SPB Git

spb/wp32_uqo

Public
22.7 KB · 908 lines json
1{2  "utc": "2026-10-31T01:34:02+00:00",3  "k": 5,4  "n_range_tabulated": [5    11,6    487  ],8  "status_counts": {9    "fully certified": 3810  },11  "fully_certified_n": [12    11,13    12,14    13,15    14,16    15,17    16,18    17,19    18,20    19,21    20,22    21,23    22,24    23,25    24,26    25,27    26,28    27,29    28,30    29,31    30,32    31,33    32,34    33,35    34,36    35,37    36,38    37,39    38,40    39,41    40,42    41,43    42,44    43,45    44,46    45,47    46,48    47,49    4850  ],51  "largest_fully_certified_n": 48,52  "values_11_to_22": {53    "11": 6,54    "12": 8,55    "13": 9,56    "14": 8,57    "15": 8,58    "16": 8,59    "17": 10,60    "18": 10,61    "19": 10,62    "20": 10,63    "21": 10,64    "22": 1165  },66  "threshold_n0": 23,67  "value_at_and_above_threshold": 12,68  "Z_P22_5": 11,69  "Z_P23_5": 12,70  "Z_P25_5": 12,71  "boundary_parameter_p": 18,72  "boundary_n1": 26,73  "boundary_c_max": 14,74  "boundary_N_max": 154,75  "boundary_window_instances": 130,76  "boundary_window_complete_26_to_154": true,77  "boundary_window_all_drat_verified": true,78  "boundary_p18_solve_seconds": {79    "min": 17.428,80    "max": 266.811,81    "median": 94.241,82    "total": 13018.683  },84  "boundary_p18_check_seconds": {85    "min": 13.275,86    "max": 231.346,87    "median": 80.59,88    "total": 11741.189  },90  "boundary_p18_proof_lines": {91    "min": 1214641,92    "max": 4923281,93    "total": 34819585794  },95  "boundary_window_solve_seconds": {96    "min": 17.428,97    "max": 266.811,98    "mean": 100.6,99    "total": 12972.1100  },101  "boundary_window_check_seconds": {102    "min": 13.275,103    "max": 231.346,104    "mean": 90.7,105    "total": 11700.7106  },107  "boundary_window_proof_lines": {108    "min": 1214641,109    "max": 4923281,110    "total": 346502796111  },112  "boundary_window_proof_bytes": 38979600989,113  "boundary_window_proof_gigabytes": 39,114  "fortcover_certified_n": [115    11,116    12,117    13,118    14,119    15,120    16,121    17,122    18,123    19,124    20,125    21,126    22127  ],128  "fortcover_largest_n": 22,129  "boundary_p18_cnf_vars_at_154": 14323,130  "boundary_p18_cnf_clauses_at_154": 28933,131  "boundary_obstruction_n25_p18_beta": 10,132  "boundary_table_cells": 234,133  "boundary_table_p_range": [134    12,135    24136  ],137  "boundary_table_n_range": [138    13,139    30140  ],141  "boundary_fails_at_25_for_all_p_tested": true,142  "brute_force_max_n": 27,143  "brute_force_total_subsets_enumerated": 432226268255,144  "brute_force_total_wall_seconds": 4125.7,145  "brute_force_n23_subsets_size11": 13340783196,146  "brute_force_n25_subsets_size11": 37353738800,147  "fortcover_certificates_verified": 14,148  "fortcover_certificates_total": 14,149  "upper_witness_replays_ok": 28,150  "upper_witness_replays_total": 28,151  "P7_replays_ok_12_to_60": true,152  "T1_all_ok": true,153  "T1_n_count": 39,154  "T2_passed": 1200,155  "T2_total": 1200,156  "CS6_mismatches": 0,157  "CS6_total": 5400,158  "T8_mismatches": 0,159  "T8_total": 5600,160  "holdout": [161    32,162    35,163    37,164    41,165    44,166    48167  ],168  "holdout_values": {169    "32": 12,170    "35": 12,171    "37": 12,172    "41": 12,173    "44": 12,174    "48": 12175  },176  "holdout_prediction_12_all_correct": true,177  "holdout_fortcover_search_timeouts": 6,178  "holdout_fortcover_search_witness_found": 0,179  "round_sat_unsat_agreements": [180    11,181    12,182    13,183    14,184    15,185    16,186    17187  ],188  "round_sat_timeouts": [189    17,190    18,191    19,192    20,193    21194  ],195  "versions": {196    "python": "3.14.7",197    "python_sat": "1.9.dev17",198    "platform": "darwin",199    "worker": "M4M64c"200  },201  "drat_trim_source_sha256": "d834b649f437e091597f5347f259b9f681087f89ca0844d0cee250a1a1a0c2ee",202  "worker": "M4M64c (16 cores, Apple Silicon, macOS 26.4)",203  "metrics": {204    "utc": "2026-10-31T01:34:02+00:00",205    "k": 5,206    "largest_fully_certified_n": 48,207    "threshold_n0": 23,208    "value_at_and_above_threshold": 12,209    "Z_P22_5": 11,210    "Z_P23_5": 12,211    "Z_P25_5": 12,212    "boundary_parameter_p": 18,213    "boundary_n1": 26,214    "boundary_c_max": 14,215    "boundary_N_max": 154,216    "boundary_window_instances": 130,217    "boundary_window_complete_26_to_154": true,218    "boundary_window_all_drat_verified": true,219    "boundary_window_proof_bytes": 38979600989,220    "boundary_window_proof_gigabytes": 39,221    "fortcover_largest_n": 22,222    "boundary_p18_cnf_vars_at_154": 14323,223    "boundary_p18_cnf_clauses_at_154": 28933,224    "boundary_obstruction_n25_p18_beta": 10,225    "boundary_table_cells": 234,226    "boundary_fails_at_25_for_all_p_tested": true,227    "brute_force_max_n": 27,228    "brute_force_total_subsets_enumerated": 432226268255,229    "brute_force_total_wall_seconds": 4125.7,230    "brute_force_n23_subsets_size11": 13340783196,231    "brute_force_n25_subsets_size11": 37353738800,232    "fortcover_certificates_verified": 14,233    "fortcover_certificates_total": 14,234    "upper_witness_replays_ok": 28,235    "upper_witness_replays_total": 28,236    "P7_replays_ok_12_to_60": true,237    "T1_all_ok": true,238    "T1_n_count": 39,239    "T2_passed": 1200,240    "T2_total": 1200,241    "CS6_mismatches": 0,242    "CS6_total": 5400,243    "T8_mismatches": 0,244    "T8_total": 5600,245    "holdout_prediction_12_all_correct": true,246    "holdout_fortcover_search_timeouts": 6,247    "holdout_fortcover_search_witness_found": 0,248    "drat_trim_source_sha256": "d834b649f437e091597f5347f259b9f681087f89ca0844d0cee250a1a1a0c2ee",249    "worker": "M4M64c (16 cores, Apple Silicon, macOS 26.4)",250    "fortcover_n23_proof_lines": "59527561",251    "fortcover_n23_checker_seconds": "2486",252    "fortcover_n23_proof_gigabytes": "4.0",253    "fortcover_n23_num_forts": "87239",254    "fortcover_n25_proof_lines_unverified": "103621714",255    "fortcover_n25_proof_gigabytes_unverified": "7.7"256  },257  "reportedValues": [258    {259      "label": "Stabilization threshold n0 for Z(P(n,5)) = 12",260      "value": "23",261      "unit": "n",262      "location": "Theorem 5.1, abstract"263    },264    {265      "label": "Z(P(n,5)) for all n >= 23",266      "value": "12",267      "unit": "vertices",268      "location": "Theorem 5.1, abstract"269    },270    {271      "label": "Z(P(22,5))",272      "value": "11",273      "unit": "vertices",274      "location": "Theorem 5.1 (sharpness), table of exact values"275    },276    {277      "label": "Boundary parameter p (first-force sources)",278      "value": "18",279      "unit": "vertices",280      "location": "Lemma 3.3, proof of Theorem 5.1"281    },282    {283      "label": "Finite window upper end N_max",284      "value": "154",285      "unit": "n",286      "location": "Lemma 3.2/3.3, proof of Theorem 5.1"287    },288    {289      "label": "DRAT-verified boundary certificates in the window 26..154",290      "value": "129",291      "unit": "certificates",292      "location": "Section 4.3, verification table"293    },294    {295      "label": "Largest n with a fully certified value in the table",296      "value": "48",297      "unit": "n",298      "location": "Table of exact values"299    },300    {301      "label": "Largest n certified by exhaustive enumeration",302      "value": "27",303      "unit": "n",304      "location": "Section 4.1"305    },306    {307      "label": "11-subsets enumerated at n = 25 (no forcing set)",308      "value": "37353738800",309      "unit": "subsets",310      "location": "Section 4.1 table, Theorem 5.1 step 4"311    },312    {313      "label": "11-subsets enumerated at n = 23 (no forcing set)",314      "value": "13340783196",315      "unit": "subsets",316      "location": "Section 4.1 table"317    },318    {319      "label": "beta_18(25): minimum boundary of an 18-set in P(25,5) (obstruction)",320      "value": "10",321      "unit": "vertices",322      "location": "Section 4.2, Section 7"323    },324    {325      "label": "Total drat-trim verification time for the p = 18 window",326      "value": "11700.7",327      "unit": "seconds",328      "location": "Section 4.3, verification scaling table"329    },330    {331      "label": "Order-independence test passes (T2)",332      "value": "1200",333      "unit": "seed sets",334      "location": "Computational framework section"335    },336    {337      "label": "Holdout predictions correct (all six holdout values equal 12)",338      "value": "6",339      "unit": "values",340      "location": "Section 4.5"341    },342    {343      "label": "Values Z(P(n,5)) for n = 11..22 (6,8,9,8,8,8,10,10,10,10,10,11)",344      "value": "6,8,9,8,8,8,10,10,10,10,10,11",345      "unit": "vertices",346      "location": "Theorem 5.1, table of exact values"347    },348    {349      "label": "Maximum number of occupied columns c_max for p = 18",350      "value": "14",351      "unit": "columns",352      "location": "Lemma 3.2, proof of Theorem 5.1"353    },354    {355      "label": "Lower end n_1 of the certified boundary window",356      "value": "26",357      "unit": "n",358      "location": "Section 4.3, proof of Theorem 5.1"359    },360    {361      "label": "Total drat-trim verification time for the p = 18 window 26..154",362      "value": "11700.7",363      "unit": "seconds",364      "location": "Section 4.3, verification scaling table"365    },366    {367      "label": "Total CaDiCaL solve time for the p = 18 window 26..154",368      "value": "12972.1",369      "unit": "seconds",370      "location": "Section 4.3, verification scaling table"371    },372    {373      "label": "Mean per-instance CaDiCaL solve time, p = 18 window",374      "value": "100.6",375      "unit": "seconds",376      "location": "Section 4.3"377    },378    {379      "label": "Mean per-instance drat-trim time, p = 18 window",380      "value": "90.7",381      "unit": "seconds",382      "location": "Section 4.3"383    },384    {385      "label": "Total DRAT proof lines, p = 18 window 26..154",386      "value": "346502796",387      "unit": "lines",388      "location": "Section 4.3"389    },390    {391      "label": "Total size of DRAT proofs on disk, p = 18 window 26..154",392      "value": "39.0",393      "unit": "GB",394      "location": "Section 4.3, Section 7"395    },396    {397      "label": "CNF variables of F(154,18)",398      "value": "14323",399      "unit": "variables",400      "location": "Section 4.3"401    },402    {403      "label": "CNF clauses of F(154,18)",404      "value": "28933",405      "unit": "clauses",406      "location": "Section 4.3"407    },408    {409      "label": "Total subsets enumerated by the C oracle, n = 11..27",410      "value": "432226268255",411      "unit": "subsets",412      "location": "Section 4.1"413    },414    {415      "label": "Second exhaustive enumeration (first-force normalization): total sets tested, 11 <= n <= 40",416      "value": "344080112924",417      "unit": "sets",418      "location": "Computational Result 6.1, abstract"419    },420    {421      "label": "Second exhaustive enumeration: total wall-clock time",422      "value": "2345.7",423      "unit": "seconds",424      "location": "Computational Result 6.1"425    },426    {427      "label": "Second exhaustive enumeration: 11-sets tested at n = 23 (none forcing)",428      "value": "472120740",429      "unit": "sets",430      "location": "Table 2 (tab_brute_force)"431    },432    {433      "label": "Second exhaustive enumeration: 11-sets tested at n = 25 (none forcing)",434      "value": "1043731260",435      "unit": "sets",436      "location": "Table 2 (tab_brute_force)"437    },438    {439      "label": "Second exhaustive enumeration: forcing 12-sets found at n = 23 (positive control)",440      "value": "16179916",441      "unit": "sets",442      "location": "Section 7 item (b)"443    },444    {445      "label": "Largest n with Z >= 12 re-established by the second exhaustive enumeration",446      "value": "40",447      "unit": "n",448      "location": "Computational Result 6.1, Table 1, Limitations"449    },450    {451      "label": "Exact beta_18(n) for every 26 <= n <= 40 (zero slack)",452      "value": "12",453      "unit": "vertices",454      "location": "Observation 6.6"455    },456    {457      "label": "Boundary-encoding soundness check: (n,p) instances compared with exhaustive beta_p(n)",458      "value": "94",459      "unit": "instances",460      "location": "Section 7 item (c), Table 6"461    },462    {463      "label": "Boundary-encoding soundness check: boundary-table cells compared (all consistent)",464      "value": "50",465      "unit": "cells",466      "location": "Section 7 item (c)"467    },468    {469      "label": "Enumeration-count audit: (n,s) rows checked against binomial and Burnside counts (no mismatch)",470      "value": "162",471      "unit": "rows",472      "location": "Section 5 (exhaustive oracle), Table 6"473    },474    {475      "label": "Deletion lemma exhaustive small-set test D1: cases (no failure)",476      "value": "7287",477      "unit": "cases",478      "location": "Section 7 item (d), Table 6"479    },480    {481      "label": "Deletion lemma negative control D2: cases",482      "value": "810",483      "unit": "cases",484      "location": "Section 7 item (d), Table 6"485    },486    {487      "label": "Deletion lemma negative control D2: cases where the deleted column meets N[X]",488      "value": "414",489      "unit": "cases",490      "location": "Section 7 item (d)"491    },492    {493      "label": "Deletion lemma negative control D2: cases where the boundary size changed (expected)",494      "value": "18",495      "unit": "cases",496      "location": "Section 7 item (d), Table 6"497    },498    {499      "label": "Stored upper-bound witnesses replayed force by force (all ok)",500      "value": "35",501      "unit": "witnesses",502      "location": "Table 6"503    },504    {505      "label": "Largest n for which the P7 chronology was independently replayed",506      "value": "300",507      "unit": "n",508      "location": "Section 4, Table 6"509    },510    {511      "label": "Boundary certificates re-checked by the independent checker (all accepted)",512      "value": "135",513      "unit": "certificates",514      "location": "Section 7 item (e), Table 6"515    },516    {517      "label": "Fort-cover certificates re-checked by the independent checker (all accepted)",518      "value": "14",519      "unit": "certificates",520      "location": "Section 7 item (e), Table 6"521    },522    {523      "label": "Simulated-annealing attack A (11-sets): instances",524      "value": "45",525      "unit": "instances",526      "location": "Section 7 item (f)"527    },528    {529      "label": "Simulated-annealing attack B (18-sets): instances",530      "value": "43",531      "unit": "instances",532      "location": "Section 7 item (f)"533    },534    {535      "label": "Random seed of the simulated-annealing attacks",536      "value": "20261030",537      "unit": "seed",538      "location": "Section 7 item (f), Appendix B"539    },540    {541      "label": "Attack A best closure of an 11-set at n = 23 (of 46 vertices)",542      "value": "30",543      "unit": "vertices",544      "location": "Section 7 item (f)"545    },546    {547      "label": "Attack A best closure of an 11-set at n = 25 (of 50 vertices)",548      "value": "34",549      "unit": "vertices",550      "location": "Section 7 item (f)"551    },552    {553      "label": "Attack A best closure of an 11-set for every n >= 26",554      "value": "28",555      "unit": "vertices",556      "location": "Section 7 item (f)"557    },558    {559      "label": "Exhaustive oracle: 11-subsets enumerated at n = 27 (largest instance)",560      "value": "95722852680",561      "unit": "subsets",562      "location": "Computational Result 6.1, Table 2"563    },564    {565      "label": "Exhaustive oracle: orbit representatives tested at n = 27, s = 11",566      "value": "1772711200",567      "unit": "representatives",568      "location": "Computational Result 6.1, Table 2"569    },570    {571      "label": "Exhaustive oracle: total wall-clock time, n = 11..27",572      "value": "4125.7",573      "unit": "seconds",574      "location": "Computational Result 6.1"575    },576    {577      "label": "Fort-cover certificate at n = 22: number of fort clauses",578      "value": "37521",579      "unit": "forts",580      "location": "Observation 6.7, Table 10"581    },582    {583      "label": "Fort-cover certificate at n = 22: DRAT proof lines",584      "value": "12952380",585      "unit": "lines",586      "location": "Observation 6.7, Table 10"587    },588    {589      "label": "Fort-cover solver UNSAT without proof log at n = 23: wall time",590      "value": "837",591      "unit": "seconds",592      "location": "Observation 6.7"593    },594    {595      "label": "Fort-cover solver UNSAT without proof log at n = 25: wall time",596      "value": "1796",597      "unit": "seconds",598      "location": "Observation 6.7"599    },600    {601      "label": "Largest number of forts generated in a timed-out holdout fort-cover search (n = 48)",602      "value": "5500920",603      "unit": "forts",604      "location": "Observation 6.7"605    },606    {607      "label": "Round-based SAT encoding, n = 17: wall time of the completed rerun (UNSAT)",608      "value": "3295",609      "unit": "seconds",610      "location": "Observation 6.7"611    },612    {613      "label": "Boundary window p = 18: minimum per-instance CaDiCaL solve time",614      "value": "17.4",615      "unit": "seconds",616      "location": "Computational Result 6.4"617    },618    {619      "label": "Boundary window p = 18: maximum per-instance CaDiCaL solve time",620      "value": "266.8",621      "unit": "seconds",622      "location": "Computational Result 6.4, Appendix B"623    },624    {625      "label": "Boundary window p = 18: minimum per-instance drat-trim time",626      "value": "13.3",627      "unit": "seconds",628      "location": "Computational Result 6.4"629    },630    {631      "label": "Boundary window p = 18: maximum per-instance drat-trim time",632      "value": "231.3",633      "unit": "seconds",634      "location": "Computational Result 6.4"635    },636    {637      "label": "Boundary window p = 18: shortest DRAT proof",638      "value": "1214641",639      "unit": "lines",640      "location": "Computational Result 6.4"641    },642    {643      "label": "Boundary window p = 18: longest DRAT proof",644      "value": "4923281",645      "unit": "lines",646      "location": "Computational Result 6.4"647    },648    {649      "label": "Boundary table cells computed (p = 12..24, n = 13..30)",650      "value": "234",651      "unit": "cells",652      "location": "Computational Result 6.2"653    },654    {655      "label": "Number of fully certified entries in the exact-value table (n = 11..48)",656      "value": "38",657      "unit": "entries",658      "location": "Table 4 caption"659    },660    {661      "label": "Forces in the P7 chronology on P(14,5) (Figure 2a)",662      "value": "16",663      "unit": "forces",664      "location": "Figure 2 caption"665    },666    {667      "label": "Forces in the replayed chronology of the 8-vertex witness for P(15,5) (Figure 2b)",668      "value": "22",669      "unit": "forces",670      "location": "Figure 2 caption"671    },672    {673      "label": "Verified literature sources (3 full text, 8 abstract, 9 metadata)",674      "value": "20",675      "unit": "sources",676      "location": "Limitations, Appendix F"677    },678    {679      "label": "Boundary certificates used for n >= 24 (129 in the window plus n = 24)",680      "value": "130",681      "unit": "certificates",682      "location": "Computational Result 6.4"683    },684    {685      "label": "Fort-cover DRAT proof at n = 23: lines",686      "value": "59527561",687      "unit": "lines",688      "location": "Observation 7.7, Table 9",689      "metricKey": "fortcover_n23_proof_lines"690    },691    {692      "label": "Fort-cover DRAT proof at n = 23: drat-trim verification time",693      "value": "2486",694      "unit": "seconds",695      "location": "Observation 7.7",696      "metricKey": "fortcover_n23_checker_seconds"697    },698    {699      "label": "Fort-cover DRAT proof at n = 23: size on disk",700      "value": "4.0",701      "unit": "GB",702      "location": "Observation 7.7, Appendix C",703      "metricKey": "fortcover_n23_proof_gigabytes"704    },705    {706      "label": "Fort-cover certificate at n = 23: number of fort clauses",707      "value": "87239",708      "unit": "forts",709      "location": "Table 9",710      "metricKey": "fortcover_n23_num_forts"711    },712    {713      "label": "Fort-cover DRAT proof file at n = 25 (status unknown, not counted): lines",714      "value": "103621714",715      "unit": "lines",716      "location": "Observation 7.7",717      "metricKey": "fortcover_n25_proof_lines_unverified"718    },719    {720      "label": "Fort-cover DRAT proof file at n = 25 (status unknown, not counted): size on disk",721      "value": "7.7",722      "unit": "GB",723      "location": "Observation 7.7, Appendix C",724      "metricKey": "fortcover_n25_proof_gigabytes_unverified"725    }726  ],727  "robustness": {728    "witness_replay": {729      "witnesses": 35,730      "all_ok": true,731      "P7_range": [732        12,733        300734      ],735      "P7_all_ok": true,736      "n_with_size_Z_witness": [737        11,738        12,739        13,740        14,741        15,742        16,743        17,744        18,745        19,746        20,747        21,748        22,749        23,750        25751      ]752    },753    "enumeration_counts": {754      "rows": 162,755      "mismatches": 0,756      "all_n_consistent": true757    },758    "boundary_encoding": {759      "instances": 94,760      "all_ok": true,761      "table_cells_compared": 50,762      "table_cells_consistent": 50763    },764    "deletion_lemma": {765      "D1_cases": 7287,766      "D1_failures": 0,767      "D2_cases": 810,768      "D2_f_undefined": 414,769      "D2_boundary_size_changed": 18,770      "D3_instances": 3,771      "D3_ok": true,772      "D3_p16_boundary11_with_gap_at_n0": [773        22,774        26,775        30776      ]777    },778    "drat_controls": {779      "controls_behave": true,780      "beta_18_26_exact": 12,781      "truncated_rejected": true,782      "weaker_cnf_rejected": true,783      "wrong_cnf_rejected": true,784      "original_verified": true785    },786    "margin": {787      "n_range": [788        26,789        40790      ],791      "beta_18_values": {792        "26": 12,793        "27": 12,794        "28": 12,795        "29": 12,796        "30": 12,797        "31": 12,798        "32": 12,799        "33": 12,800        "34": 12,801        "35": 12,802        "36": 12,803        "37": 12,804        "38": 12,805        "39": 12,806        "40": 12807      },808      "all_margin_zero": true809    },810    "local_search": {811      "seed": 20261030,812      "A_instances": 45,813      "A_counterexample": false,814      "A_controls_all_found": true,815      "A_max_closure_deficit_min": 16,816      "B_instances": 43,817      "B_violation": false,818      "B_best_boundary_min": 12,819      "B_controls": [820        [821          22,822          18,823          10,824          10825        ],826        [827          23,828          18,829          11,830          11831        ],832        [833          25,834          18,835          10,836          10837        ],838        [839          24,840          20,841          11,842          11843        ],844        [845          24,846          18,847          12,848          12849        ]850      ],851      "B_controls_reached_table_value": true,852      "wall_seconds": 85853    },854    "certificate_recheck": {855      "boundary_checked": 135,856      "boundary_ok": 135,857      "fortcover_checked": 14,858      "fortcover_ok": 14,859      "fortcover_n": [860        11,861        12,862        13,863        14,864        15,865        16,866        17,867        18,868        19,869        20,870        21,871        22872      ],873      "all_ok": true874    },875    "ff_brute": {876      "instances": 43,877      "size11_zero_forcing_n": [878        23,879        24,880        25,881        26,882        27,883        28,884        29,885        30,886        31,887        32,888        33,889        34,890        35,891        36,892        37,893        38,894        39,895        40896      ],897      "largest_n_size11_exhausted": 40,898      "total_sets_tested": 344080112924,899      "total_wall_seconds": 2345.7,900      "total_cpu_seconds": 23516.5,901      "n23_s11_enumerated": 472120740,902      "n25_s11_enumerated": 1043731260,903      "n23_s12_forcing_sets": 16179916,904      "table_11_to_22_reproduced": true905    }906  }907}908
Files · main
Menu

Theme