON', 'AN', 'WS'], 0], [1, 1]), ('regression: Arabic letter strength', [['ON', 'AL'], 1], [1, 1]), ('FSI content skipped', [['FSI', 'R', 'PDI', 'L'], 1], [0, 3]), ('numbers are not strong', [['EN', 'ON', 'R'], 0], [1, 2]), ('control layout', [['WS'], 0], [0, None]), ('control layout', [['EN'], 0], [0, None])]]\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 toy bidi model over stipulated class labels and integer levels; it is inspired by, but does not claim conformance to, any published algorithm. 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-bidirectional-text-layout-paragraph-direction-arabic-letter-strength","generated_at":"2026-09-29T14:49:52.893595+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Mixed right-to-left and left-to-right text must resolve levels and visual order exactly, or words, numbers and carets land in the wrong place.","repair":"Treat both R and AL as strong right-to-left.","root_cause":"Only class R is treated as a right-to-left strong character; AL is skipped.","sha256":"7c092b15693f46f036f658bf382f2b6d654c48a95f233ac18c11438d664161a7","title":"First-strong paragraph direction: Arabic letter strength · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.632,"exit_code":1,"observations":[{"actual":[0,2],"check":"Arabic letter decides","expected":[1,1],"passed":false},{"actual":[0,null],"check":"regression: Arabic letter strength","expected":[1,0],"passed":false},{"actual":[1,null],"check":"regression: Arabic letter strength","expected":[1,0],"passed":false},{"actual":[1,0],"check":"partial-repair probe","expected":[1,1],"passed":false},{"actual":[1,2],"check":"numbers are not strong","expected":[1,2],"passed":true},{"actual":[1,4],"check":"stray PDI before isolate","expected":[1,4],"passed":true},{"actual":[0,null],"check":"control layout","expected":[0,null],"passed":true},{"actual":[1,1],"check":"control layout","expected":[1,1],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"Arabic letter decides\", \"actual\": [0, 2], \"expected\": [1, 1], \"passed\": false}, {\"check\": \"regression: Arabic letter strength\", \"actual\": [0, null], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"regression: Arabic letter strength\", \"actual\": [1, null], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"partial-repair probe\", \"actual\": [1, 0], \"expected\": [1, 1], \"passed\": false}, {\"check\": \"numbers are not strong\", \"actual\": [1, 2], \"expected\": [1, 2], \"passed\": true}, {\"check\": \"stray PDI before isolate\", \"actual\": [1, 4], \"expected\": [1, 4], \"passed\": true}, {\"check\": \"control layout\", \"actual\": [0, null], \"expected\": [0, null], \"passed\": true}, {\"check\": \"control layout\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.429,"exit_code":1,"observations":[{"actual":[0,2],"check":"Arabic letter decides","expected":[1,1],"passed":false},{"actual":[0,null],"check":"regression: Arabic letter strength","expected":[1,0],"passed":false},{"actual":[1,null],"check":"regression: Arabic letter strength","expected":[1,0],"passed":false},{"actual":[1,1],"check":"partial-repair probe","expected":[1,1],"passed":true},{"actual":[1,2],"check":"numbers are not strong","expected":[1,2],"passed":true},{"actual":[1,4],"check":"stray PDI before isolate","expected":[1,4],"passed":true},{"actual":[0,null],"check":"control layout","expected":[0,null],"passed":true},{"actual":[1,1],"check":"control layout","expected":[1,1],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"Arabic letter decides\", \"actual\": [0, 2], \"expected\": [1, 1], \"passed\": false}, {\"check\": \"regression: Arabic letter strength\", \"actual\": [0, null], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"regression: Arabic letter strength\", \"actual\": [1, null], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"partial-repair probe\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}, {\"check\": \"numbers are not strong\", \"actual\": [1, 2], \"expected\": [1, 2], \"passed\": true}, {\"check\": \"stray PDI before isolate\", \"actual\": [1, 4], \"expected\": [1, 4], \"passed\": true}, {\"check\": \"control layout\", \"actual\": [0, null], \"expected\": [0, null], \"passed\": true}, {\"check\": \"control layout\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.317,"exit_code":0,"observations":[{"actual":[1,1],"check":"Arabic letter decides","expected":[1,1],"passed":true},{"actual":[1,0],"check":"regression: Arabic letter strength","expected":[1,0],"passed":true},{"actual":[1,0],"check":"regression: Arabic letter strength","expected":[1,0],"passed":true},{"actual":[1,1],"check":"partial-repair probe","expected":[1,1],"passed":true},{"actual":[1,2],"check":"numbers are not strong","expected":[1,2],"passed":true},{"actual":[1,4],"check":"stray PDI before isolate","expected":[1,4],"passed":true},{"actual":[0,null],"check":"control layout","expected":[0,null],"passed":true},{"actual":[1,1],"check":"control layout","expected":[1,1],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"Arabic letter decides\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}, {\"check\": \"regression: Arabic letter strength\", \"actual\": [1, 0], \"expected\": [1, 0], \"passed\": true}, {\"check\": \"regression: Arabic letter strength\", \"actual\": [1, 0], \"expected\": [1, 0], \"passed\": true}, {\"check\": \"partial-repair probe\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}, {\"check\": \"numbers are not strong\", \"actual\": [1, 2], \"expected\": [1, 2], \"passed\": true}, {\"check\": \"stray PDI before isolate\", \"actual\": [1, 4], \"expected\": [1, 4], \"passed\": true}, {\"check\": \"control layout\", \"actual\": [0, null], \"expected\": [0, null], \"passed\": true}, {\"check\": \"control layout\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}