diff --git "a/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.json" "b/PL9fwy3NUQKwb1GEXKToPBRkVqqPyEiz9Z/HP5sWDWTp34_raw.json"
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+{"segments": [{"id": 1, "seek": 4795, "start": 19.35, "end": 47.95, "text": "بسم الله الرحمن الرحيم محاضرة رقم 27 وهي عبارة عن مناقشة لـ Chapter 6 سنناقش اليوم موضوعين الموضوع الأول اللي هو number and sum of divisors والموضوع التاني اللي هو Mobius inversion formula نبدأ ب 6 واحد اللي هو number and sum of divisors", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 3714, 5016, 46958, 25720, 12602, 4587, 2304, 7634, 37037, 1829, 6225, 3555, 9640, 3660, 18871, 3714, 8315, 4587, 8592, 3660, 5296, 39184, 18874, 1386, 8608, 1863, 8315, 4587, 8592, 45595, 20498, 3714, 2407, 11242, 45367, 9957, 9673, 2407, 11242, 45367, 16247, 12610, 13672, 1829, 31439, 1230, 293, 2408, 295, 25974, 830, 4032, 45340, 2407, 11242, 45367, 16712, 7649, 1829, 13672, 1829, 31439, 37920, 4872, 43576, 8513, 8717, 44510, 10721, 4724, 1386, 36764, 24401, 13672, 1829, 31439, 1230, 293, 2408, 295, 25974, 830], "avg_logprob": -0.14121942691828893, "compression_ratio": 1.7019230769230769, 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أنه ممكن ينقص لأنه ممكن يكون اللي هو الـD والأن ع دي في حالة إيش بيساوي .. بيساوي واحدة في النهاية اللي هو دائما توف أن أظل سوى اتنين جدر الأن اللي بعده السؤال اللي بعده", "tokens": [6027, 20292, 31439, 25724, 3215, 2288, 16247, 1863, 6156, 3555, 9381, 13546, 15844, 16247, 4117, 2655, 2288, 15844, 16247, 4117, 2655, 2288, 13672, 1829, 31439, 10874, 3215, 33599, 6225, 3215, 3215, 2423, 39184, 25974, 830, 1975, 2655, 1863, 9957, 10874, 3215, 2288, 16247, 1863, 20449, 14739, 3224, 3714, 43020, 7251, 1863, 4587, 9381, 5296, 33456, 3224, 3714, 43020, 7251, 30544, 13672, 1829, 31439, 2423, 39184, 35, 16070, 10721, 1863, 6225, 11778, 1829, 8978, 11331, 6027, 3660, 11933, 1829, 8592, 4724, 1829, 3794, 995, 45865, 4386, 4724, 1829, 3794, 995, 45865, 36764, 24401, 3660, 8978, 28239, 11296, 10632, 13672, 1829, 31439, 11778, 16373, 15042, 6055, 38688, 14739, 5551, 19913, 1211, 8608, 2407, 7578, 1975, 2655, 1863, 9957, 10874, 3215, 2288, 16247, 1863, 13672, 1829, 39182, 3224, 21136, 33604, 6027, 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" برايم", "probability": 0.8375651041666666}], "temperature": 1.0}, {"id": 21, "seek": 56900, "start": 557.24, "end": 569.0, "text": "وبعد ما أحسب للـ prime بحسب لمين للـ function نفسها خصوصاً إذا كانت الـ function is multiplicative بتصير الأمور سهلة نشوف أشي المقصود", "tokens": [37746, 22488, 19446, 5551, 5016, 35457, 24976, 39184, 5835, 4724, 5016, 35457, 32767, 9957, 24976, 39184, 2445, 8717, 36178, 11296, 16490, 9381, 2407, 9381, 995, 14111, 11933, 15730, 25961, 2655, 2423, 39184, 2445, 307, 17596, 1166, 39894, 9381, 13546, 16247, 2304, 13063, 8608, 3224, 37977, 8717, 8592, 38688, 5551, 8592, 1829, 9673, 4587, 9381, 23328], "avg_logprob": -0.2783203178218433, "compression_ratio": 1.3529411764705883, "no_speech_prob": 0.0, "words": [{"start": 557.24, "end": 557.96, "word": "وبعد", "probability": 0.716796875}, {"start": 557.96, "end": 558.08, "word": " ما", "probability": 0.28125}, {"start": 558.08, "end": 558.34, "word": " أحسب", "probability": 0.7572428385416666}, {"start": 558.34, 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"word": " or", "probability": 0.681640625}, {"start": 884.64, "end": 885.86, "word": " twice", "probability": 0.9619140625}, {"start": 885.86, "end": 886.34, "word": " perfect", "probability": 0.9091796875}, {"start": 886.34, "end": 887.02, "word": " square", "probability": 0.8876953125}], "temperature": 1.0}, {"id": 34, "seek": 91749, "start": 887.81, "end": 917.49, "text": "يعني بيقول لي أن الـ N يا هتكون على صورة N تربيع اللي هي perfect square أو اتنين N تربيع for some M ثمان مرة السؤال السؤال اللي بيقول لي prove that sigma of N is odd if and only if N is a perfect square or twice perfect square واضح؟ نيجي البرهن", "tokens": [40228, 22653, 4724, 1829, 39648, 32239, 14739, 2423, 39184, 426, 35186, 8032, 2655, 30544, 15844, 20328, 13063, 3660, 426, 6055, 2288, 21292, 3615, 13672, 1829, 39896, 2176, 3732, 34051, 1975, 2655, 1863, 9957, 426, 6055, 2288, 21292, 3615, 337, 512, 376, 38637, 2304, 7649, 3714, 25720, 21136, 33604, 6027, 21136, 33604, 6027, 13672, 1829, 4724, 1829, 39648, 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ال R في الحالة اللي N بتساوي 2N تربيع اللي هو ركزوا معاه فN بتساوي اللي هو 2", "tokens": [9566, 1829, 3555, 13412, 2407, 426, 39894, 3794, 995, 45865, 426, 6055, 2288, 21292, 3615, 8717, 25957, 1211, 11296, 12174, 36150, 4724, 8592, 2407, 10632, 37495, 22653, 426, 39894, 3794, 995, 45865, 363, 16, 13672, 1829, 31439, 8132, 16, 5296, 3615, 9957, 11568, 8132, 49, 3714, 19913, 3555, 2407, 9566, 4032, 2423, 497, 8978, 21542, 6027, 3660, 13672, 1829, 426, 39894, 3794, 995, 45865, 568, 45, 6055, 2288, 21292, 3615, 13672, 1829, 31439, 12602, 4117, 11622, 14407, 20449, 40294, 6156, 45, 39894, 3794, 995, 45865, 13672, 1829, 31439, 568], "avg_logprob": -0.32899306184715693, "compression_ratio": 1.8116883116883118, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 946.7, "end": 947.4, "word": "طيب", "probability": 0.8043619791666666}, {"start": 947.4, "end": 948.22, "word": " شو", "probability": 0.6187744140625}, {"start": 948.22, "end": 948.42, "word": " N", "probability": 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0.93701171875}, {"start": 2097.87, "end": 2098.67, "word": " باتجاه", "probability": 0.921875}, {"start": 2098.67, "end": 2099.61, "word": " ان", "probability": 0.35693359375}, {"start": 2099.61, "end": 2100.29, "word": " ال", "probability": 0.923828125}, {"start": 2100.29, "end": 2100.81, "word": " summation", "probability": 0.39306640625}, {"start": 2100.81, "end": 2101.31, "word": " كله", "probability": 0.966064453125}, {"start": 2101.31, "end": 2101.43, "word": " مع", "probability": 0.9794921875}, {"start": 2101.43, "end": 2101.55, "word": " ال", "probability": 0.94482421875}, {"start": 2101.55, "end": 2101.83, "word": " function", "probability": 0.55029296875}, {"start": 2101.83, "end": 2102.07, "word": " اللي", "probability": 0.983642578125}, {"start": 2102.07, "end": 2102.57, "word": " جوا", "probability": 0.8525390625}, {"start": 2102.57, "end": 2103.55, "word": " اني", "probability": 0.550537109375}, {"start": 2103.55, "end": 2104.03, "word": " أقول", "probability": 0.8955078125}, {"start": 2104.03, "end": 2104.43, "word": " عنها", "probability": 0.995361328125}, {"start": 2104.43, "end": 2104.91, "word": " رايحة", "probability": 0.984375}, {"start": 2104.91, "end": 2105.45, "word": " باتجاه", "probability": 0.96240234375}, {"start": 2105.45, "end": 2105.59, "word": " ال", "probability": 0.60205078125}, {"start": 2105.59, "end": 2106.41, "word": " multiplicative", "probability": 0.908203125}, {"start": 2106.41, "end": 2106.81, "word": " ومن", "probability": 0.86669921875}, {"start": 2106.81, "end": 2107.25, "word": " ثم", "probability": 0.990478515625}, {"start": 2107.25, "end": 2109.41, "word": " إيجادها", "probability": 0.90087890625}, {"start": 2109.41, "end": 2110.63, "word": " بيصير", "probability": 0.8721923828125}, {"start": 2110.63, "end": 2111.07, "word": " سهل", "probability": 0.9973958333333334}, {"start": 2111.07, "end": 2111.89, "word": " باستخدام", "probability": 0.9842936197916666}, {"start": 2111.89, "end": 2112.13, "word": " ال", "probability": 0.794921875}, {"start": 2112.13, "end": 2113.05, "word": " multiplicative", "probability": 0.94921875}, {"start": 2113.05, "end": 2113.89, "word": " إيش", "probability": 0.7835286458333334}, {"start": 2113.89, "end": 2113.99, "word": " اللي", "probability": 0.97998046875}, {"start": 2113.99, "end": 2114.41, "word": " بقوله؟", "probability": 0.8670654296875}, {"start": 2114.41, "end": 2114.71, "word": " خليني", "probability": 0.876953125}, {"start": 2114.71, "end": 2114.95, "word": " أشوف", "probability": 0.93115234375}], "temperature": 1.0}, {"id": 82, "seek": 214423, "start": 2116.16, "end": 2144.24, "text": "بس على الحالة سؤال قبل الـ 1 على D لما أخد فانشين F of D بيسوي 1 على D multiplicative برضه اللي هو شعوري ان هو multiplicative و هتلاقي انه فعلا multiplicative وسادف بقى انها multiplicative اذا اول اشي بدي احاول اجايف هذه للصورة هذه بدي اقول له let F of D بيسوي 1 على D ماشي الحالة الان F بتدعي انها multiplicative", "tokens": [3555, 3794, 15844, 21542, 6027, 3660, 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"word": " على", "probability": 0.283447265625}, {"start": 2116.6, "end": 2116.88, "word": " الحالة", "probability": 0.7408040364583334}, {"start": 2116.88, "end": 2117.06, "word": " سؤال", "probability": 0.91796875}, {"start": 2117.06, "end": 2117.28, "word": " قبل", "probability": 0.5921630859375}, {"start": 2117.28, "end": 2117.48, "word": " الـ", "probability": 0.6044921875}, {"start": 2117.48, "end": 2117.66, "word": " 1", "probability": 0.53173828125}, {"start": 2117.66, "end": 2117.9, "word": " على", "probability": 0.4443359375}, {"start": 2117.9, "end": 2118.02, "word": " D", "probability": 0.7060546875}, {"start": 2118.02, "end": 2118.22, "word": " لما", "probability": 0.865234375}, {"start": 2118.22, "end": 2118.46, "word": " أخد", "probability": 0.8294270833333334}, {"start": 2118.46, "end": 2118.84, "word": " فانشين", "probability": 0.59521484375}, {"start": 2118.84, "end": 2118.94, "word": " F", "probability": 0.58642578125}, {"start": 2118.94, "end": 2119.06, "word": " of", "probability": 0.38134765625}, {"start": 2119.06, "end": 2119.16, "word": " D", "probability": 0.9853515625}, {"start": 2119.16, "end": 2119.4, "word": " بيسوي", "probability": 0.6575927734375}, {"start": 2119.4, "end": 2119.54, "word": " 1", "probability": 0.91650390625}, {"start": 2119.54, "end": 2119.7, "word": " على", "probability": 0.8603515625}, {"start": 2119.7, "end": 2119.84, "word": " D", "probability": 0.9912109375}, {"start": 2119.84, "end": 2120.66, "word": " multiplicative", "probability": 0.5758056640625}, {"start": 2120.66, "end": 2122.02, "word": " برضه", "probability": 0.9239908854166666}, {"start": 2122.02, "end": 2122.36, "word": " اللي", "probability": 0.85205078125}, {"start": 2122.36, "end": 2122.72, "word": " هو", "probability": 0.9697265625}, {"start": 2122.72, "end": 2123.46, "word": " شعوري", "probability": 0.9169921875}, {"start": 2123.46, "end": 2123.58, "word": " ان", "probability": 0.2467041015625}, {"start": 2123.58, "end": 2123.78, "word": " هو", "probability": 0.3203125}, {"start": 2123.78, "end": 2124.76, "word": " multiplicative", "probability": 0.857421875}, {"start": 2124.76, "end": 2124.88, "word": " و", "probability": 0.42236328125}, {"start": 2124.88, "end": 2125.32, "word": " هتلاقي", "probability": 0.8409423828125}, {"start": 2125.32, "end": 2125.94, "word": " انه", "probability": 0.801025390625}, {"start": 2125.94, "end": 2126.36, "word": " فعلا", "probability": 0.9480794270833334}, {"start": 2126.36, "end": 2127.1, "word": " multiplicative", "probability": 0.730712890625}, {"start": 2127.1, "end": 2127.62, "word": " وسادف", "probability": 0.6102701822916666}, {"start": 2127.62, "end": 2127.8, "word": " بقى", "probability": 0.87841796875}, {"start": 2127.8, "end": 2128.0, "word": " انها", "probability": 0.840576171875}, {"start": 2128.0, "end": 2128.68, "word": " multiplicative", "probability": 0.8896484375}, {"start": 2128.68, "end": 2129.6, "word": " اذا", "probability": 0.6971435546875}, {"start": 2129.6, "end": 2129.96, "word": " اول", "probability": 0.78369140625}, {"start": 2129.96, "end": 2130.18, "word": " اشي", "probability": 0.8406575520833334}, {"start": 2130.18, "end": 2130.42, "word": " بدي", "probability": 0.58251953125}, {"start": 2130.42, "end": 2130.84, "word": " احاول", "probability": 0.76226806640625}, {"start": 2130.84, "end": 2131.76, "word": " اجايف", "probability": 0.758544921875}, {"start": 2131.76, "end": 2132.16, "word": " هذه", "probability": 0.65380859375}, {"start": 2132.16, "end": 2133.26, "word": " للصورة", "probability": 0.95458984375}, {"start": 2133.26, "end": 2133.56, "word": " هذه", "probability": 0.7578125}, {"start": 2133.56, "end": 2134.5, "word": " بدي", "probability": 0.827880859375}, {"start": 2134.5, "end": 2134.74, "word": " اقول", "probability": 0.911865234375}, {"start": 2134.74, "end": 2134.84, "word": " له", "probability": 0.4765625}, {"start": 2134.84, "end": 2135.26, "word": " let", "probability": 0.6083984375}, {"start": 2135.26, "end": 2136.8, "word": " F", "probability": 0.85546875}, {"start": 2136.8, "end": 2137.04, "word": " of", "probability": 0.92529296875}, {"start": 2137.04, "end": 2137.36, "word": " D", "probability": 0.99462890625}, {"start": 2137.36, "end": 2138.84, "word": " بيسوي", "probability": 0.7939453125}, {"start": 2138.84, "end": 2139.14, "word": " 1", "probability": 0.9677734375}, {"start": 2139.14, "end": 2139.5, "word": " على", "probability": 0.90576171875}, {"start": 2139.5, "end": 2139.8, "word": " D", "probability": 0.9931640625}, {"start": 2139.8, "end": 2140.56, "word": " ماشي", "probability": 0.8219401041666666}, {"start": 2140.56, "end": 2141.64, "word": " الحالة", "probability": 0.762451171875}, {"start": 2141.64, "end": 2142.02, "word": " الان", "probability": 0.7200927734375}, {"start": 2142.02, "end": 2142.58, "word": " F", "probability": 0.875}, {"start": 2142.58, "end": 2143.22, "word": " بتدعي", "probability": 0.8494873046875}, {"start": 2143.22, "end": 2143.44, "word": " انها", "probability": 0.944091796875}, {"start": 2143.44, "end": 2144.24, "word": " multiplicative", "probability": 0.925048828125}], "temperature": 1.0}, {"id": 83, "seek": 215871, "start": 2144.95, "end": 2158.71, "text": "ليش Multiplicative؟ تستسهل Let D1 وD2 element in Z بحيث الـ Greatest common divisor بينهما يكون 1 وحسبني F of D1 في D2 بساوة", "tokens": [20292, 8592, 29238, 4770, 1166, 22807, 6055, 14851, 3794, 3224, 1211, 961, 413, 16, 4032, 35, 17, 4478, 294, 1176, 4724, 5016, 1829, 12984, 2423, 39184, 3769, 377, 2689, 25974, 284, 49374, 3224, 15042, 7251, 30544, 502, 4032, 5016, 35457, 22653, 479, 295, 413, 16, 8978, 413, 17, 4724, 3794, 995, 2407, 3660], "avg_logprob": -0.4401041556287695, "compression_ratio": 1.1073825503355705, "no_speech_prob": 0.0, "words": [{"start": 2144.95, "end": 2145.25, "word": "ليش", "probability": 0.5889892578125}, {"start": 2145.25, "end": 2145.97, "word": " Multiplicative؟", "probability": 0.626861572265625}, {"start": 2145.97, "end": 2146.91, "word": " تستسهل", "probability": 0.87744140625}, {"start": 2146.91, "end": 2148.17, "word": " Let", "probability": 0.2393798828125}, {"start": 2148.17, "end": 2149.07, "word": " D1", "probability": 0.833251953125}, {"start": 2149.07, "end": 2149.63, "word": " وD2", "probability": 0.86767578125}, {"start": 2149.63, "end": 2150.09, "word": " element", "probability": 0.58642578125}, {"start": 2150.09, "end": 2150.33, "word": " in", "probability": 0.86669921875}, {"start": 2150.33, "end": 2150.55, "word": " Z", "probability": 0.79248046875}, {"start": 2150.55, "end": 2150.85, "word": " بحيث", "probability": 0.8345947265625}, {"start": 2150.85, "end": 2151.03, "word": " الـ", "probability": 0.62060546875}, {"start": 2151.03, "end": 2151.35, "word": " Greatest", "probability": 0.27691650390625}, {"start": 2151.35, "end": 2151.49, "word": " common", "probability": 0.393310546875}, {"start": 2151.49, "end": 2151.93, "word": " divisor", "probability": 0.7255859375}, {"start": 2151.93, "end": 2152.25, "word": " بينهما", "probability": 0.7233072916666666}, {"start": 2152.25, "end": 2152.37, "word": " يكون", "probability": 0.434814453125}, {"start": 2152.37, "end": 2153.55, "word": " 1", "probability": 0.40673828125}, {"start": 2153.55, "end": 2154.97, "word": " وحسبني", "probability": 0.60711669921875}, {"start": 2154.97, "end": 2155.33, "word": " F", "probability": 0.69140625}, {"start": 2155.33, "end": 2156.17, "word": " of", "probability": 0.306640625}, {"start": 2156.17, "end": 2156.93, "word": " D1", "probability": 0.949462890625}, {"start": 2156.93, "end": 2157.17, "word": " في", "probability": 0.5537109375}, {"start": 2157.17, "end": 2157.81, "word": " D2", "probability": 0.99072265625}, {"start": 2157.81, "end": 2158.71, "word": " بساوة", "probability": 0.6634765625}], "temperature": 1.0}, {"id": 84, "seek": 218683, "start": 2159.69, "end": 2186.83, "text": "اللي هو حسب القانون هو 1 على D1 في D2 صح ولا لأ اللي هي بيساوي 1 على D1 في 1 على D2 ويساوي F of D1 في F of D إذا واضح أن F is a multiplicative function ماشي الحال طيب مدام F multiplicative بتشجعني أن أقول let F of N", "tokens": [6027, 20292, 31439, 11331, 35457, 25062, 7649, 11536, 31439, 502, 15844, 413, 16, 8978, 413, 17, 20328, 5016, 49429, 5296, 10721, 13672, 1829, 39896, 4724, 1829, 3794, 995, 45865, 502, 15844, 413, 16, 8978, 502, 15844, 413, 17, 4032, 1829, 3794, 995, 45865, 479, 295, 413, 16, 8978, 479, 295, 413, 11933, 15730, 4032, 46958, 5016, 14739, 479, 307, 257, 17596, 1166, 2445, 3714, 33599, 1829, 21542, 6027, 23032, 1829, 3555, 3714, 3215, 10943, 479, 17596, 1166, 39894, 8592, 7435, 3615, 22653, 14739, 5551, 39648, 718, 479, 295, 426], "avg_logprob": -0.18107638623979355, "compression_ratio": 1.6197916666666667, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 2159.69, "end": 2160.01, "word": "اللي", "probability": 0.744873046875}, {"start": 2160.01, "end": 2160.23, "word": " هو", "probability": 0.94384765625}, {"start": 2160.23, "end": 2160.55, "word": " حسب", 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واحد كي واحد بي ار كي ار بي برايم factorization of n أكبر من واحد إذا كانت f is multiplicative prove that اللي موجود انتبهوا عن دي خليني برضه أذكركم بعض النظريات", "tokens": [3794, 33604, 6027, 6055, 1211, 9307, 3660, 718, 718, 718, 297, 39894, 3794, 995, 45865, 4724, 1829, 36764, 24401, 9122, 1829, 36764, 24401, 4724, 1829, 1975, 2288, 9122, 1829, 1975, 2288, 4724, 1829, 4724, 23557, 32640, 5952, 2144, 295, 297, 5551, 4117, 26890, 9154, 36764, 24401, 11933, 15730, 25961, 2655, 283, 307, 17596, 1166, 7081, 300, 13672, 1829, 3714, 29245, 23328, 16472, 2655, 3555, 3224, 14407, 18871, 11778, 1829, 16490, 1211, 9957, 1829, 4724, 43042, 3224, 5551, 8848, 37983, 24793, 45030, 11242, 28239, 19913, 16572, 9307], "avg_logprob": -0.2500000013702217, "compression_ratio": 1.5435897435897437, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4328.91, "end": 4329.39, "word": "سؤال", "probability": 0.912109375}, {"start": 4329.39, "end": 4330.15, "word": " تلاتة", "probability": 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لعند مين مع عند انا واضح اه؟ طيب عندي F is multiplicative مع ان في نظرية بتحكي على طول بالجيبة F multiplicative و Mu multiplicative هتطلع عندي Mu في F أشمالها is multiplicative بتعرف��ا تعملوها اه؟", "tokens": [40, 9154, 36764, 24401, 5296, 3615, 41260, 3714, 9957, 20449, 43242, 1975, 8315, 4032, 46958, 5016, 1975, 3224, 22807, 23032, 1829, 3555, 18871, 16254, 479, 307, 17596, 1166, 20449, 16472, 8978, 8717, 19913, 2288, 10632, 39894, 5016, 4117, 1829, 15844, 23032, 12610, 20666, 7435, 1829, 49401, 479, 17596, 1166, 4032, 15601, 17596, 1166, 8032, 2655, 9566, 1211, 3615, 18871, 16254, 15601, 8978, 479, 5551, 8592, 2304, 6027, 11296, 307, 17596, 1166, 39894, 3615, 28480, 14407, 6055, 25957, 1211, 2407, 11296, 1975, 3224, 22807], "avg_logprob": -0.28627233526536394, "compression_ratio": 1.6630434782608696, "no_speech_prob": 9.179115295410156e-06, "words": [{"start": 4386.52, "end": 4387.06, "word": "I", "probability": 0.7177734375}, {"start": 4387.06, "end": 4387.8, "word": " من", 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