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عندى الـ summation هذا N على D دا ناقص واحد بس N على D دايما اللي هو ده المقدرش بيساوي ناقص واحد، مظبوط؟ إذا صار عندى then صار عندى ال summation ناقص واحد بس N على D Phi of D دي بتجسم ال N بساوي ناقص واحد دايما اللي هو ناقص ال summation Phi of D", "tokens": [28814, 15730, 20328, 9640, 43242, 7578, 2423, 39184, 28811, 23758, 426, 15844, 413, 11778, 995, 8717, 995, 4587, 9381, 36764, 24401, 4724, 3794, 426, 15844, 413, 11778, 47302, 15042, 13672, 1829, 31439, 11778, 3224, 9673, 28543, 2288, 8592, 4724, 1829, 3794, 995, 45865, 8717, 995, 4587, 9381, 36764, 24401, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 20328, 9640, 43242, 7578, 550, 20328, 9640, 43242, 7578, 2423, 28811, 8717, 995, 4587, 9381, 36764, 24401, 4724, 3794, 426, 15844, 413, 41435, 295, 413, 11778, 1829, 39894, 7435, 38251, 2423, 426, 4724, 3794, 995, 45865, 8717, 995, 4587, 9381, 36764, 24401, 11778, 47302, 15042, 13672, 1829, 31439, 8717, 995, 4587, 9381, 2423, 28811, 41435, 295, 413], "avg_logprob": 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"word": " واحد،", "probability": 0.783447265625}, {"start": 659.47, "end": 660.51, "word": " مظبوط؟", "probability": 0.910888671875}, {"start": 660.51, "end": 660.71, "word": " إذا", "probability": 0.941162109375}, {"start": 660.71, "end": 660.99, "word": " صار", "probability": 0.984619140625}, {"start": 660.99, "end": 661.51, "word": " عندى", "probability": 0.94775390625}, {"start": 661.51, "end": 662.07, "word": " then", "probability": 0.4228515625}, {"start": 662.07, "end": 663.45, "word": " صار", "probability": 0.8603515625}, {"start": 663.45, "end": 663.71, "word": " عندى", "probability": 0.96923828125}, {"start": 663.71, "end": 663.79, "word": " ال", "probability": 0.64794921875}, {"start": 663.79, "end": 664.33, "word": " summation", "probability": 0.830078125}, {"start": 664.33, "end": 664.87, "word": " ناقص", "probability": 0.9835205078125}, {"start": 664.87, "end": 665.33, "word": " واحد", "probability": 0.9951171875}, {"start": 665.33, "end": 665.59, "word": " بس", 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"end": 672.91, "word": " واحد", "probability": 0.99609375}, {"start": 672.91, "end": 673.73, "word": " دايما", "probability": 0.7887369791666666}, {"start": 673.73, "end": 674.33, "word": " اللي", "probability": 0.77783203125}, {"start": 674.33, "end": 674.47, "word": " هو", "probability": 0.98388671875}, {"start": 674.47, "end": 674.95, "word": " ناقص", "probability": 0.9974365234375}, {"start": 674.95, "end": 675.11, "word": " ال", "probability": 0.94677734375}, {"start": 675.11, "end": 675.63, "word": " summation", "probability": 0.939453125}, {"start": 675.63, "end": 676.11, "word": " Phi", "probability": 0.91650390625}, {"start": 676.11, "end": 676.35, "word": " of", "probability": 0.96728515625}, {"start": 676.35, "end": 676.65, "word": " D", "probability": 0.99609375}], "temperature": 1.0}, {"id": 27, "seek": 70452, "start": 677.18, "end": 704.52, "text": "دي بتجسم الان لكن ال summation 5D دي بتجسم الان ايش بيساوي حسب نظرية سابقة بيساوي هذا بيساوي الان فبصير بيساوي سالر الان لإن احنا أخدنا نظرية في ال section 7-4 بتقول ان ال summation 5D لدي بتجسم الان دايما ايش بتساوي بتساوي الان", "tokens": [3215, 1829, 39894, 7435, 38251, 2423, 7649, 44381, 2423, 28811, 1025, 35, 11778, 1829, 39894, 7435, 38251, 2423, 7649, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 11331, 35457, 8717, 19913, 2288, 10632, 8608, 16758, 28671, 4724, 1829, 3794, 995, 45865, 23758, 4724, 1829, 3794, 995, 45865, 2423, 7649, 6156, 3555, 9381, 13546, 4724, 1829, 3794, 995, 45865, 8608, 6027, 2288, 2423, 7649, 5296, 28814, 1863, 1975, 5016, 8315, 5551, 9778, 3215, 8315, 8717, 19913, 2288, 10632, 8978, 2423, 3541, 1614, 12, 19, 39894, 39648, 16472, 2423, 28811, 1025, 35, 5296, 16254, 39894, 7435, 38251, 2423, 7649, 11778, 47302, 15042, 1975, 1829, 8592, 39894, 3794, 995, 45865, 39894, 3794, 995, 45865, 2423, 7649], "avg_logprob": -0.24191337196450485, "compression_ratio": 2.0706521739130435, "no_speech_prob": 2.562999725341797e-06, "words": [{"start": 677.18, "end": 677.92, "word": "دي", 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"end": 700.04, "word": " لدي", "probability": 0.63134765625}, {"start": 700.04, "end": 700.58, "word": " بتجسم", "probability": 0.91943359375}, {"start": 700.58, "end": 701.16, "word": " الان", "probability": 0.985107421875}, {"start": 701.16, "end": 702.1, "word": " دايما", "probability": 0.8583984375}, {"start": 702.1, "end": 702.4, "word": " ايش", "probability": 0.9021809895833334}, {"start": 702.4, "end": 703.1, "word": " بتساوي", "probability": 0.98046875}, {"start": 703.1, "end": 704.3, "word": " بتساوي", "probability": 0.8900146484375}, {"start": 704.3, "end": 704.52, "word": " الان", "probability": 0.912841796875}], "temperature": 1.0}, {"id": 28, "seek": 72083, "start": 706.23, "end": 720.83, "text": "إذا نادي الجزئية الأولى الان بدنا ناخد if if if if if and is even if and is even", "tokens": [28814, 15730, 8717, 995, 16254, 25724, 11622, 19986, 10632, 16247, 12610, 7578, 2423, 7649, 47525, 8315, 8717, 47283, 3215, 498, 498, 498, 498, 498, 293, 307, 754, 498, 293, 307, 754], 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"text": "الان هذا مادام even معناته صار هذا عبارة عن واحد إذا هذا عبارة عن summation لل 5D لل D بتكسب mean 2K-1 في H في N", "tokens": [6027, 7649, 23758, 3714, 18513, 10943, 754, 20449, 8315, 47395, 20328, 9640, 23758, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 11933, 15730, 23758, 6225, 3555, 9640, 3660, 18871, 28811, 24976, 1025, 35, 24976, 413, 39894, 4117, 35457, 914, 568, 42, 12, 16, 8978, 389, 8978, 426], "avg_logprob": -0.3786569212345367, "compression_ratio": 1.300751879699248, "no_speech_prob": 0.0, "words": [{"start": 971.59, "end": 972.01, "word": "الان", "probability": 0.619140625}, {"start": 972.01, "end": 972.33, "word": " هذا", "probability": 0.467041015625}, {"start": 972.33, "end": 972.71, "word": " مادام", "probability": 0.6082356770833334}, {"start": 972.71, "end": 973.23, "word": " even", "probability": 0.6474609375}, {"start": 973.23, "end": 974.21, "word": " معناته", "probability": 0.8590494791666666}, {"start": 974.21, "end": 974.45, "word": " صار", 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multiplicative function وهدي Odd وهدي Even وما فيش بينهم اي عامل مشتركة لأن هو دي بس Power of Two إذا بيصير عبارة عن Summation Phi of 2 أس K في Phi of D Prime وSummation شغالة على D Prime بتجسمين الان واضح ها؟ طيب خليني أكتب فوق", "tokens": [6027, 7649, 2423, 39184, 8626, 76, 399, 2423, 39184, 41435, 307, 17596, 1166, 2445, 37037, 16254, 43630, 37037, 16254, 2754, 4032, 15042, 8978, 8592, 49374, 16095, 1975, 1829, 6225, 10943, 1211, 37893, 2655, 31747, 3660, 5296, 33456, 31439, 11778, 1829, 4724, 3794, 7086, 295, 4453, 11933, 15730, 4724, 1829, 9381, 13546, 6225, 3555, 9640, 3660, 18871, 8626, 76, 399, 41435, 295, 568, 5551, 3794, 591, 8978, 41435, 295, 413, 9655, 4032, 50, 40879, 399, 13412, 17082, 6027, 3660, 15844, 413, 9655, 39894, 7435, 38251, 9957, 2423, 7649, 4032, 46958, 5016, 8032, 995, 22807, 23032, 1829, 3555, 16490, 1211, 9957, 1829, 5551, 4117, 2655, 3555, 6156, 30543], "avg_logprob": -0.40741822875548744, "compression_ratio": 1.4701195219123506, "no_speech_prob": 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0.76171875}, {"start": 1045.86, "end": 1046.42, "word": " Phi", "probability": 0.912109375}, {"start": 1046.42, "end": 1046.76, "word": " of", "probability": 0.93798828125}, {"start": 1046.76, "end": 1047.02, "word": " D", "probability": 0.9638671875}, {"start": 1047.02, "end": 1047.38, "word": " Prime", "probability": 0.4228515625}, {"start": 1047.38, "end": 1048.0, "word": " وSummation", "probability": 0.643798828125}, {"start": 1048.0, "end": 1048.56, "word": " شغالة", "probability": 0.97705078125}, {"start": 1048.56, "end": 1048.72, "word": " على", "probability": 0.8798828125}, {"start": 1048.72, "end": 1048.92, "word": " D", "probability": 0.98681640625}, {"start": 1048.92, "end": 1049.64, "word": " Prime", "probability": 0.81494140625}, {"start": 1049.64, "end": 1051.12, "word": " بتجسمين", "probability": 0.605072021484375}, {"start": 1051.12, "end": 1052.02, "word": " الان", "probability": 0.707275390625}, {"start": 1052.02, "end": 1053.9, "word": " واضح", "probability": 0.9308268229166666}, {"start": 1053.9, "end": 1055.6, "word": " ها؟", "probability": 0.4812825520833333}, {"start": 1055.6, "end": 1056.52, "word": " طيب", "probability": 0.7755533854166666}, {"start": 1056.52, "end": 1057.54, "word": " خليني", "probability": 0.8341064453125}, {"start": 1057.54, "end": 1057.86, "word": " أكتب", "probability": 0.8802490234375}, {"start": 1057.86, "end": 1058.28, "word": " فوق", "probability": 0.868896484375}], "temperature": 1.0}, {"id": 43, "seek": 108524, "start": 1060.44, "end": 1085.24, "text": "أكمل هنا بصينعين D التكملة ويساوي summation تبعنا هنا هي طلع بيساوي هذا المقدار ناقص هذا المقدار ويساوي ويساوي اتنين أسكي minus واحد في N ناقص", "tokens": [10721, 24793, 1211, 34105, 4724, 9381, 9957, 3615, 9957, 413, 16712, 24793, 37977, 4032, 1829, 3794, 995, 45865, 28811, 6055, 3555, 3615, 8315, 34105, 39896, 23032, 1211, 3615, 4724, 1829, 3794, 995, 45865, 23758, 9673, 28543, 9640, 8717, 995, 4587, 9381, 23758, 9673, 28543, 9640, 4032, 1829, 3794, 995, 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بتقسم الان", "tokens": [2994, 257, 3353, 24922, 293, 257, 8177, 300, 257, 8177, 300, 28811, 2992, 6055, 2288, 21292, 3224, 295, 413, 15844, 6156, 47302, 295, 413, 11778, 1829, 39894, 4587, 38251, 2423, 7649], "avg_logprob": -0.38720702286809683, "compression_ratio": 1.1363636363636365, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1182.7899999999997, "end": 1184.1899999999998, "word": "for", "probability": 0.280517578125}, {"start": 1184.1899999999998, "end": 1185.59, "word": " a", "probability": 0.77001953125}, {"start": 1185.59, "end": 1186.33, "word": " positive", "probability": 0.900390625}, {"start": 1186.33, "end": 1191.79, "word": " integer", "probability": 0.85693359375}, {"start": 1191.79, "end": 1193.79, "word": " and", "probability": 0.70703125}, {"start": 1193.79, "end": 1195.27, "word": " a", "probability": 0.384521484375}, {"start": 1195.27, "end": 1195.59, "word": " proof", "probability": 0.93359375}, {"start": 1195.59, "end": 1196.19, "word": " that", 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"probability": 0.919921875}, {"start": 1206.53, "end": 1207.73, "word": " دي", "probability": 0.6949462890625}, {"start": 1207.73, "end": 1208.25, "word": " بتقسم", "probability": 0.8419596354166666}, {"start": 1208.25, "end": 1208.71, "word": " الان", "probability": 0.664794921875}], "temperature": 1.0}, {"id": 49, "seek": 121352, "start": 1209.56, "end": 1213.52, "text": "بساوي N على Phi of N", "tokens": [3555, 3794, 995, 45865, 426, 15844, 41435, 295, 426], "avg_logprob": -0.6457031428813934, "compression_ratio": 0.7567567567567568, "no_speech_prob": 0.0, "words": [{"start": 1209.56, "end": 1210.16, "word": "بساوي", "probability": 0.46319580078125}, {"start": 1210.16, "end": 1210.62, "word": " N", "probability": 0.46630859375}, {"start": 1210.62, "end": 1211.88, "word": " على", "probability": 0.6748046875}, {"start": 1211.88, "end": 1212.46, "word": " Phi", "probability": 0.1666259765625}, {"start": 1212.46, "end": 1213.28, "word": " of", "probability": 0.67529296875}, {"start": 1213.28, "end": 1213.52, "word": " N", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 50, "seek": 126860, "start": 1242.81, "end": 1268.61, "text": "طيب خلّيني أبدن السؤال نشوف إيش السؤال اللي عندي عندي for a positive integer n بيدنالت بيت ال summation ميوتر بيعديها على 5DD بتكسم N هو بسوء N على مين على Phi of N لو جينا لاحظنا ال N على ال Phi of N ال N على Phi of N is a multiplicative function وسهل اعتبادها", "tokens": [9566, 1829, 3555, 16490, 1211, 11703, 9957, 1829, 5551, 44510, 1863, 21136, 33604, 6027, 8717, 8592, 38688, 11933, 1829, 8592, 21136, 33604, 6027, 13672, 1829, 18871, 16254, 18871, 16254, 337, 257, 3353, 24922, 297, 4724, 25708, 1863, 6027, 2655, 4724, 36081, 2423, 28811, 3714, 1829, 35473, 2288, 4724, 1829, 22488, 1829, 11296, 15844, 1025, 20818, 39894, 4117, 38251, 426, 31439, 4724, 3794, 2407, 38207, 426, 15844, 3714, 9957, 15844, 41435, 295, 426, 45164, 10874, 1829, 8315, 20193, 5016, 19913, 8315, 2423, 426, 15844, 2423, 41435, 295, 426, 2423, 426, 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"probability": 0.9384765625}, {"start": 1258.51, "end": 1258.71, "word": " N", "probability": 0.890625}, {"start": 1258.71, "end": 1259.85, "word": " لو", "probability": 0.91162109375}, {"start": 1259.85, "end": 1260.13, "word": " جينا", "probability": 0.6411946614583334}, {"start": 1260.13, "end": 1260.83, "word": " لاحظنا", "probability": 0.9541015625}, {"start": 1260.83, "end": 1261.95, "word": " ال", "probability": 0.919921875}, {"start": 1261.95, "end": 1262.23, "word": " N", "probability": 0.81103515625}, {"start": 1262.23, "end": 1262.45, "word": " على", "probability": 0.82568359375}, {"start": 1262.45, "end": 1262.61, "word": " ال", "probability": 0.440673828125}, {"start": 1262.61, "end": 1262.87, "word": " Phi", "probability": 0.397705078125}, {"start": 1262.87, "end": 1262.97, "word": " of", "probability": 0.93994140625}, {"start": 1262.97, "end": 1263.27, "word": " N", "probability": 0.9921875}, {"start": 1263.27, "end": 1264.53, "word": " ال", "probability": 0.91015625}, {"start": 1264.53, "end": 1264.81, "word": " N", "probability": 0.94140625}, {"start": 1264.81, "end": 1265.47, "word": " على", "probability": 0.92919921875}, {"start": 1265.47, "end": 1265.75, "word": " Phi", "probability": 0.86669921875}, {"start": 1265.75, "end": 1265.83, "word": " of", "probability": 0.95947265625}, {"start": 1265.83, "end": 1266.03, "word": " N", "probability": 0.9931640625}, {"start": 1266.03, "end": 1266.25, "word": " is", "probability": 0.94189453125}, {"start": 1266.25, "end": 1266.41, "word": " a", "probability": 0.91943359375}, {"start": 1266.41, "end": 1267.13, "word": " multiplicative", "probability": 0.9365234375}, {"start": 1267.13, "end": 1267.65, "word": " function", "probability": 0.96923828125}, {"start": 1267.65, "end": 1268.05, "word": " وسهل", "probability": 0.7748209635416666}, {"start": 1268.05, "end": 1268.61, "word": " اعتبادها", "probability": 0.640625}], "temperature": 1.0}, {"id": 51, "seek": 129823, "start": 1269.25, "end": 1298.23, "text": "و لو جينا طلعنا لهذا اللي جوا ال summation اللي هو اللي مُ multiplicative و ال file مُ multiplicative إذا كل هذا على بعض إيش ماله مُ multiplicative و مادام هذا مُ multiplicative إذا كل على بعض إيش ماله مُ multiplicative إذا ال multiplicative بشجعني أن أروح باتجاه الإثبات بس ل prime b to the alpha و بيصير حصل الدرب هو بحصل ليه كل اللي بديها", "tokens": [2407, 45164, 10874, 1829, 8315, 23032, 1211, 3615, 8315, 46740, 15730, 13672, 1829, 10874, 14407, 2423, 28811, 13672, 1829, 31439, 13672, 1829, 3714, 10859, 17596, 1166, 4032, 2423, 3991, 3714, 10859, 17596, 1166, 11933, 15730, 28242, 23758, 15844, 45030, 11242, 11933, 1829, 8592, 3714, 6027, 3224, 3714, 10859, 17596, 1166, 4032, 3714, 18513, 10943, 23758, 3714, 10859, 17596, 1166, 11933, 15730, 28242, 15844, 45030, 11242, 11933, 1829, 8592, 3714, 6027, 3224, 3714, 10859, 17596, 1166, 11933, 15730, 2423, 17596, 1166, 4724, 8592, 7435, 3615, 22653, 14739, 5551, 32887, 5016, 4724, 9307, 7435, 40294, 33688, 12984, 3555, 9307, 4724, 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ال", "probability": 0.61572265625}, {"start": 1317.27, "end": 1317.27, "word": " ال", "probability": 0.5966796875}, {"start": 1317.27, "end": 1317.27, "word": " ال", "probability": 0.60986328125}, {"start": 1317.27, "end": 1317.27, "word": " ال", "probability": 0.5966796875}, {"start": 1317.27, "end": 1317.65, "word": " ال", "probability": 0.52490234375}, {"start": 1317.65, "end": 1317.65, "word": " ال", "probability": 0.60498046875}, {"start": 1317.65, "end": 1317.65, "word": " ال", "probability": 0.3212890625}, {"start": 1317.65, "end": 1317.65, "word": " ال", "probability": 0.262451171875}, {"start": 1317.65, "end": 1317.65, "word": " ال", "probability": 0.464111328125}, {"start": 1317.65, "end": 1317.65, "word": " ال", "probability": 0.274169921875}, {"start": 1317.65, "end": 1317.65, "word": " ال", "probability": 0.51171875}], "temperature": 1.0}, {"id": 53, "seek": 134202, "start": 1321.58, "end": 1342.02, "text": "to see that summation mu تربيع of D على فاي of D دي بتكسب الواحد 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"probability": 0.315673828125}, {"start": 1365.27, "end": 1365.75, "word": " 1", "probability": 0.765625}, {"start": 1365.75, "end": 1366.61, "word": " لعند", "probability": 0.7122395833333334}, {"start": 1366.61, "end": 1367.27, "word": " PR", "probability": 0.255615234375}, {"start": 1367.27, "end": 1368.05, "word": " Alpha", "probability": 0.9189453125}, {"start": 1368.05, "end": 1368.61, "word": " R", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 55, "seek": 139725, "start": 1370.27, "end": 1397.25, "text": "P1 لعند PR are distinct primes والألفة I أكبر أو يساوي واحد لكل I من واحد لعند ال R وال R أكبر أو يساوي واحد طيب الان let let F of N بساوي ال summation", "tokens": [47, 16, 5296, 3615, 41260, 11568, 366, 10644, 582, 1532, 16070, 10721, 46538, 3660, 286, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401, 5296, 28820, 286, 9154, 36764, 24401, 5296, 3615, 41260, 2423, 497, 16070, 497, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401, 23032, 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" أكبر", "probability": 0.9827473958333334}, {"start": 1387.13, "end": 1387.37, "word": " أو", "probability": 0.90576171875}, {"start": 1387.37, "end": 1387.87, "word": " يساوي", "probability": 0.97021484375}, {"start": 1387.87, "end": 1388.57, "word": " واحد", "probability": 0.98876953125}, {"start": 1388.57, "end": 1390.17, "word": " طيب", "probability": 0.83837890625}, {"start": 1390.17, "end": 1391.51, "word": " الان", "probability": 0.562744140625}, {"start": 1391.51, "end": 1392.07, "word": " let", "probability": 0.8046875}, {"start": 1392.07, "end": 1393.75, "word": " let", "probability": 0.442626953125}, {"start": 1393.75, "end": 1394.49, "word": " F", "probability": 0.5869140625}, {"start": 1394.49, "end": 1394.75, "word": " of", "probability": 0.54931640625}, {"start": 1394.75, "end": 1395.13, "word": " N", "probability": 0.8896484375}, {"start": 1395.13, "end": 1396.53, "word": " بساوي", "probability": 0.862548828125}, {"start": 1396.53, "end": 1396.67, "word": " ال", 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"probability": 0.7205810546875}, {"start": 1678.18, "end": 1678.48, "word": " عندي", "probability": 0.62939453125}, {"start": 1678.48, "end": 1678.84, "word": " الان", "probability": 0.622802734375}, {"start": 1678.84, "end": 1680.02, "word": " f", "probability": 0.38916015625}, {"start": 1680.02, "end": 1680.46, "word": " of", "probability": 0.67431640625}, {"start": 1680.46, "end": 1681.22, "word": " bi", "probability": 0.59423828125}, {"start": 1681.22, "end": 1682.08, "word": " alpha", "probability": 0.0706787109375}, {"start": 1682.08, "end": 1682.78, "word": " bi", "probability": 0.50830078125}, {"start": 1682.78, "end": 1683.76, "word": " بسوى", "probability": 0.66943359375}, {"start": 1683.76, "end": 1684.34, "word": " bi", "probability": 0.783203125}, {"start": 1684.34, "end": 1684.64, "word": " على", "probability": 0.64794921875}, {"start": 1684.64, "end": 1685.32, "word": " bi", "probability": 0.87158203125}, {"start": 1685.32, "end": 1685.9, "word": " نقص", "probability": 0.8191731770833334}, {"start": 1685.9, "end": 1686.26, "word": " واحد", "probability": 0.9755859375}, {"start": 1686.26, "end": 1686.74, "word": " هذا", "probability": 0.71484375}, {"start": 1686.74, "end": 1687.34, "word": " تلاتة", "probability": 0.9149169921875}, {"start": 1687.34, "end": 1688.82, "word": " الان", "probability": 0.6868896484375}, {"start": 1688.82, "end": 1690.64, "word": " من", "probability": 0.97314453125}, {"start": 1690.64, "end": 1691.44, "word": " اللي", "probability": 0.883544921875}, {"start": 1691.44, "end": 1691.74, "word": " هو", "probability": 0.98291015625}, {"start": 1691.74, "end": 1692.16, "word": " اتنين", "probability": 0.9107666015625}, {"start": 1692.16, "end": 1692.3, "word": " و", "probability": 0.748046875}, {"start": 1692.3, "end": 1693.7, "word": " تلاتة", "probability": 0.9073486328125}, {"start": 1693.7, "end": 1694.46, "word": " from", "probability": 0.8642578125}, {"start": 1694.46, "end": 1697.02, "word": " from", "probability": 0.59033203125}, {"start": 1697.02, "end": 1700.86, "word": " اتنين", "probability": 0.937744140625}, {"start": 1700.86, "end": 1702.12, "word": " and", "probability": 0.89453125}, {"start": 1702.12, "end": 1703.1, "word": " تلاتة", "probability": 0.986083984375}, {"start": 1703.1, "end": 1704.38, "word": " we", "probability": 0.79736328125}, {"start": 1704.38, "end": 1705.3, "word": " get", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 68, "seek": 172681, "start": 1706.15, "end": 1726.81, "text": "we get ماذا؟ we get F of N F of N بسوّله product A حصل الدرب ل B I على B I ناقص واحد I من عند واحد لعند مين لعند R", "tokens": [826, 483, 3714, 45636, 995, 22807, 321, 483, 479, 295, 426, 479, 295, 426, 4724, 3794, 2407, 11703, 43761, 1674, 316, 11331, 36520, 32748, 25513, 5296, 363, 286, 15844, 363, 286, 8717, 995, 4587, 9381, 36764, 24401, 286, 9154, 43242, 36764, 24401, 5296, 3615, 41260, 3714, 9957, 5296, 3615, 41260, 497], "avg_logprob": -0.3485576934539355, 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"end": 1712.27, "word": " بسوّله", "probability": 0.61484375}, {"start": 1712.27, "end": 1713.05, "word": " product", "probability": 0.693359375}, {"start": 1713.05, "end": 1714.55, "word": " A", "probability": 0.359375}, {"start": 1714.55, "end": 1715.23, "word": " حصل", "probability": 0.765380859375}, {"start": 1715.23, "end": 1715.73, "word": " الدرب", "probability": 0.469970703125}, {"start": 1715.73, "end": 1716.69, "word": " ل", "probability": 0.814453125}, {"start": 1716.69, "end": 1716.95, "word": " B", "probability": 0.15185546875}, {"start": 1716.95, "end": 1717.63, "word": " I", "probability": 0.69287109375}, {"start": 1717.63, "end": 1719.53, "word": " على", "probability": 0.8115234375}, {"start": 1719.53, "end": 1720.01, "word": " B", "probability": 0.7861328125}, {"start": 1720.01, "end": 1720.57, "word": " I", "probability": 0.9638671875}, {"start": 1720.57, "end": 1721.67, "word": " ناقص", "probability": 0.884521484375}, {"start": 1721.67, "end": 1722.33, "word": " واحد", "probability": 0.978271484375}, {"start": 1722.33, "end": 1723.29, "word": " I", "probability": 0.88525390625}, {"start": 1723.29, "end": 1723.55, "word": " من", "probability": 0.98486328125}, {"start": 1723.55, "end": 1723.87, "word": " عند", "probability": 0.98681640625}, {"start": 1723.87, "end": 1724.29, "word": " واحد", "probability": 0.95263671875}, {"start": 1724.29, "end": 1724.65, "word": " لعند", "probability": 0.8675130208333334}, {"start": 1724.65, "end": 1725.15, "word": " مين", "probability": 0.670166015625}, {"start": 1725.15, "end": 1726.43, "word": " لعند", "probability": 0.9000651041666666}, {"start": 1726.43, "end": 1726.81, "word": " R", "probability": 0.892578125}], "temperature": 1.0}, {"id": 69, "seek": 175574, "start": 1728.12, "end": 1755.74, "text": "معايا اه الان بس اضرب لفوق عشان اقول لك ايه اضرب لفوق في بي اي اص الف اي ماقص واحد و تحت في بي اي اص الف اي ماقص واحد في نفس النقطة اضربت و يساوي ال product لأ ال بي اي اص الف اي معايا على اللي هو", 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R اللي فوق هذه مين هي أصلا؟ هذه مين هي؟ هي عبارة عن الـ N", "tokens": [6027, 39184, 22005, 5296, 39184, 13007, 5551, 10859, 3794, 20588, 286, 8717, 995, 4587, 9381, 36764, 24401, 3714, 11242, 32887, 3555, 8978, 2423, 39184, 13007, 8717, 995, 4587, 9381, 36764, 24401, 286, 9154, 36764, 24401, 5296, 3615, 41260, 497, 4032, 286, 9154, 43242, 36764, 24401, 5296, 3615, 41260, 497, 13672, 1829, 6156, 30543, 29538, 3714, 9957, 39896, 5551, 9381, 15040, 22807, 29538, 3714, 9957, 39896, 22807, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 426], "avg_logprob": -0.1772203874823294, "compression_ratio": 1.6666666666666667, "no_speech_prob": 2.6226043701171875e-06, "words": [{"start": 1757.07, "end": 1757.45, "word": "الـ", "probability": 0.59765625}, {"start": 1757.45, "end": 1758.15, "word": " Product", "probability": 0.70458984375}, {"start": 1758.15, "end": 1760.53, "word": " لـ", "probability": 0.71728515625}, {"start": 1760.53, "end": 1761.53, "word": " Bi", "probability": 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"word": " واحد", "probability": 0.9951171875}, {"start": 2217.71, "end": 2219.05, "word": " proof", "probability": 0.470947265625}, {"start": 2219.05, "end": 2224.75, "word": " الملاحظة", "probability": 0.95859375}, {"start": 2224.75, "end": 2225.29, "word": " الأولى", "probability": 0.88525390625}], "temperature": 1.0}, {"id": 87, "seek": 224185, "start": 2226.37, "end": 2241.85, "text": "إنه عندي الـ Phi is multiplicative و ال identity function multiplicative إذا D في Phi of D أشمالها is multiplicative بناء عليه لأن since اللي هو N في Phi of N", "tokens": [28814, 1863, 3224, 18871, 16254, 2423, 39184, 41435, 307, 17596, 1166, 4032, 2423, 6575, 2445, 17596, 1166, 11933, 15730, 413, 8978, 41435, 295, 413, 5551, 8592, 2304, 6027, 11296, 307, 17596, 1166, 44945, 16606, 47356, 5296, 33456, 1670, 13672, 1829, 31439, 426, 8978, 41435, 295, 426], "avg_logprob": -0.30535240376249273, "compression_ratio": 1.3835616438356164, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 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"probability": 0.927734375}, {"start": 3022.27, "end": 3022.49, "word": " يعني", "probability": 0.768798828125}, {"start": 3022.49, "end": 3022.89, "word": " تلاتة", "probability": 0.96875}, {"start": 3022.89, "end": 3023.39, "word": " تربيع", "probability": 0.931884765625}, {"start": 3023.39, "end": 3023.95, "word": " بساوي", "probability": 0.950927734375}, {"start": 3023.95, "end": 3024.77, "word": " اللي", "probability": 0.924072265625}, {"start": 3024.77, "end": 3024.89, "word": " هو", "probability": 0.96044921875}, {"start": 3024.89, "end": 3025.19, "word": " بتعرف", "probability": 0.9462890625}, {"start": 3025.19, "end": 3025.41, "word": " كيف", "probability": 0.73046875}, {"start": 3025.41, "end": 3025.67, "word": " نوجد", "probability": 0.8748372395833334}, {"start": 3025.67, "end": 3026.01, "word": " Tau", "probability": 0.799560546875}, {"start": 3026.01, "end": 3026.33, "word": " of", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 116, "seek": 305528, "start": 3027.34, "end": 3055.28, "text": "Tau of B أُس Alpha بساوي اللي هو Alpha ثائد واحد عدد ال divisors دمية لل B Alpha بيصير عندي Tau تلاتة تربيع عيش بساوي اتنين زائد واحد ويساوي تلاتة اذا واضح انه في حالة الان بتساوي تلاتة Tau of N تربيع بساوي الان conversely conversely", "tokens": [51, 1459, 295, 363, 5551, 10859, 3794, 20588, 4724, 3794, 995, 45865, 13672, 1829, 31439, 20588, 38637, 16373, 3215, 36764, 24401, 6225, 3215, 3215, 2423, 25974, 830, 11778, 2304, 10632, 24976, 363, 20588, 4724, 1829, 9381, 13546, 18871, 16254, 314, 1459, 6055, 1211, 9307, 3660, 6055, 2288, 21292, 3615, 6225, 1829, 8592, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 36764, 24401, 4032, 1829, 3794, 995, 45865, 6055, 1211, 9307, 3660, 1975, 15730, 4032, 46958, 5016, 16472, 3224, 8978, 11331, 6027, 3660, 2423, 7649, 39894, 3794, 995, 45865, 6055, 1211, 9307, 3660, 314, 1459, 295, 426, 6055, 2288, 21292, 3615, 4724, 3794, 995, 45865, 2423, 7649, 2615, 736, 2615, 736], "avg_logprob": -0.28618421915330383, "compression_ratio": 1.7745098039215685, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3027.34, "end": 3027.88, "word": "Tau", "probability": 0.5826416015625}, {"start": 3027.88, "end": 3028.58, "word": " of", "probability": 0.77685546875}, {"start": 3028.58, "end": 3028.82, "word": " B", "probability": 0.5517578125}, {"start": 3028.82, "end": 3029.08, "word": " أُس", "probability": 0.4937337239583333}, {"start": 3029.08, "end": 3029.48, "word": " Alpha", "probability": 0.55615234375}, {"start": 3029.48, "end": 3030.76, "word": " بساوي", "probability": 0.7042236328125}, {"start": 3030.76, "end": 3030.94, "word": " اللي", "probability": 0.71240234375}, {"start": 3030.94, "end": 3031.22, "word": " هو", "probability": 0.9814453125}, {"start": 3031.22, "end": 3031.76, "word": " Alpha", "probability": 0.87451171875}, {"start": 3031.76, "end": 3032.84, "word": " ثائد", "probability": 0.5664876302083334}, {"start": 3032.84, "end": 3033.72, "word": " واحد", "probability": 0.923583984375}, {"start": 3033.72, "end": 3034.1, "word": " عدد", "probability": 0.9205729166666666}, {"start": 3034.1, "end": 3034.24, "word": " ال", "probability": 0.91162109375}, {"start": 3034.24, "end": 3034.78, "word": " divisors", "probability": 0.6475830078125}, {"start": 3034.78, "end": 3035.24, "word": " دمية", "probability": 0.4676106770833333}, {"start": 3035.24, "end": 3036.0, "word": " لل", "probability": 0.43359375}, {"start": 3036.0, "end": 3036.26, "word": " B", "probability": 0.431396484375}, {"start": 3036.26, "end": 3036.74, "word": " Alpha", "probability": 0.748046875}, {"start": 3036.74, "end": 3037.98, "word": " بيصير", "probability": 0.8524169921875}, {"start": 3037.98, "end": 3038.22, "word": " عندي", "probability": 0.796630859375}, {"start": 3038.22, "end": 3038.54, "word": " Tau", "probability": 0.73974609375}, {"start": 3038.54, "end": 3038.94, "word": " تلاتة", "probability": 0.64117431640625}, {"start": 3038.94, "end": 3039.26, "word": " تربيع", "probability": 0.8807373046875}, {"start": 3039.26, "end": 3039.44, "word": " عيش", "probability": 0.568603515625}, {"start": 3039.44, "end": 3039.98, "word": " بساوي", "probability": 0.8580322265625}, {"start": 3039.98, "end": 3040.84, "word": " اتنين", "probability": 0.9036865234375}, {"start": 3040.84, "end": 3041.88, "word": " زائد", "probability": 0.8792317708333334}, {"start": 3041.88, "end": 3042.46, "word": " واحد", "probability": 0.984619140625}, {"start": 3042.46, "end": 3043.34, "word": " ويساوي", "probability": 0.88408203125}, {"start": 3043.34, "end": 3044.16, "word": " تلاتة", "probability": 0.972412109375}, {"start": 3044.16, "end": 3044.88, "word": " اذا", "probability": 0.56756591796875}, {"start": 3044.88, "end": 3045.98, "word": " واضح", "probability": 0.9650065104166666}, {"start": 3045.98, "end": 3046.32, "word": " انه", "probability": 0.875732421875}, {"start": 3046.32, "end": 3046.42, "word": " في", "probability": 0.91015625}, {"start": 3046.42, "end": 3046.76, "word": " حالة", "probability": 0.9788411458333334}, {"start": 3046.76, "end": 3047.0, "word": " الان", "probability": 0.609619140625}, {"start": 3047.0, "end": 3047.48, "word": " بتساوي", "probability": 0.95654296875}, {"start": 3047.48, "end": 3048.2, "word": " تلاتة", "probability": 0.98681640625}, {"start": 3048.2, "end": 3048.98, "word": " Tau", "probability": 0.84326171875}, {"start": 3048.98, "end": 3049.34, "word": " of", "probability": 0.904296875}, {"start": 3049.34, "end": 3049.68, "word": " N", "probability": 0.2529296875}, {"start": 3049.68, "end": 3050.3, "word": " تربيع", "probability": 0.9293212890625}, {"start": 3050.3, "end": 3050.96, "word": " بساوي", "probability": 0.94384765625}, {"start": 3050.96, "end": 3051.98, "word": " الان", "probability": 0.83642578125}, {"start": 3051.98, "end": 3053.42, "word": " conversely", "probability": 0.60614013671875}, {"start": 3053.42, "end": 3055.28, "word": " conversely", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 117, "seek": 308384, "start": 3058.18, "end": 3083.84, "text": "Suppose that Tau of N تربيع بساوي N باشي لإن ما أعطيك ال N إيه اشمله three three او square three integer لإن since N أكبر من واحد is square او the square three integer", "tokens": [50, 10504, 541, 300, 314, 1459, 295, 426, 6055, 2288, 21292, 3615, 4724, 3794, 995, 45865, 426, 4724, 33599, 1829, 5296, 28814, 1863, 19446, 5551, 3615, 9566, 1829, 4117, 2423, 426, 11933, 1829, 3224, 1975, 8592, 42213, 3224, 1045, 1045, 1975, 2407, 3732, 1045, 24922, 5296, 28814, 1863, 1670, 426, 5551, 4117, 26890, 9154, 36764, 24401, 307, 3732, 1975, 2407, 264, 3732, 1045, 24922], "avg_logprob": -0.3858173076923077, "compression_ratio": 1.4155844155844155, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3058.1800000000003, "end": 3059.3, "word": "Suppose", "probability": 0.6521199544270834}, {"start": 3059.3, "end": 3060.42, "word": " that", "probability": 0.7265625}, {"start": 3060.42, "end": 3061.86, "word": " Tau", "probability": 0.42626953125}, {"start": 3061.86, "end": 3061.98, "word": " of", "probability": 0.6923828125}, {"start": 3061.98, "end": 3062.26, "word": " N", "probability": 0.85107421875}, {"start": 3062.26, "end": 3063.02, "word": " تربيع", "probability": 0.8819580078125}, {"start": 3063.02, "end": 3063.56, "word": " بساوي", "probability": 0.58538818359375}, {"start": 3063.56, "end": 3064.04, "word": " N", "probability": 0.880859375}, {"start": 3064.04, "end": 3065.46, "word": " باشي", "probability": 0.5717366536458334}, {"start": 3065.46, "end": 3066.24, "word": " لإن", "probability": 0.701904296875}, {"start": 3066.24, "end": 3066.32, "word": " ما", "probability": 0.86962890625}, {"start": 3066.32, "end": 3066.66, "word": " أعطيك", "probability": 0.9302734375}, {"start": 3066.66, "end": 3066.8, "word": " ال", "probability": 0.90771484375}, {"start": 3066.8, "end": 3066.96, "word": " N", "probability": 0.50634765625}, {"start": 3066.96, "end": 3067.16, "word": " إيه", "probability": 0.796875}, {"start": 3067.16, "end": 3067.72, "word": " اشمله", "probability": 0.64776611328125}, {"start": 3067.72, "end": 3068.56, "word": " three", "probability": 0.1212158203125}, {"start": 3068.56, "end": 3069.22, "word": " three", "probability": 0.41064453125}, {"start": 3069.22, "end": 3069.92, "word": " او", "probability": 0.7401123046875}, {"start": 3069.92, "end": 3070.26, "word": " square", "probability": 0.5810546875}, {"start": 3070.26, "end": 3070.68, "word": " three", "probability": 0.84814453125}, {"start": 3070.68, "end": 3071.32, "word": " integer", "probability": 0.83203125}, {"start": 3071.32, "end": 3072.16, "word": " لإن", "probability": 0.9208984375}, {"start": 3072.16, "end": 3072.7, "word": " since", "probability": 0.57421875}, {"start": 3072.7, "end": 3074.7, "word": " N", "probability": 0.8173828125}, {"start": 3074.7, "end": 3075.1, "word": " أكبر", "probability": 0.9298502604166666}, {"start": 3075.1, "end": 3075.24, "word": " من", "probability": 0.990234375}, {"start": 3075.24, "end": 3075.68, "word": " واحد", "probability": 0.931640625}, {"start": 3075.68, "end": 3076.1, "word": " is", "probability": 0.88916015625}, {"start": 3076.1, "end": 3077.72, "word": " square", "probability": 0.447509765625}, {"start": 3077.72, "end": 3079.36, "word": " او", "probability": 0.62744140625}, {"start": 3079.36, "end": 3079.56, "word": " the", "probability": 0.50048828125}, {"start": 3079.56, "end": 3080.24, "word": " square", "probability": 0.84521484375}, {"start": 3080.24, "end": 3081.08, "word": " three", "probability": 0.86962890625}, {"start": 3081.08, "end": 3083.84, "word": " integer", "probability": 0.873046875}], "temperature": 1.0}, {"id": 118, "seek": 310709, "start": 3085.25, "end": 3107.09, "text": "إذا مافيش فيه أي مربع كامل، then N can be written as B1 لعندي R where B1 لعندي R are distinct primes لأنه في Ray Square", "tokens": [28814, 15730, 19446, 41185, 8592, 8978, 3224, 36632, 3714, 25513, 3615, 9122, 10943, 1211, 12399, 550, 426, 393, 312, 3720, 382, 363, 16, 5296, 3615, 1863, 16254, 497, 689, 363, 16, 5296, 3615, 1863, 16254, 497, 366, 10644, 582, 1532, 5296, 33456, 3224, 8978, 10883, 16463], "avg_logprob": -0.33128325228995464, "compression_ratio": 1.162962962962963, "no_speech_prob": 0.0, "words": [{"start": 3085.25, "end": 3085.59, "word": "إذا", "probability": 0.873046875}, {"start": 3085.59, "end": 3085.99, "word": " مافيش", "probability": 0.8483072916666666}, {"start": 3085.99, "end": 3086.27, "word": " فيه", "probability": 0.8798828125}, {"start": 3086.27, "end": 3086.43, "word": " أي", "probability": 0.80712890625}, {"start": 3086.43, "end": 3086.87, "word": " مربع", "probability": 0.900390625}, {"start": 3086.87, "end": 3087.93, "word": " كامل،", "probability": 0.862548828125}, {"start": 3087.93, "end": 3088.27, "word": " then", "probability": 0.52294921875}, {"start": 3088.27, "end": 3088.61, "word": " N", "probability": 0.1259765625}, {"start": 3088.61, "end": 3088.97, "word": " can", "probability": 0.931640625}, {"start": 3088.97, "end": 3089.27, "word": " be", "probability": 0.9521484375}, {"start": 3089.27, "end": 3089.71, "word": " written", "probability": 0.9208984375}, {"start": 3089.71, "end": 3090.51, "word": " as", "probability": 0.96240234375}, {"start": 3090.51, "end": 3091.81, "word": " B1", "probability": 0.5377197265625}, {"start": 3091.81, "end": 3092.81, "word": " لعندي", "probability": 0.58673095703125}, {"start": 3092.81, "end": 3093.49, "word": " R", "probability": 0.4560546875}, {"start": 3093.49, "end": 3094.75, "word": " where", "probability": 0.634765625}, {"start": 3094.75, "end": 3095.97, "word": " B1", "probability": 0.96923828125}, {"start": 3095.97, "end": 3096.53, "word": " لعندي", "probability": 0.9561767578125}, {"start": 3096.53, "end": 3097.29, "word": " R", "probability": 0.97998046875}, {"start": 3097.29, "end": 3099.05, "word": " are", "probability": 0.86328125}, {"start": 3099.05, "end": 3102.31, "word": " distinct", "probability": 0.93212890625}, {"start": 3102.31, "end": 3104.35, "word": " primes", "probability": 0.656982421875}, {"start": 3104.35, "end": 3105.93, "word": " لأنه", "probability": 0.6517740885416666}, {"start": 3105.93, "end": 3106.03, "word": " في", "probability": 0.81982421875}, {"start": 3106.03, "end": 3106.31, "word": " Ray", "probability": 0.47509765625}, {"start": 3106.31, "end": 3107.09, "word": " Square", "probability": 0.22705078125}], "temperature": 1.0}, {"id": 119, "seek": 313698, "start": 3108.22, "end": 3136.98, "text": "أو square free مافيش فيه أي مربع كامل يعني مانعته أنه الأسس اللي عندي هنا بس واحد وال بي لعند واحد لعند ال بي ار اللي هو distinct primes هذا يعني then tau of n تربيع معطيني ايه ايه ايش بيساوي n تساوي tau of n تربيع هذا مقطع مين ال n", "tokens": [10721, 2407, 3732, 1737, 19446, 41185, 8592, 8978, 3224, 36632, 3714, 25513, 3615, 9122, 10943, 1211, 37495, 22653, 3714, 7649, 34268, 3224, 14739, 3224, 16247, 3794, 3794, 13672, 1829, 18871, 16254, 34105, 4724, 3794, 36764, 24401, 16070, 4724, 1829, 5296, 3615, 41260, 36764, 24401, 5296, 3615, 41260, 2423, 4724, 1829, 1975, 2288, 13672, 1829, 31439, 10644, 2886, 279, 23758, 37495, 22653, 550, 17842, 295, 297, 6055, 2288, 21292, 3615, 20449, 9566, 9957, 1829, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 297, 6055, 3794, 995, 45865, 17842, 295, 297, 6055, 2288, 21292, 3615, 23758, 3714, 47432, 3615, 3714, 9957, 2423, 297], "avg_logprob": -0.3188657459837419, "compression_ratio": 1.8009708737864079, "no_speech_prob": 2.7418136596679688e-06, "words": [{"start": 3108.22, "end": 3108.48, "word": "أو", "probability": 0.6328125}, {"start": 3108.48, "end": 3108.76, "word": " square", "probability": 0.509765625}, {"start": 3108.76, "end": 3109.12, "word": " free", "probability": 0.4033203125}, {"start": 3109.12, "end": 3109.56, "word": " مافيش", "probability": 0.757568359375}, {"start": 3109.56, "end": 3109.8, "word": " فيه", "probability": 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