diff --git a/research/quantitative-rank-library/INDEPENDENT-RESULT.json b/research/quantitative-rank-library/INDEPENDENT-RESULT.json new file mode 100644 index 0000000000..20aa3866ea --- /dev/null +++ b/research/quantitative-rank-library/INDEPENDENT-RESULT.json @@ -0,0 +1,2161 @@ +{ + "status": "PASS_INDEPENDENT_RANK_LIBRARY", + "method": "literal role words and unique parent edges", + "rules": 7, + "ranks": 336, + "cases": [ + { + "targets": [ + 2, + 3 + ], + "paid": [ + 1, + 1 + ], + "cap": 48, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 2, + "O": 0 + }, + "3": { + "a": 1, + "B": 2, + "P": 3, + "O": 1 + }, + "4": { + "a": 1, + "B": 2, + "P": 5, + "O": 1 + }, + "5": { + "a": 2, + "B": 4, + "P": 11, + "O": 3 + }, + "6": { + "a": 1, + "B": 4, + "P": 9, + "O": 4 + }, + "7": { + "a": 2, + "B": 8, + "P": 23, + "O": 9 + }, + "8": { + "a": 2, + "B": 8, + "P": 28, + "O": 10 + }, + "9": { + "a": 4, + "B": 16, + "P": 39, + "O": 23 + }, + "10": { + "a": 4, + "B": 16, + "P": 49, + "O": 24 + }, + "11": { + "a": 8, + "B": 32, + "P": 115, + "O": 53 + }, + "12": { + "a": 2, + "B": 16, + "P": 45, + "O": 29 + }, + "13": { + "a": 4, + "B": 32, + "P": 113, + "O": 61 + }, + "14": { + "a": 4, + "B": 32, + "P": 127, + "O": 66 + }, + "15": { + "a": 8, + "B": 64, + "P": 213, + "O": 147 + }, + "16": { + "a": 8, + "B": 64, + "P": 256, + "O": 152 + }, + "17": { + "a": 16, + "B": 128, + "P": 553, + "O": 325 + }, + "18": { + "a": 16, + "B": 128, + "P": 363, + "O": 294 + }, + "19": { + "a": 32, + "B": 256, + "P": 907, + "O": 609 + }, + "20": { + "a": 16, + "B": 128, + "P": 520, + "O": 318 + }, + "21": { + "a": 32, + "B": 256, + "P": 879, + "O": 699 + }, + "22": { + "a": 32, + "B": 256, + "P": 1063, + "O": 716 + }, + "23": { + "a": 64, + "B": 512, + "P": 2275, + "O": 1529 + }, + "24": { + "a": 16, + "B": 256, + "P": 939, + "O": 773 + }, + "25": { + "a": 16, + "B": 256, + "P": 1090, + "O": 798 + }, + "26": { + "a": 32, + "B": 512, + "P": 2437, + "O": 1665 + }, + "27": { + "a": 32, + "B": 512, + "P": 1782, + "O": 1586 + }, + "28": { + "a": 32, + "B": 512, + "P": 2102, + "O": 1618 + }, + "29": { + "a": 64, + "B": 1024, + "P": 4721, + "O": 3381 + }, + "30": { + "a": 64, + "B": 1024, + "P": 3783, + "O": 3438 + }, + "31": { + "a": 128, + "B": 2048, + "P": 8915, + "O": 7057 + }, + "32": { + "a": 64, + "B": 1024, + "P": 4940, + "O": 3674 + }, + "33": { + "a": 128, + "B": 2048, + "P": 8682, + "O": 7826 + }, + "34": { + "a": 128, + "B": 2048, + "P": 9800, + "O": 7946 + }, + "35": { + "a": 256, + "B": 4096, + "P": 21176, + "O": 16560 + }, + "36": { + "a": 128, + "B": 2048, + "P": 6810, + "O": 6962 + }, + "37": { + "a": 256, + "B": 4096, + "P": 16369, + "O": 14241 + }, + "38": { + "a": 256, + "B": 4096, + "P": 18839, + "O": 14660 + }, + "39": { + "a": 512, + "B": 8192, + "P": 33015, + "O": 31581 + }, + "40": { + "a": 256, + "B": 4096, + "P": 19237, + "O": 16029 + }, + "41": { + "a": 256, + "B": 4096, + "P": 20579, + "O": 16785 + }, + "42": { + "a": 512, + "B": 8192, + "P": 34569, + "O": 33869 + }, + "43": { + "a": 512, + "B": 8192, + "P": 38822, + "O": 34530 + }, + "44": { + "a": 512, + "B": 8192, + "P": 43036, + "O": 35552 + }, + "45": { + "a": 1024, + "B": 16384, + "P": 69849, + "O": 71389 + }, + "46": { + "a": 1024, + "B": 16384, + "P": 79063, + "O": 72462 + }, + "47": { + "a": 2048, + "B": 32768, + "P": 173455, + "O": 149789 + }, + "48": { + "a": 256, + "B": 8192, + "P": 35913, + "O": 37278 + } + }, + "source_fields": 542, + "units": 831, + "incoming_edges": 1120, + "exit_pooling_witness": null + }, + { + "targets": [ + 3, + 4, + 6 + ], + "paid": [ + 1, + 2, + 2 + ], + "cap": 48, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 2, + "O": 0 + }, + "3": { + "a": 1, + "B": 1, + "P": 3, + "O": 0 + }, + "4": { + "a": 1, + "B": 1, + "P": 4, + "O": 0 + }, + "5": { + "a": 1, + "B": 1, + "P": 5, + "O": 0 + }, + "6": { + "a": 1, + "B": 3, + "P": 10, + "O": 1 + }, + "7": { + "a": 1, + "B": 3, + "P": 13, + "O": 1 + }, + "8": { + "a": 1, + "B": 3, + "P": 16, + "O": 1 + }, + "9": { + "a": 3, + "B": 9, + "P": 49, + "O": 4 + }, + "10": { + "a": 3, + "B": 9, + "P": 50, + "O": 5 + }, + "11": { + "a": 3, + "B": 9, + "P": 59, + "O": 5 + }, + "12": { + "a": 9, + "B": 27, + "P": 172, + "O": 19 + }, + "13": { + "a": 9, + "B": 27, + "P": 183, + "O": 21 + }, + "14": { + "a": 9, + "B": 27, + "P": 202, + "O": 22 + }, + "15": { + "a": 27, + "B": 81, + "P": 631, + "O": 73 + }, + "16": { + "a": 27, + "B": 81, + "P": 640, + "O": 82 + }, + "17": { + "a": 27, + "B": 81, + "P": 697, + "O": 85 + }, + "18": { + "a": 27, + "B": 243, + "P": 1766, + "O": 218 + }, + "19": { + "a": 81, + "B": 729, + "P": 5851, + "O": 676 + }, + "20": { + "a": 81, + "B": 729, + "P": 6292, + "O": 712 + }, + "21": { + "a": 81, + "B": 729, + "P": 6533, + "O": 773 + }, + "22": { + "a": 243, + "B": 2187, + "P": 20066, + "O": 2426 + }, + "23": { + "a": 729, + "B": 6561, + "P": 65143, + "O": 7480 + }, + "24": { + "a": 243, + "B": 2187, + "P": 18032, + "O": 2498 + }, + "25": { + "a": 729, + "B": 6561, + "P": 57457, + "O": 7894 + }, + "26": { + "a": 729, + "B": 6561, + "P": 62002, + "O": 8146 + }, + "27": { + "a": 729, + "B": 6561, + "P": 63707, + "O": 8429 + }, + "28": { + "a": 2187, + "B": 19683, + "P": 196244, + "O": 26999 + }, + "29": { + "a": 6561, + "B": 59049, + "P": 631909, + "O": 82981 + }, + "30": { + "a": 2187, + "B": 19683, + "P": 193466, + "O": 27650 + }, + "31": { + "a": 6561, + "B": 59049, + "P": 616327, + "O": 85516 + }, + "32": { + "a": 6561, + "B": 59049, + "P": 653600, + "O": 88238 + }, + "33": { + "a": 6561, + "B": 59049, + "P": 660305, + "O": 92270 + }, + "34": { + "a": 19683, + "B": 177147, + "P": 1990982, + "O": 284951 + }, + "35": { + "a": 59049, + "B": 531441, + "P": 6380443, + "O": 870346 + }, + "36": { + "a": 6561, + "B": 59049, + "P": 571508, + "O": 90197 + }, + "37": { + "a": 19683, + "B": 177147, + "P": 1811903, + "O": 280454 + }, + "38": { + "a": 59049, + "B": 531441, + "P": 5786902, + "O": 860977 + }, + "39": { + "a": 19683, + "B": 177147, + "P": 1981709, + "O": 295982 + }, + "40": { + "a": 59049, + "B": 531441, + "P": 6009760, + "O": 919810 + }, + "41": { + "a": 59049, + "B": 531441, + "P": 6394801, + "O": 938110 + }, + "42": { + "a": 59049, + "B": 531441, + "P": 5884178, + "O": 946301 + }, + "43": { + "a": 177147, + "B": 1594323, + "P": 18551609, + "O": 2902373 + }, + "44": { + "a": 531441, + "B": 4782969, + "P": 58782268, + "O": 8911144 + }, + "45": { + "a": 59049, + "B": 531441, + "P": 6526813, + "O": 1015204 + }, + "46": { + "a": 177147, + "B": 1594323, + "P": 19730970, + "O": 3139497 + }, + "47": { + "a": 531441, + "B": 4782969, + "P": 62792175, + "O": 9560622 + }, + "48": { + "a": 177147, + "B": 1594323, + "P": 19332296, + "O": 3191795 + } + }, + "source_fields": 315, + "units": 174, + "incoming_edges": 207, + "exit_pooling_witness": null + }, + { + "targets": [ + 3, + 4 + ], + "paid": [ + 2, + 2 + ], + "cap": 32, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 2, + "O": 0 + }, + "3": { + "a": 1, + "B": 1, + "P": 3, + "O": 0 + }, + "4": { + "a": 1, + "B": 2, + "P": 5, + "O": 1 + }, + "5": { + "a": 1, + "B": 2, + "P": 7, + "O": 1 + }, + "6": { + "a": 1, + "B": 2, + "P": 9, + "O": 1 + }, + "7": { + "a": 2, + "B": 4, + "P": 19, + "O": 3 + }, + "8": { + "a": 2, + "B": 4, + "P": 20, + "O": 4 + }, + "9": { + "a": 2, + "B": 4, + "P": 24, + "O": 4 + }, + "10": { + "a": 4, + "B": 8, + "P": 53, + "O": 9 + }, + "11": { + "a": 4, + "B": 8, + "P": 55, + "O": 11 + }, + "12": { + "a": 2, + "B": 8, + "P": 36, + "O": 12 + }, + "13": { + "a": 2, + "B": 8, + "P": 41, + "O": 13 + }, + "14": { + "a": 2, + "B": 8, + "P": 49, + "O": 13 + }, + "15": { + "a": 2, + "B": 8, + "P": 54, + "O": 14 + }, + "16": { + "a": 4, + "B": 16, + "P": 79, + "O": 31 + }, + "17": { + "a": 4, + "B": 16, + "P": 92, + "O": 32 + }, + "18": { + "a": 4, + "B": 16, + "P": 108, + "O": 32 + }, + "19": { + "a": 8, + "B": 32, + "P": 233, + "O": 69 + }, + "20": { + "a": 8, + "B": 32, + "P": 235, + "O": 79 + }, + "21": { + "a": 8, + "B": 32, + "P": 240, + "O": 80 + }, + "22": { + "a": 8, + "B": 32, + "P": 263, + "O": 83 + }, + "23": { + "a": 8, + "B": 32, + "P": 277, + "O": 89 + }, + "24": { + "a": 8, + "B": 32, + "P": 246, + "O": 94 + }, + "25": { + "a": 16, + "B": 64, + "P": 499, + "O": 195 + }, + "26": { + "a": 16, + "B": 64, + "P": 554, + "O": 198 + }, + "27": { + "a": 16, + "B": 64, + "P": 594, + "O": 206 + }, + "28": { + "a": 32, + "B": 128, + "P": 1013, + "O": 433 + }, + "29": { + "a": 32, + "B": 128, + "P": 1087, + "O": 451 + }, + "30": { + "a": 32, + "B": 128, + "P": 1188, + "O": 452 + }, + "31": { + "a": 32, + "B": 128, + "P": 1265, + "O": 469 + }, + "32": { + "a": 32, + "B": 128, + "P": 1225, + "O": 501 + } + }, + "source_fields": 100, + "units": 88, + "incoming_edges": 76, + "exit_pooling_witness": { + "rank": 12, + "exit_rank": 4, + "width": 2, + "replication": 1, + "exit_count": 4 + } + }, + { + "targets": [ + 3, + 3, + 5 + ], + "paid": [ + 2, + 2 + ], + "cap": 48, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 2, + "O": 0 + }, + "3": { + "a": 1, + "B": 1, + "P": 3, + "O": 0 + }, + "4": { + "a": 1, + "B": 1, + "P": 4, + "O": 0 + }, + "5": { + "a": 1, + "B": 3, + "P": 8, + "O": 1 + }, + "6": { + "a": 1, + "B": 3, + "P": 11, + "O": 1 + }, + "7": { + "a": 1, + "B": 3, + "P": 14, + "O": 1 + }, + "8": { + "a": 3, + "B": 9, + "P": 37, + "O": 5 + }, + "9": { + "a": 3, + "B": 9, + "P": 46, + "O": 5 + }, + "10": { + "a": 3, + "B": 9, + "P": 48, + "O": 6 + }, + "11": { + "a": 9, + "B": 27, + "P": 143, + "O": 22 + }, + "12": { + "a": 9, + "B": 27, + "P": 170, + "O": 22 + }, + "13": { + "a": 9, + "B": 27, + "P": 169, + "O": 26 + }, + "14": { + "a": 27, + "B": 81, + "P": 532, + "O": 86 + }, + "15": { + "a": 3, + "B": 24, + "P": 108, + "O": 18 + }, + "16": { + "a": 3, + "B": 24, + "P": 132, + "O": 18 + }, + "17": { + "a": 9, + "B": 72, + "P": 412, + "O": 62 + }, + "18": { + "a": 9, + "B": 72, + "P": 456, + "O": 66 + }, + "19": { + "a": 9, + "B": 72, + "P": 500, + "O": 70 + }, + "20": { + "a": 27, + "B": 216, + "P": 1436, + "O": 250 + }, + "21": { + "a": 27, + "B": 216, + "P": 1596, + "O": 258 + }, + "22": { + "a": 27, + "B": 216, + "P": 1700, + "O": 274 + }, + "23": { + "a": 81, + "B": 648, + "P": 5104, + "O": 914 + }, + "24": { + "a": 162, + "B": 1296, + "P": 9292, + "O": 1658 + }, + "25": { + "a": 18, + "B": 162, + "P": 1068, + "O": 192 + }, + "26": { + "a": 54, + "B": 486, + "P": 3298, + "O": 632 + }, + "27": { + "a": 54, + "B": 486, + "P": 3700, + "O": 644 + }, + "28": { + "a": 54, + "B": 486, + "P": 3878, + "O": 688 + }, + "29": { + "a": 162, + "B": 1458, + "P": 11804, + "O": 2248 + }, + "30": { + "a": 54, + "B": 486, + "P": 3576, + "O": 708 + }, + "31": { + "a": 54, + "B": 486, + "P": 3950, + "O": 724 + }, + "32": { + "a": 162, + "B": 1458, + "P": 12160, + "O": 2336 + }, + "33": { + "a": 324, + "B": 2916, + "P": 24016, + "O": 4646 + }, + "34": { + "a": 162, + "B": 1458, + "P": 12192, + "O": 2298 + }, + "35": { + "a": 486, + "B": 4374, + "P": 36484, + "O": 7532 + }, + "36": { + "a": 486, + "B": 4374, + "P": 39514, + "O": 7724 + }, + "37": { + "a": 486, + "B": 4374, + "P": 41648, + "O": 8044 + }, + "38": { + "a": 1458, + "B": 13122, + "P": 125606, + "O": 25912 + }, + "39": { + "a": 972, + "B": 8748, + "P": 78420, + "O": 16530 + }, + "40": { + "a": 1944, + "B": 17496, + "P": 154316, + "O": 31978 + }, + "41": { + "a": 5832, + "B": 52488, + "P": 478252, + "O": 101246 + }, + "42": { + "a": 5832, + "B": 52488, + "P": 496412, + "O": 102262 + }, + "43": { + "a": 5832, + "B": 52488, + "P": 511464, + "O": 104298 + }, + "44": { + "a": 17496, + "B": 157464, + "P": 1551772, + "O": 332906 + }, + "45": { + "a": 162, + "B": 3240, + "P": 20724, + "O": 5106 + }, + "46": { + "a": 486, + "B": 9720, + "P": 68812, + "O": 15758 + }, + "47": { + "a": 486, + "B": 9720, + "P": 71644, + "O": 16742 + }, + "48": { + "a": 486, + "B": 9720, + "P": 78368, + "O": 17170 + } + }, + "source_fields": 370, + "units": 198, + "incoming_edges": 224, + "exit_pooling_witness": null + }, + { + "targets": [ + 2 + ], + "paid": [ + 1, + 1 + ], + "cap": 48, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 2, + "O": 1 + }, + "3": { + "a": 1, + "B": 1, + "P": 3, + "O": 1 + }, + "4": { + "a": 1, + "B": 1, + "P": 4, + "O": 3 + }, + "5": { + "a": 1, + "B": 1, + "P": 5, + "O": 3 + }, + "6": { + "a": 1, + "B": 1, + "P": 6, + "O": 4 + }, + "7": { + "a": 1, + "B": 1, + "P": 7, + "O": 4 + }, + "8": { + "a": 1, + "B": 1, + "P": 8, + "O": 7 + }, + "9": { + "a": 1, + "B": 1, + "P": 9, + "O": 7 + }, + "10": { + "a": 1, + "B": 1, + "P": 10, + "O": 8 + }, + "11": { + "a": 1, + "B": 1, + "P": 11, + "O": 8 + }, + "12": { + "a": 1, + "B": 1, + "P": 12, + "O": 10 + }, + "13": { + "a": 1, + "B": 1, + "P": 13, + "O": 10 + }, + "14": { + "a": 1, + "B": 1, + "P": 14, + "O": 11 + }, + "15": { + "a": 1, + "B": 1, + "P": 15, + "O": 11 + }, + "16": { + "a": 1, + "B": 1, + "P": 16, + "O": 15 + }, + "17": { + "a": 1, + "B": 1, + "P": 17, + "O": 15 + }, + "18": { + "a": 1, + "B": 1, + "P": 18, + "O": 16 + }, + "19": { + "a": 1, + "B": 1, + "P": 19, + "O": 16 + }, + "20": { + "a": 1, + "B": 1, + "P": 20, + "O": 18 + }, + "21": { + "a": 1, + "B": 1, + "P": 21, + "O": 18 + }, + "22": { + "a": 1, + "B": 1, + "P": 22, + "O": 19 + }, + "23": { + "a": 1, + "B": 1, + "P": 23, + "O": 19 + }, + "24": { + "a": 1, + "B": 1, + "P": 24, + "O": 22 + }, + "25": { + "a": 1, + "B": 1, + "P": 25, + "O": 22 + }, + "26": { + "a": 1, + "B": 1, + "P": 26, + "O": 23 + }, + "27": { + "a": 1, + "B": 1, + "P": 27, + "O": 23 + }, + "28": { + "a": 1, + "B": 1, + "P": 28, + "O": 25 + }, + "29": { + "a": 1, + "B": 1, + "P": 29, + "O": 25 + }, + "30": { + "a": 1, + "B": 1, + "P": 30, + "O": 26 + }, + "31": { + "a": 1, + "B": 1, + "P": 31, + "O": 26 + }, + "32": { + "a": 1, + "B": 1, + "P": 32, + "O": 31 + }, + "33": { + "a": 1, + "B": 1, + "P": 33, + "O": 31 + }, + "34": { + "a": 1, + "B": 1, + "P": 34, + "O": 32 + }, + "35": { + "a": 1, + "B": 1, + "P": 35, + "O": 32 + }, + "36": { + "a": 1, + "B": 1, + "P": 36, + "O": 34 + }, + "37": { + "a": 1, + "B": 1, + "P": 37, + "O": 34 + }, + "38": { + "a": 1, + "B": 1, + "P": 38, + "O": 35 + }, + "39": { + "a": 1, + "B": 1, + "P": 39, + "O": 35 + }, + "40": { + "a": 1, + "B": 1, + "P": 40, + "O": 38 + }, + "41": { + "a": 1, + "B": 1, + "P": 41, + "O": 38 + }, + "42": { + "a": 1, + "B": 1, + "P": 42, + "O": 39 + }, + "43": { + "a": 1, + "B": 1, + "P": 43, + "O": 39 + }, + "44": { + "a": 1, + "B": 1, + "P": 44, + "O": 41 + }, + "45": { + "a": 1, + "B": 1, + "P": 45, + "O": 41 + }, + "46": { + "a": 1, + "B": 1, + "P": 46, + "O": 42 + }, + "47": { + "a": 1, + "B": 1, + "P": 47, + "O": 42 + }, + "48": { + "a": 1, + "B": 1, + "P": 48, + "O": 46 + } + }, + "source_fields": 47, + "units": 837, + "incoming_edges": 790, + "exit_pooling_witness": null + }, + { + "targets": [ + 2 + ], + "paid": [ + 1, + 1, + 1 + ], + "cap": 48, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 3, + "O": 1 + }, + "3": { + "a": 1, + "B": 1, + "P": 4, + "O": 1 + }, + "4": { + "a": 1, + "B": 1, + "P": 9, + "O": 4 + }, + "5": { + "a": 1, + "B": 1, + "P": 10, + "O": 4 + }, + "6": { + "a": 1, + "B": 1, + "P": 12, + "O": 5 + }, + "7": { + "a": 1, + "B": 1, + "P": 13, + "O": 5 + }, + "8": { + "a": 1, + "B": 1, + "P": 27, + "O": 13 + }, + "9": { + "a": 1, + "B": 1, + "P": 28, + "O": 13 + }, + "10": { + "a": 1, + "B": 1, + "P": 30, + "O": 14 + }, + "11": { + "a": 1, + "B": 1, + "P": 31, + "O": 14 + }, + "12": { + "a": 1, + "B": 1, + "P": 36, + "O": 17 + }, + "13": { + "a": 1, + "B": 1, + "P": 37, + "O": 17 + }, + "14": { + "a": 1, + "B": 1, + "P": 39, + "O": 18 + }, + "15": { + "a": 1, + "B": 1, + "P": 40, + "O": 18 + }, + "16": { + "a": 1, + "B": 1, + "P": 81, + "O": 40 + }, + "17": { + "a": 1, + "B": 1, + "P": 82, + "O": 40 + }, + "18": { + "a": 1, + "B": 1, + "P": 84, + "O": 41 + }, + "19": { + "a": 1, + "B": 1, + "P": 85, + "O": 41 + }, + "20": { + "a": 1, + "B": 1, + "P": 90, + "O": 44 + }, + "21": { + "a": 1, + "B": 1, + "P": 91, + "O": 44 + }, + "22": { + "a": 1, + "B": 1, + "P": 93, + "O": 45 + }, + "23": { + "a": 1, + "B": 1, + "P": 94, + "O": 45 + }, + "24": { + "a": 1, + "B": 1, + "P": 108, + "O": 53 + }, + "25": { + "a": 1, + "B": 1, + "P": 109, + "O": 53 + }, + "26": { + "a": 1, + "B": 1, + "P": 111, + "O": 54 + }, + "27": { + "a": 1, + "B": 1, + "P": 112, + "O": 54 + }, + "28": { + "a": 1, + "B": 1, + "P": 117, + "O": 57 + }, + "29": { + "a": 1, + "B": 1, + "P": 118, + "O": 57 + }, + "30": { + "a": 1, + "B": 1, + "P": 120, + "O": 58 + }, + "31": { + "a": 1, + "B": 1, + "P": 121, + "O": 58 + }, + "32": { + "a": 1, + "B": 1, + "P": 243, + "O": 121 + }, + "33": { + "a": 1, + "B": 1, + "P": 244, + "O": 121 + }, + "34": { + "a": 1, + "B": 1, + "P": 246, + "O": 122 + }, + "35": { + "a": 1, + "B": 1, + "P": 247, + "O": 122 + }, + "36": { + "a": 1, + "B": 1, + "P": 252, + "O": 125 + }, + "37": { + "a": 1, + "B": 1, + "P": 253, + "O": 125 + }, + "38": { + "a": 1, + "B": 1, + "P": 255, + "O": 126 + }, + "39": { + "a": 1, + "B": 1, + "P": 256, + "O": 126 + }, + "40": { + "a": 1, + "B": 1, + "P": 270, + "O": 134 + }, + "41": { + "a": 1, + "B": 1, + "P": 271, + "O": 134 + }, + "42": { + "a": 1, + "B": 1, + "P": 273, + "O": 135 + }, + "43": { + "a": 1, + "B": 1, + "P": 274, + "O": 135 + }, + "44": { + "a": 1, + "B": 1, + "P": 279, + "O": 138 + }, + "45": { + "a": 1, + "B": 1, + "P": 280, + "O": 138 + }, + "46": { + "a": 1, + "B": 1, + "P": 282, + "O": 139 + }, + "47": { + "a": 1, + "B": 1, + "P": 283, + "O": 139 + }, + "48": { + "a": 1, + "B": 1, + "P": 324, + "O": 161 + } + }, + "source_fields": 47, + "units": 2819, + "incoming_edges": 2772, + "exit_pooling_witness": null + }, + { + "targets": [ + 2, + 4, + 8 + ], + "paid": [ + 1, + 1 + ], + "cap": 64, + "rows": { + "1": { + "a": 1, + "B": 1, + "P": 1, + "O": 0 + }, + "2": { + "a": 1, + "B": 1, + "P": 2, + "O": 0 + }, + "3": { + "a": 1, + "B": 1, + "P": 3, + "O": 0 + }, + "4": { + "a": 1, + "B": 1, + "P": 4, + "O": 0 + }, + "5": { + "a": 1, + "B": 1, + "P": 5, + "O": 0 + }, + "6": { + "a": 1, + "B": 1, + "P": 6, + "O": 0 + }, + "7": { + "a": 1, + "B": 1, + "P": 7, + "O": 0 + }, + "8": { + "a": 1, + "B": 3, + "P": 12, + "O": 1 + }, + "9": { + "a": 1, + "B": 3, + "P": 15, + "O": 1 + }, + "10": { + "a": 3, + "B": 9, + "P": 42, + "O": 4 + }, + "11": { + "a": 3, + "B": 9, + "P": 51, + "O": 4 + }, + "12": { + "a": 9, + "B": 27, + "P": 132, + "O": 16 + }, + "13": { + "a": 9, + "B": 27, + "P": 159, + "O": 16 + }, + "14": { + "a": 27, + "B": 81, + "P": 474, + "O": 55 + }, + "15": { + "a": 27, + "B": 81, + "P": 555, + "O": 55 + }, + "16": { + "a": 9, + "B": 63, + "P": 276, + "O": 52 + }, + "17": { + "a": 9, + "B": 63, + "P": 339, + "O": 52 + }, + "18": { + "a": 27, + "B": 189, + "P": 1014, + "O": 172 + }, + "19": { + "a": 27, + "B": 189, + "P": 1203, + "O": 172 + }, + "20": { + "a": 63, + "B": 441, + "P": 2256, + "O": 457 + }, + "21": { + "a": 63, + "B": 441, + "P": 2697, + "O": 457 + }, + "22": { + "a": 189, + "B": 1323, + "P": 8250, + "O": 1468 + }, + "23": { + "a": 189, + "B": 1323, + "P": 9573, + "O": 1468 + }, + "24": { + "a": 147, + "B": 1029, + "P": 5364, + "O": 1311 + }, + "25": { + "a": 147, + "B": 1029, + "P": 6393, + "O": 1311 + }, + "26": { + "a": 441, + "B": 3087, + "P": 19170, + "O": 4191 + }, + "27": { + "a": 441, + "B": 3087, + "P": 22257, + "O": 4191 + }, + "28": { + "a": 9261, + "B": 64827, + "P": 369276, + "O": 97459 + }, + "29": { + "a": 9261, + "B": 64827, + "P": 434103, + "O": 97459 + }, + "30": { + "a": 27783, + "B": 194481, + "P": 1311054, + "O": 307855 + }, + "31": { + "a": 27783, + "B": 194481, + "P": 1505535, + "O": 307855 + }, + "32": { + "a": 3087, + "B": 52479, + "P": 237144, + "O": 75920 + }, + "33": { + "a": 3087, + "B": 52479, + "P": 289623, + "O": 75920 + }, + "34": { + "a": 9261, + "B": 157437, + "P": 895674, + "O": 238646 + }, + "35": { + "a": 9261, + "B": 157437, + "P": 1053111, + "O": 238646 + }, + "36": { + "a": 21609, + "B": 367353, + "P": 2092728, + "O": 598823 + }, + "37": { + "a": 21609, + "B": 367353, + "P": 2460081, + "O": 598823 + }, + "38": { + "a": 64827, + "B": 1102059, + "P": 7639914, + "O": 1866668 + }, + "39": { + "a": 64827, + "B": 1102059, + "P": 8741973, + "O": 1866668 + }, + "40": { + "a": 17493, + "B": 297381, + "P": 1517232, + "O": 514125 + }, + "41": { + "a": 17493, + "B": 297381, + "P": 1814613, + "O": 514125 + }, + "42": { + "a": 52479, + "B": 892143, + "P": 5471010, + "O": 1614456 + }, + "43": { + "a": 52479, + "B": 892143, + "P": 6363153, + "O": 1614456 + }, + "44": { + "a": 1102059, + "B": 18735003, + "P": 112872120, + "O": 36329983 + }, + "45": { + "a": 1102059, + "B": 18735003, + "P": 131607123, + "O": 36329983 + }, + "46": { + "a": 3306177, + "B": 56205009, + "P": 402208458, + "O": 113058109 + }, + "47": { + "a": 3306177, + "B": 56205009, + "P": 458413467, + "O": 113058109 + }, + "48": { + "a": 892143, + "B": 15166431, + "P": 79984956, + "O": 30572978 + }, + "49": { + "a": 892143, + "B": 15166431, + "P": 95151387, + "O": 30572978 + }, + "50": { + "a": 2676429, + "B": 45499293, + "P": 288338754, + "O": 95270159 + }, + "51": { + "a": 2676429, + "B": 45499293, + "P": 333838047, + "O": 95270159 + }, + "52": { + "a": 6245001, + "B": 106165017, + "P": 662299896, + "O": 235509644 + }, + "53": { + "a": 6245001, + "B": 106165017, + "P": 768464913, + "O": 235509644 + }, + "54": { + "a": 18735003, + "B": 318495051, + "P": 2356382838, + "O": 728821178 + }, + "55": { + "a": 18735003, + "B": 318495051, + "P": 2674877889, + "O": 728821178 + }, + "56": { + "a": 5055477, + "B": 85943109, + "P": 488423400, + "O": 200241681 + }, + "57": { + "a": 5055477, + "B": 85943109, + "P": 574366509, + "O": 200241681 + }, + "58": { + "a": 15166431, + "B": 257829327, + "P": 1733930190, + "O": 621308265 + }, + "59": { + "a": 15166431, + "B": 257829327, + "P": 1991759517, + "O": 621308265 + }, + "60": { + "a": 318495051, + "B": 5414415867, + "P": 35466946764, + "O": 13749712603 + }, + "61": { + "a": 318495051, + "B": 5414415867, + "P": 40881362631, + "O": 13749712603 + }, + "62": { + "a": 955485153, + "B": 16243247601, + "P": 124777561686, + "O": 42424952293 + }, + "63": { + "a": 955485153, + "B": 16243247601, + "P": 141020809287, + "O": 42424952293 + }, + "64": { + "a": 15166431, + "B": 652156533, + "P": 2790396300, + "O": 1319493419 + } + }, + "source_fields": 723, + "units": 371, + "incoming_edges": 390, + "exit_pooling_witness": null + } + ], + "controls": [ + "exit pooling rejected by original rank-4 cut at n=12", + "explicit rank budget failure", + "nonseparated rule rejected" + ], + "core_sha256": { + "library.py": "06e3b44704048461de0ff0ab55fe158b95df412688324b88fd3d81b929ef0d92", + "PROOF.md": "05a04e5ba1db71b9e40397e3220f047411906a5e8a70609c7a879499e6325e88" + } +} diff --git a/research/quantitative-rank-library/NOTICE.md b/research/quantitative-rank-library/NOTICE.md new file mode 100644 index 0000000000..4deb1f486b --- /dev/null +++ b/research/quantitative-rank-library/NOTICE.md @@ -0,0 +1,16 @@ +# Attribution and license notice + +New material is prepared for CubeJerry with substantial OpenAI assistance +under the repository's Apache-2.0 license. It is a scoped proof, an exact +metadata reference and a bounded literal-word checker. + +The unchanged reference texts preserve their own authorship and assistance +notices. SOURCES.json pins their exact canonical commits, paths and bytes. +The principal premises are Jacob Alan Sussman's integer compiler, zxv's +chronological construction, Mihir Srivastava's batch/growth work, +codyw912's plateau divisor, Nick Petalas's rank/homogeneous bounds and +#5071's symbolic recurrence. None is claimed as new here. + +The tape worker independently supplied and checked the n=135 exit-pooling +control. Root and peer reviews describe their own methods and snapshots. +No independent human or proof-kernel acceptance is implied. diff --git a/research/quantitative-rank-library/PR-TITLE.txt b/research/quantitative-rank-library/PR-TITLE.txt new file mode 100644 index 0000000000..0a55ef6432 --- /dev/null +++ b/research/quantitative-rank-library/PR-TITLE.txt @@ -0,0 +1 @@ +Generate exact chronological compiler library tables with product aggregation and explicit binary and tape cost bounds diff --git a/research/quantitative-rank-library/PR.md b/research/quantitative-rank-library/PR.md new file mode 100644 index 0000000000..ecb2a25fae --- /dev/null +++ b/research/quantitative-rank-library/PR.md @@ -0,0 +1,113 @@ +## Change and mathematical scope + +The retained compiler proofs bound finite widths but leave numerical library +generation and full native-word generation as different obligations. This +package supplies an exact evaluator for all smaller-rank metadata under the +fixed separated default-height, least-chronological batching policy. It +constructs evaluated integer replication, productive width, expanded +rank-one leaf count and expanded mixed-unit count at every rank through N. + +Ordered target-role and paid-position product tables recover the source +census without enumerating paid paths or individual unit slots. Every +source-complement divisor and every original one-job exit divisor remains +present. Repeated exits may aggregate additive cost, but their counts may +not cancel individual invocation denominators. + +The written theorem gives explicit parameter-dependent K/Z bounds. For +each fixed rule, the indexed metadata computation takes N times a fixed +power of log N in bit work. A separately specified fixed-tape scan +construction takes N squared times a fixed power of log N, with library +access, arithmetic, sorting, copies, resets, erasure and historical backing +charged. This outputs N rows; it is not polynomial in the input length log N. + +## Exact result and novelty + +The gcd/LCM law is inherited from #4507 and #5071. The width divisor comes +from #4638, with #5962's sharper multiplicative-rank refinement credited. +The new result is compressed exact all-rank metadata generation and its +complete bit-cost accounting. A normalized contracting-chain argument +bounds fully expanded leaf and mixed-unit counts without assuming positive +rank surplus. No factorization or unevaluated arithmetic-expression oracle +is used. Old nested widths are a different policy and are not substituted. + +This complements the source-occurrence and complement-port codecs at +[CubeJerry commit bd63147](https://github.com/CubeJerry/integer-mult-bounds/tree/bd63147b1a193f68b5713e5814ac3b2c743beff8/research/source-complement-port-index). +It supplies their numerical smaller-library data, not the validity or +physical implementation of the smaller native programs. + +## Sources and reproduction + +Canonical base: `e54523517d0f03e58352e647c403a5af3e525a57`. +`SOURCES.json` authenticates eight unchanged theorem/context texts by exact +commit, path, Git blob and SHA-256. There are no imported predecessor +executables. From the package directory, Python 3.12 and standard library: + +```sh +python -I -W error -B verify.py +python -I -O -W error -B verify.py +``` + +Expected status: `PASS_QUANTITATIVE_RANK_LIBRARY`. Normal and optimized +receipts agree. An independent literal role-word/path oracle checks all +four library integers via prime deficits and normalized Fraction recurrences: +35 fixtures, 1,061 library rows, 24,586 units, 51,727 cuts and 14,278 sources. +Fifteen rejection controls include cut pooling, product overwrite, missing +matched-job subtraction, fit equality, missing outer units and merged roles. +Two fixtures have negative rank surplus. + +A larger 2,048-row negative-surplus case has maximum 336-bit output values. +It inspects 85,044 product pairs while leaving 387,420,489 maximum-depth +paid paths unexpanded. The #6612 homogeneous formula is checked on 1,023 +rows as credited calibration. Separate root and tape-worker reviews add +their own literal constructions and complete-cost checks. + +## Limitations and kappa status + +**No new kappa.** The selected conditional `0.00363005817` is unchanged. +No selected certificate is edited and no selected astronomical library or +1920-fold word is emitted. Fully encoded native-word size still needs +local scalar-word, coefficient and adapter production bounds. Native +all-column semantics, whole-job adapters, ownership/erasure, physical +stock/routing, precision/tapes, analytic recovery and all five foundational +assumptions remain conditional. O_n counts expanded mixed-unit occurrences; +it is not live memory. Python is not the separately priced tape procedure. + +## Credit and assistance + +Prepared for @CubeJerry with substantial OpenAI assistance in proof, +implementation and verification. Credit Jacob Alan Sussman for the integer +lockstep compiler; zxv for the retained flow; Mihir Srivastava (#4507/#4586), +codyw912 (#4638), Nick Petalas (#5962/#6612), #5071's symbolic recurrence, +the published source-row/port packages and all retained native/flow lineage. +The separate tape worker supplied the strict-separation n=135 pooling +control. Reference notices are unchanged. Independent human and formal +proof-kernel acceptance are not claimed. + +## Independent acceptance checks + +[REVIEW.md](REVIEW.md) records the root's separate proof/code review and +literal target-field/parent-edge oracle. That oracle checks every census and +all four library outputs for seven fixed rules and 336 complete ranks, with +zero/negative surplus and coincident products included. It rejects an actual +exit-pooling mutant on the smaller n=12 witness, an exceeded rank budget and +a nonseparated rule. [The complementary peer review](peer-review/REVIEW.md) +independently authenticates the retained width/flow sources, audits all +indexed and sequential costs, and verifies a different n=135 cut witness. + +```sh +python3 -I -W error -B research/quantitative-rank-library/independent_check.py +python3 -I -W error -B research/quantitative-rank-library/peer-review/exit_cut_control.py +``` + +Final packaged author normal and optimized runs agree. The independent +scientific receipts pin the reviewed bytes. No human or proof-kernel +acceptance is inferred. The complete proposed PR description is `PR.md`. + +## Open next questions + +Can the evaluated leaf/unit counts be bound to an actual emitted native +scalar-word and owner manifest with a complete bit-output/production bound? +This matters because numerical library generation does not by itself +construct the smaller programs. The first step is to audit the retained +#6878 occurrence adapters and the native word's constant encodings; the +obligation is blocked by any missing uniform local-word/adapter producer. diff --git a/research/quantitative-rank-library/PROOF.md b/research/quantitative-rank-library/PROOF.md new file mode 100644 index 0000000000..36df151594 --- /dev/null +++ b/research/quantitative-rank-library/PROOF.md @@ -0,0 +1,297 @@ +# Exact all-rank compiler metadata without expanding paid paths + +Written proof with bounded exact corroboration; independent review is +recorded separately. No native admission or new kappa. Exact base and +predecessor pins are in `SOURCES.json`; the scope is recorded in `TASK.json`. + +## 1. The retained flow and outputs + +Fix nonempty target and paid histograms `(k,W_k)` and `(r,P_r)`, with +positive integer multiplicities and + +``` +2<=k_min<=k<=m=max k, 1<=r<=r_max=m. A depth-h path has paid +product rho; a unit profile of degree G_n-h has target product c and +multiplicity u(alpha). It is present iff `m*rho*c<=n`. Its target k and +paid r jobs have true ranks rho*c*k and rho*c*r. Pascal matching is a +bijection of formal occurrences, never a quotient by equal products. + +The outputs are evaluated binary integers: replication a_n, productive +width B_n, expanded rank-one leaf count P_n and expanded mixed-unit count +O_n. O_n is not peak live storage. If an actual unit contract supplies h +owned fields, h*O_n is a safe no-reuse count, before their physical extent. +Base rows are `a_n=B_n=1, P_n=n, O_n=0` for 1<=n0. (1) +``` + +Proof: A counts all target slots with their complete formal multiplicity. +Every nondeepest paid demand is matched: after removing target factor k, +its child has dilation rho*r and column c/k, and +`m*rho*r*c/k < m*rho*c<=n`. The Pascal identity partitions the parent +occurrences among these child slots, including their first role. Conversely +every matched target slot has this incoming demand at the same true rank. +Subtracting counts leaves exactly the fresh targets, hence S_s>=0. A root +unit of column k_min^G exists, so S>0. This is a universal matching proof; +an executable nonnegativity assertion would not replace it. + +Every deepest path is present because +`rho<=r_max^G<=k_min^G<=n/m`. It has one degree-zero unit and all its paid +jobs exit. Therefore + +``` +E_e=R_(G+1)(e) (2) +``` + +counts distinct one-job cuts of rank e. E_e is not the number of arrays +available at any one cut. These counts agree with the source-row and +complement-port codecs' fresh physical identities; this evaluator does +not enumerate or route their physical rows. + +## 3. Every batch constraint and expanded-count recurrence + +Source complements occur upfront, so each s0} + union {B_e:E_e>0}), +B_n=a_n*S, (3) +P_n=sum_(s=k_min^(G+1)>floor(n/m)` and integrality gives s>n/m. A nonroot +fresh source has a missing parent above the cap; multiplying that parent's +integer product by its positive last paid rank gives the same s>n/m. +Fit gives s<=n. Thus positive complement ranks obey +`n-s<(m-1)n/m`. Each exit obeys `e<=r_max*n/m<=(m-1)n/m`. +Set alpha=(m-1)/m: every recursive edge contracts by alpha. + +Evaluating (1)--(4) for n=1,...,N therefore gives exactly the separated +literal flow's least-chronological library metadata. Native arbitrary-input +correctness, all-column lift, adapters, disjoint splitting and physical +finite closure remain the source's separate hypotheses. + +## 4. Fully evaluated output sizes, without positive rank surplus + +Assume N>=m; otherwise all rows are base rows. For positive x let +ell(x)=bit_length(x). Put L=ell(N), G=G_N, K0=max(W,P), and + +``` +Ubar=(G+1)*K0^G, Sbar=W*Ubar, +F=1+(W+1)*Ubar+P^(G+1), D=m*L. (5) +``` + +Deleting eligibility tests gives +`U_n<=sum_(h=0)^G P^h W^(G-h)<=Ubar`, and hence S_n<=Sbar. +The sum of smaller-batch multiplicities is at most Sbar+P^(G+1). +These bounds hold for every n<=N since G_n<=G. + +### A cited width divisor, with no factorization cost + +Let b count distinct integers >=2 among all target and paid ranks. +The rank semigroup has at most (L+1)^b products <=floor(N/m): each has +a representation whose b generator exponents are <=L. Repeated +representations only loosen this upper bound. Rank one is omitted. + +#4638 proves, for this default policy, the all-prime divisor +`B_n | product_gamma S(gamma)^tau` for every n<=N, over source-count +plateaus up to the cap, with `tau=m*ceil(log2 k_min)`. Substituting the +generator-box and Sbar bounds yields the explicit integer envelope + +``` +beta=tau*(L+1)^b*ell(Sbar), +log2 B_n<=beta, log2 a_n<=beta. (6) +``` + +This uses all primes of the source counts, including new ones absent from +rank factors. No factorization, valuation algorithm or shared unevaluated +expression is used. The sharper multiplicative-rank result of #5962 is +available but unnecessary. Equation (6) instantiates an existing theorem; +it is not a new width asymptotic. It does not apply to the old nested +choice a_n=B_(n-1), which can have Theta(N log N) width bits. + +### Expanded leaves and mixed-unit occurrences + +Set Y_n=(B_n+P_n+O_n)/B_n. From (4), positivity and S>=1, + +``` +Y_n=1+U_n/S+sum_batches(t/S)*(P_q+O_q)/B_q + <=(1+U_n+sum_batches t)*max_child Y_q + <=F*max_child Y_q. (7) +``` + +There is a deepest exit since P>0, so the maximum is nonempty. Base +ratios are n+1<=m. Bernoulli gives alpha^m<1/2; after D=m*ell(N) +contracting edges a positive rank would be below one. Every actual chain +therefore reaches a base rank in at most D edges. Iterating (7) gives + +``` +B_n+P_n+O_n<=B_n*m*F^D, +ell(B_n+P_n+O_n)<=beta+ell(m)+D*ell(F)+1. (8) +``` + +This holds also for formal rules with zero or negative rank surplus. +No saving, moment-root or native-existence assertion is needed. All +replicated child copies remain counted. + +## 5. Record counts and an explicit common bit cap + +The total product-table and current-rank record counts are bounded by + +``` +M_T=binomial(G+d,d), M_R=binomial(G+q+1,q), +V=binomial(G+d+q-1,d+q-1), E=binomial(G+q,q-1). (9) +``` + +M_T covers target degrees 0..G; M_R covers paid degrees 0..G+1. For +h+g=G, stars and bars and convolution give at most V product pairs, +including rejected fits. The signed source list has at most (d+q)V +contributions before deduplication; E bounds distinct exits. Coincident +products do not increase these bounds. G=0 and singleton alphabets are +included in the displayed formulas. + +Let S_bit encode both nonempty lists as Gamma(list length), followed by +Gamma(rank) and Gamma(multiplicity) for each entry. This counts supplied +histogram bits, not an independently supplied native word. Define + +``` +K=(S_bit+1)^2+d*M_T+q*M_R + +(N+1)*((d+q+2)*V+E+G+2), +Z=8*(S_bit+L+(G+2)*ell(m+W+P+2) + +beta+ell(m)+D*ell(F)+ell(K)+2), +J=M_T+M_R+(d+q+2)*V+E+G+S_bit+2, +L_local=J*Z. (10) +``` + +Z bounds ordinary integer fields and arithmetic temporaries. Word-product +keys are at most m^(G+1). Weighted counts are at most the corresponding +powers of W and P. All target contributions together are <=W*Ubar; +matched incoming contributions are no larger, so signed partial sums +have magnitude <=2*W*Ubar. Equations (6)--(8) bound library values. +Division numerators such as a*S_s have at most the sum of operand bit +lengths, while each nonnegative completed summand is <=its final sum. +Loop counters and record addresses are covered by L, S_bit and ell(K). +Binomial bounds can be computed by successive exact multiply/divide +steps, whose intermediates add at most one factor's length. The generous +factor eight absorbs these fixed additions. No bound is emitted in unary. + +Build each T/R degree by generating fixed-rank extensions, sorting and +adding equal keys. At most d*M_T+q*M_R records are generated. At each n, +enumerate (9), aggregate signed source records by sorting, and evaluate +(3)--(4) against the earlier completed library rows. All zero candidates, +all actual recursive ranks and every chronological exit divisor are paid. + +## 6. Indexed and sequential construction models + +### Indexed metadata + +Specify indexed storage explicitly: fetching/storing an O(Z)-bit record +with an O(Z)-bit address costs O(Z) bit work. Schoolbook multiplication +and division cost O(Z^2). Euclid takes O(Z) divisions, so a conservative +gcd charge is O(Z^3). Comparison sorting k records costs O(k log k) +comparisons; log k=O(Z), so its bit bill fits O(k Z^2). Thus + +``` +T_indexed=O(K*Z^3). (11) +``` + +The reference integer operations can be replaced by these elementary +algorithms. This is not a literal CPython-runtime guarantee or a claim +of free random access to native payloads. + +### Sequential companion, with library access charged + +Keep completed library rows in an append-only sequence with rank tags. +For every child access, scan at most N records, copy the selected row to +arithmetic tapes, and return the library head. Comparisons, copying and +return together cost O(N*Z). The earlier child values remain immutable. + +Keep product tables and current-rank contributions in fixed local regions +of total extent O(L_local). Full scans and insertion sorting, including +copies, counter updates and head resets, cost at most O(L_local^2) per +generated record or recurrence operation. Elementary arithmetic uses +O(Z) workspace and O(Z^3) time per operation. Erase and reuse the same +local regions; their historical backing remains charged. These explicit +scan recipes give a fixed-number-of-tapes companion with + +``` +T_sequential=O(K*(N*Z+L_local^2+Z^3)). (12) +``` + +Python list access is not asserted to be a tape instruction. The four +library values, rank tags and work regions use O((N+J)*Z) historical +cells. Optionally retaining every per-rank source/exit census adds at +most O(K*Z) output bits; their writing fits both time bounds and their +backing is retained. Neither erasure nor streaming makes written output +free. Uniform parsing, validation and bound setup fit the S_bit term and +the explicitly counted arithmetic; alphabet-size dependence is retained. + +For each fixed rule, G=O(log N) and all parameters in (9)--(10), apart +from N in K, are fixed powers of log N. Thus the indexed bound is +N*polylog N and the sequential bound is N^2*polylog N. Every output is a +fully evaluated integer of polylogarithmic bit length. Constants and +powers depend on the fixed rule through the displayed formulas. This +is not polynomial in log N: the output contains N library rows. + +## 7. Scope and remaining obligations + +This quantitatively evaluates the complete formal rank-induction +metadata for the separated default-height least-chronological policy. +It includes every source complement and each original exit divisor, +without enumerating P^G paid paths or W^G unit slots. The new computation +uses the existing width theorem; the normalized count estimate also +bounds expanded leaves/units when no positive rank surplus is assumed. + +Actual scalar-word size is not determined by rank counts. It additionally +depends on the native word's instruction/constant encodings and on +whole-job adapter production. Such production bounds must be supplied +before an encoded native word or its physical runtime can be bounded. +An evaluated B_q is not proof of a valid smaller program. No arrays are +routed by this evaluator, and the native/all-column, ownership, precision, +fixed-tape payload, analytic and outer interfaces remain conditional. +No selected astronomical rank library or 1920-fold word is materialized. +There is no new kappa or foundational assumption discharge. + +Credit #4507/#5071 for batch recurrences, #4638/#5962 for width envelopes, +Jacob Alan Sussman and zxv for the lockstep/Pascal flow, and the published +source-row/port packages for exact occurrence binding. All original source +notices are retained. Prepared for CubeJerry with substantial OpenAI +assistance; independent human or proof-kernel acceptance is not claimed. diff --git a/research/quantitative-rank-library/README.md b/research/quantitative-rank-library/README.md new file mode 100644 index 0000000000..acbc7ec3f4 --- /dev/null +++ b/research/quantitative-rank-library/README.md @@ -0,0 +1,135 @@ +# Generate exact chronological compiler libraries from product tables + +For a fixed separated default-height mixed rule, this package computes +every replication, productive width, expanded rank-one leaf count and +expanded mixed-unit count through rank N as evaluated binary integers. +It avoids enumerating paid paths and individual unit slots. + +The [proof](PROOF.md) gives explicit parameter-dependent bounds. In its +declared indexed metadata model the bit work is `N*polylog N`; a separately +specified fixed-tape scan construction costs `N^2*polylog N`. The powers +and constants depend on the fixed rule through K, Z and the local-table +formulas. This is not polynomial in log N: N completed library rows are +output. No native scalar word or physical source-routing program is emitted. + +## Exact result and predecessor delta + +The least chronological gcd/LCM policy is unchanged. Source complements +retain their actual multiplicities, and each deepest exit retains its +original one-job cut. Ordered target-word and paid-word product tables +recover fresh sources by subtracting matched incoming jobs from all target +slots. Coincident products add counts; paid positions retain multiplicity. +Source rank n has no complementary program. + +``` +a_n=lcm({B_(n-s)/gcd(B_(n-s),S_s):s