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1{2 "experiment": "sha256_local_collision_9step",3 "timestamp_utc": "2026-11-01T06:21:52+00:00",4 "command": "experiments/reduced_round_sha256/local_collision.py --seed 1 --n 100000 --sat-bits all --sat-timeout 120 --out results/reduced_round_sha256/local_collision.json",5 "cwd": "/Users/simon-pierreboucher/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier",6 "seed": 1,7 "host": {8  "hostname": "MacBookPro-de-simon-pierre-2.local",9  "os": "Darwin 27.0.0 (27.0)",10  "machine": "arm64",11  "python": "3.12.13",12  "cpu": "Apple M5 Max",13  "cores": 18,14  "ram_gb": 48.015 },16 "software": {17  "numpy": "2.5.4",18  "scipy": "1.18.1",19  "sympy": "1.14.0",20  "gmpy2": "2.3.2",21  "z3": "5.3.3",22  "pysat": "1.9.dev17",23  "ecdsa": "0.19.2",24  "coincurve": "21.0.0"25 },26 "params": {27  "n_per_bit": 100000,28  "start_step": 0,29  "sat_bits": [30   0,31   1,32   2,33   3,34   4,35   5,36   6,37   7,38   8,39   9,40   10,41   11,42   12,43   13,44   14,45   15,46   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"000000000102601c80180000d40804420cc00418100d646025c886f4993cb56e",5376    "W_hex": [5377     "80000000",5378     "dff26fe4",5379     "6f13da3a",5380     "2ef58d78",5381     "a1cfd379",5382     "048aa133",5383     "8276bb7b",5384     "1c883e0e",5385     "00008000"5386    ],5387    "W_prime_hex": [5388     "80008000",5389     "ddb24df0",5390     "7f8b98bf",5391     "2ef58d78",5392     "a1cf5379",5393     "06ca8327",5394     "8276bb7b",5395     "1c883e0e",5396     "00000000"5397    ],5398    "verified": true,5399    "final_state_hex": "26d75eb69fee5ac8a4f2cc875439e9c432a1cc1a00000000ffff8000da006d4e"5400   },5401   {5402    "bit": 16,5403    "n_vars": 15218,5404    "n_clauses": 66208,5405    "status": "sat",5406    "wall_s": 23.338,5407    "conflicts": 2123944,5408    "decisions": 8700760,5409    "propagations": 84537859,5410    "restarts": 77709,5411    "solver_real_s": 23.33,5412    "cadical_rss_mb": 102.17,5413    "seed": 1,5414    "state_hex": "008c984da04041d08155603c146f03c9001300f120334b5f00106b715433ae7d",5415    "W_hex": [5416     "0120b00c",5417     "982023f0",5418     "dcaf8aa3",5419     "a0430e1b",5420     "8a2307b3",5421     "8481476a",5422     "188dd298",5423     "492af788",5424     "00010000"5425    ],5426    "W_prime_hex": [5427     "0121b00c",5428     "9ca067d8",5429     "fd9f0fa9",5430     "a0430e1b",5431     "8a2207b3",5432     "80010342",5433     "188dd298",5434     "492af788",5435     "00000000"5436    ],5437    "verified": true,5438    "final_state_hex": "fcb9d6833497a2bb861797ec1b1a33c4685938d4000000000001000052e27018"5439   },5440   {5441    "bit": 17,5442    "n_vars": 15218,5443    "n_clauses": 66208,5444    "status": "sat",5445    "wall_s": 29.696,5446    "conflicts": 2444800,5447    "decisions": 10377362,5448    "propagations": 114111042,5449    "restarts": 75610,5450    "solver_real_s": 29.69,5451    "cadical_rss_mb": 115.08,5452    "seed": 1,5453    "state_hex": "feffee68fabfba5285bc7efd34f1041ef3a3beffbd9f0304f6fffffa7ca5082f",5454    "W_hex": [5455     "6bff92b2",5456     "aebf45d4",5457     "37400bb4",5458     "7a52966d",5459     "7ffd9096",5460     "77ffffe2",5461     "66746744",5462     "83c70b18",5463     "35f90203"5464    ],5465    "W_prime_hex": [5466     "6bfd92b2",5467     "a7bfcd84",5468     "752101a0",5469     "7a52966d",5470     "7fff9096",5471     "7eff77b2",5472     "66746744",5473     "83c70b18",5474     "35fb0203"5475    ],5476    "verified": true,5477    "final_state_hex": "937352050baa613130df08a6f0027cec904fb764ffffffffffffffff4b250351"5478   },5479   {5480    "bit": 18,5481    "n_vars": 15218,5482    "n_clauses": 66208,5483    "status": "sat",5484    "wall_s": 17.998,5485    "conflicts": 1722686,5486    "decisions": 7357263,5487    "propagations": 73169181,5488    "restarts": 56672,5489    "solver_real_s": 17.99,5490    "cadical_rss_mb": 100.92,5491    "seed": 1,5492    "state_hex": "6404a1dc000360c135800001d2059b6a00aa0100020ec85031a9000e7df4931e",5493    "W_hex": [5494     "101064aa",5495     "814860e6",5496     "98b6c0fa",5497     "33c13011",5498     "63cfd18e",5499     "96bc6212",5500     "fed54c23",5501     "92f3dcde",5502     "00040000"5503    ],5504    "W_prime_hex": [5505     "101464aa",5506     "93497046",5507     "1c74d4d2",5508     "33c13011",5509     "63cbd18e",5510     "84bd72b2",5511     "fed54c23",5512     "92f3dcde",5513     "00000000"5514    ],5515    "verified": true,5516    "final_state_hex": "e51e89d05f213868e21fe74c7b297e5c775acc45000000005efc000075010fa7"5517   },5518   {5519    "bit": 19,5520    "n_vars": 15218,5521    "n_clauses": 66208,5522    "status": "sat",5523    "wall_s": 17.758,5524    "conflicts": 1155321,5525    "decisions": 7687357,5526    "propagations": 99298310,5527    "restarts": 36609,5528    "solver_real_s": 17.75,5529    "cadical_rss_mb": 124.08,5530    "seed": 1,5531    "state_hex": "a6e63434a0817673ea798e428d0ec50d642304301936172024120108d673bb06",5532    "W_hex": [5533     "adf6fcf3",5534     "6ced3a0d",5535     "53e0bb75",5536     "03815fb5",5537     "a70d98a6",5538     "049fff75",5539     "fcd81141",5540     "7c80cb07",5541     "80080f0a"5542    ],5543    "W_prime_hex": [5544     "adfefcf3",5545     "48ef1b4d",5546     "5a649324",5547     "03815fb5",5548     "a70598a6",5549     "209dde35",5550     "fcd81141",5551     "7c80cb07",5552     "80000f0a"5553    ],5554    "verified": true,5555    "final_state_hex": "ac984c12a2571334a9b9fe4e7c16a4c7296803b40a6510237ff967f639061026"5556   },5557   {5558    "bit": 20,5559    "n_vars": 15218,5560    "n_clauses": 66208,5561    "status": "sat",5562    "wall_s": 10.65,5563    "conflicts": 949738,5564    "decisions": 3587060,5565    "propagations": 44253912,5566    "restarts": 26921,5567    "solver_real_s": 10.64,5568    "cadical_rss_mb": 90.3,5569    "seed": 1,5570    "state_hex": "fb3df0b9a47694a06e7b33a3dc1fffff0c4b077dcf670197c1fc8ffd396b2ad9",5571    "W_hex": [5572     "36c08322",5573     "85b58c3d",5574     "975431ea",5575     "d832ffab",5576     "1c3f96b6",5577     "debbbc80",5578     "ca6474e3",5579     "da3670e9",5580     "3c5c0000"5581    ],5582    "W_prime_hex": [5583     "36d08322",5584     "cdb1cebd",5585     "845c6148",5586     "d832ffab",5587     "1c2f96b6",5588     "96bffe00",5589     "ca6474e3",5590     "da3670e9",5591     "3c4c0000"5592    ],5593    "verified": true,5594    "final_state_hex": "3d4aa7a66bebff94438e6924f10c9b99c93970d9fe3fb98ce7fe4c85b9027208"5595   },5596   {5597    "bit": 21,5598    "n_vars": 15218,5599    "n_clauses": 66208,5600    "status": "sat",5601    "wall_s": 10.886,5602    "conflicts": 1037511,5603    "decisions": 5132226,5604    "propagations": 50228702,5605    "restarts": 38391,5606    "solver_real_s": 10.88,5607    "cadical_rss_mb": 87.53,5608    "seed": 1,5609    "state_hex": "08000000038003645c382402f40001fb816008f828ff80d110a94ea4617ab93a",5610    "W_hex": [5611     "00000001",5612     "21a00785",5613     "0514f4a6",5614     "642244aa",5615     "823ad853",5616     "900f0012",5617     "f7205f88",5618     "be62d54f",5619     "80200000"5620    ],5621    "W_prime_hex": [5622     "00200001",5623     "b1a88285",5624     "230455e2",5625     "642244aa",5626     "821ad853",5627     "00078512",5628     "f7205f88",5629     "be62d54f",5630     "80000000"5631    ],5632    "verified": true,5633    "final_state_hex": "04456967da2327b5c18c693357a09ddb10f9f0fe0000000000200000f8406456"5634   },5635   {5636    "bit": 22,5637    "n_vars": 15218,5638    "n_clauses": 66208,5639    "status": "sat",5640    "wall_s": 16.55,5641    "conflicts": 1500553,5642    "decisions": 6375011,5643    "propagations": 70061380,5644    "restarts": 47386,5645    "solver_real_s": 16.54,5646    "cadical_rss_mb": 101.95,5647    "seed": 1,5648    "state_hex": "99eb374ff07e6c45b0971049b0f80d79c259015adc6c13f271cabec2e7498e5a",5649    "W_hex": [5650     "86f77432",5651     "25f2760c",5652     "13bbbc4d",5653     "6fe8795e",5654     "0e3f59b5",5655     "ac48d1ff",5656     "7cedecdb",5657     "208bbd4d",5658     "00000003"5659    ],5660    "W_prime_hex": [5661     "86b77432",5662     "05e37c0d",5663     "5f9afec5",5664     "6fe8795e",5665     "0e7f59b5",5666     "8c59dbfe",5667     "7cedecdb",5668     "208bbd4d",5669     "00400003"5670    ],5671    "verified": true,5672    "final_state_hex": "0349b1791c18c8ea0bab0569f5a72bbdceb8119d7041050af5548440578d77e8"5673   },5674   {5675    "bit": 23,5676    "n_vars": 15218,5677    "n_clauses": 66208,5678    "status": "sat",5679    "wall_s": 12.336,5680    "conflicts": 926607,5681    "decisions": 4953432,5682    "propagations": 60123378,5683    "restarts": 27828,5684    "solver_real_s": 12.33,5685    "cadical_rss_mb": 90.73,5686    "seed": 1,5687    "state_hex": "2ea863074c92302c05f0e35c960c797d3ff4814496ae186689c5f71f0177cb80",5688    "W_hex": [5689     "177924c6",5690     "80844c3f",5691     "fc0bf510",5692     "ef7fa907",5693     "f0feacec",5694     "d0f5f91d",5695     "65f218fb",5696     "a5033a8c",5697     "b0800000"5698    ],5699    "W_prime_hex": [5700     "17f924c6",5701     "c0a6583d",5702     "64497000",5703     "ef7fa907",5704     "f07eacec",5705     "90d7ed1f",5706     "65f218fb",5707     "a5033a8c",5708     "b0000000"5709    ],5710    "verified": true,5711    "final_state_hex": "f4de1d1d7b92b483187901b7aa86eb761fb9197b5783a0b981f7b841376ceb10"5712   },5713   {5714    "bit": 24,5715    "n_vars": 15218,5716    "n_clauses": 66208,5717    "status": "sat",5718    "wall_s": 26.798,5719    "conflicts": 2016371,5720    "decisions": 9645806,5721    "propagations": 119748788,5722    "restarts": 56534,5723    "solver_real_s": 26.79,5724    "cadical_rss_mb": 108.08,5725    "seed": 1,5726    "state_hex": "fffeb0effe647401fffec1fcff4260f4ffdfffdef73f00a33f26a771d357644f",5727    "W_hex": [5728     "ffbca2b0",5729     "0ffff11c",5730     "e35e5995",5731     "146a2234",5732     "7e0457c6",5733     "ffbffffb",5734     "6b252070",5735     "93c0a4f8",5736     "b6800800"5737    ],5738    "W_prime_hex": [5739     "febca2b0",5740     "8fbbd918",5741     "d3db53b4",5742     "146a2234",5743     "7f0457c6",5744     "7ffbd7ff",5745     "6b252070",5746     "93c0a4f8",5747     "b7800800"5748    ],5749    "verified": true,5750    "final_state_hex": "fab45021f655ea395ccc8ab5fa17f31efb3a1e9fffffffffffffffff127ff9fe"5751   },5752   {5753    "bit": 25,5754    "n_vars": 15218,5755    "n_clauses": 66208,5756    "status": "sat",5757    "wall_s": 14.602,5758    "conflicts": 996570,5759    "decisions": 5713497,5760    "propagations": 71610094,5761    "restarts": 34664,5762    "solver_real_s": 14.6,5763    "cadical_rss_mb": 82.03,5764    "seed": 1,5765    "state_hex": 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"b8473bdd70f83d12865fefff7ab2c663feffdffefdffcb79ffefffcc67ae04fd",5805    "W_hex": [5806     "7f588d89",5807     "5f22e8fc",5808     "2deb97b8",5809     "e34204cf",5810     "59dadd0e",5811     "76ef5fed",5812     "61d7e209",5813     "c9ea367e",5814     "aac00000"5815    ],5816    "W_prime_hex": [5817     "7b588d89",5818     "5e3248ee",5819     "efffbf3c",5820     "e34204cf",5821     "5ddadd0e",5822     "77ffffff",5823     "61d7e209",5824     "c9ea367e",5825     "aec00000"5826    ],5827    "verified": true,5828    "final_state_hex": "5a0bf38feadb47486ced3a8422290dde501805eaefa23ba5dc9fb43ba10dc9aa"5829   },5830   {5831    "bit": 27,5832    "n_vars": 15218,5833    "n_clauses": 66208,5834    "status": "sat",5835    "wall_s": 5.561,5836    "conflicts": 529386,5837    "decisions": 2571829,5838    "propagations": 25498840,5839    "restarts": 18965,5840    "solver_real_s": 5.55,5841    "cadical_rss_mb": 84.14,5842    "seed": 1,5843    "state_hex": "9bcefdbff9a680673e37ffe8a78cb58e7fdffffffbdebcbeffa9fc3e2fa7d82b",5844    "W_hex": [5845     "7c430a25",5846     "498efb7a",5847     "9915c3e2",5848     "fbefbf4c",5849     "77da062c",5850     "7e6fbfd8",5851     "c4c56d97",5852     "61122261",5853     "f6000802"5854    ],5855    "W_prime_hex": [5856     "74430a25",5857     "4bafbb5e",5858     "1d3d92eb",5859     "fbefbf4c",5860     "7fda062c",5861     "7c4efffc",5862     "c4c56d97",5863     "61122261",5864     "fe000802"5865    ],5866    "verified": true,5867    "final_state_hex": "9cd23baf9a195d3165073a473157e84d2075f6cdffffffffffffffff81cf6c0a"5868   },5869   {5870    "bit": 28,5871    "n_vars": 15218,5872    "n_clauses": 66208,5873    "status": "sat",5874    "wall_s": 6.334,5875    "conflicts": 613160,5876    "decisions": 2445590,5877    "propagations": 26214269,5878    "restarts": 15820,5879    "solver_real_s": 6.33,5880    "cadical_rss_mb": 89.97,5881    "seed": 1,5882    "state_hex": "87b5dfe4ac3b5fbf43be8f57fd0464c6b15a4fc76ec34f40a6313c3107fdff4a",5883    "W_hex": [5884     "adc0a6b1",5885     "ec3a8479",5886     "806b588f",5887     "ff2f3e5f",5888     "54f9dda2",5889     "e89114e0",5890     "6122f5d3",5891     "0853b8cb",5892     "32020202"5893    ],5894    "W_prime_hex": [5895     "bdc0a6b1",5896     "e8780431",5897     "883bfa9c",5898     "ff2f3e5f",5899     "44f9dda2",5900     "ecd394a8",5901     "6122f5d3",5902     "0853b8cb",5903     "22020202"5904    ],5905    "verified": true,5906    "final_state_hex": "16b22d70bf6d1dab5f1c621cda3ef52d0b45fae55c57c25ffe6f5e1f01910324"5907   },5908   {5909    "bit": 29,5910    "n_vars": 15218,5911    "n_clauses": 66208,5912    "status": "sat",5913    "wall_s": 4.361,5914    "conflicts": 445009,5915    "decisions": 1646284,5916    "propagations": 19606726,5917    "restarts": 14625,5918    "solver_real_s": 4.35,5919    "cadical_rss_mb": 83.27,5920    "seed": 1,5921    "state_hex": "45ebc993a4cdf964a4c0de4490709db111bfee8191ffb35efaf596a415e2957e",5922    "W_hex": [5923     "408ec966",5924     "d25bfc82",5925     "4a1210ff",5926     "f1fe9893",5927     "2d55a6fc",5928     "885e7d68",5929     "e1e91c37",5930     "9b1fa3e2",5931     "30000000"5932    ],5933    "W_prime_hex": [5934     "608ec966",5935     "dadefc12",5936     "5ab354d9",5937     "f1fe9893",5938     "0d55a6fc",5939     "80db7df8",5940     "e1e91c37",5941     "9b1fa3e2",5942     "10000000"5943    ],5944    "verified": true,5945    "final_state_hex": "a9b46956af942cc2fbb07b83c817f66504366c13b6c0c20ff74cafb6d0c66eeb"5946   },5947   {5948    "bit": 30,5949    "n_vars": 15218,5950    "n_clauses": 66208,5951    "status": "sat",5952    "wall_s": 6.554,5953    "conflicts": 358785,5954    "decisions": 3309484,5955    "propagations": 35670870,5956    "restarts": 16573,5957    "solver_real_s": 6.55,5958    "cadical_rss_mb": 74.31,5959    "seed": 1,5960    "state_hex": "da53ff7deff5fcfc807f88926310f483f3b5c47cfe5a546a7ffffed49868b1b8",5961    "W_hex": [5962     "30e41c55",5963     "0ba88244",5964     "c1f60309",5965     "34302b7d",5966     "fe4e92f9",5967     "15b2a736",5968     "7ffe7b73",5969     "7ffffff3",5970     "4297feab"5971    ],5972    "W_prime_hex": [5973     "70e41c55",5974     "1aa28364",5975     "e0b48b45",5976     "34302b7d",5977     "be4e92f9",5978     "04b8a616",5979     "7ffe7b73",5980     "7ffffff3",5981     "0297feab"5982    ],5983    "verified": true,5984    "final_state_hex": "01610d9fcec6022ae679f55ed331b09607857f3b521bc7dc56bf46e105a8229f"5985   },5986   {5987    "bit": 31,5988    "n_vars": 15218,5989    "n_clauses": 66208,5990    "status": "sat",5991    "wall_s": 5.12,5992    "conflicts": 328099,5993    "decisions": 2428883,5994    "propagations": 26791219,5995    "restarts": 9451,5996    "solver_real_s": 5.11,5997    "cadical_rss_mb": 69.12,5998    "seed": 1,5999    "state_hex": "3ffffe317ff49fa267ff13c8ffe19d9bdffae8dbff73ee77ff7dfdfeb91789e0",6000    "W_hex": [6001     "88f6da84",6002     "dd518e9d",6003     "094ddd6f",6004     "3e9f5b2d",6005     "ae8d60e9",6006     "ffeff1bf",6007     "b652c097",6008     "b7f66631",6009     "80000000"6010    ],6011    "W_prime_hex": [6012     "08f6da84",6013     "ff458cdd",6014     "4bc8cdf7",6015     "3e9f5b2d",6016     "2e8d60e9",6017     "ddfbf3ff",6018     "b652c097",6019     "b7f66631",6020     "00000000"6021    ],6022    "verified": true,6023    "final_state_hex": "517f001336a383057f256ec22ff407db7fdad4d12c00c000ffffffff37ab8cb0"6024   }6025  ],6026  "pattern_formula": "(d, S0(d)^S1(d), S1(S0(d)), 0, d, S0(d)^S1(d), 0, 0, d)"6027 },6028 "elapsed_s": 943.727,6029 "op_stats": {6030  "wall_s": 943.466,6031  "peak_rss_mb": 64.5,6032  "step_evaluations_real": 576000006033 }6034}
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