files / problems / kissing-5d / compute / q5 / t5_share_pruned.json
{
"n": 355,
"share": 23,
"need": 13,
"n_samples": 10000,
"node_limit": 2000000,
"seed": 20260827,
"found_36": false,
"found_41": false,
"found_from": null,
"by_code": {
"D5": {
"n_outsiders_deg_ge_23": 320,
"n_outsiders_deg_ge_22": 320,
"n_outsiders_deg_ge_21": 320,
"max_dC": 32,
"degC_hist": {
"30": 96,
"31": 64,
"32": 160
},
"common_N_of_C": 0,
"common_N_in_outsiders": 0,
"other_published_outside_C": {
"L5": 8,
"Q5": 10,
"R5": 14
},
"outsider_clique": {
"best": 25,
"nodes": 2000001,
"complete": false,
"found_target": false,
"seed_best": 14
},
"outsider_independence": {
"best": 24,
"nodes": 165,
"complete": true,
"found_target": false,
"seed_best": 0
},
"sample_N_hist": {
"0": 928,
"1": 138,
"2": 1311,
"3": 278,
"4": 1794,
"5": 388,
"6": 1363,
"7": 434,
"8": 1016,
"9": 416,
"10": 439,
"11": 336,
"12": 279,
"13": 184,
"14": 156,
"15": 145,
"16": 94,
"17": 48,
"18": 69,
"19": 43,
"20": 40,
"21": 14,
"22": 35,
"23": 9,
"24": 12,
"25": 4,
"26": 10,
"27": 1,
"28": 7,
"29": 1,
"30": 1,
"32": 3,
"34": 1,
"36": 3
},
"n_N_ge_13": 880,
"n_N_ge_13_rate": 0.088,
"n_searched_13": 880,
"n_search_complete": 880,
"n_search_incomplete": 0,
"best_clique_in_N": 8,
"found_13_clique": false,
"need": 13
},
"L5": {
"n_outsiders_deg_ge_23": 320,
"n_outsiders_deg_ge_22": 320,
"n_outsiders_deg_ge_21": 320,
"max_dC": 32,
"degC_hist": {
"28": 20,
"29": 12,
"30": 60,
"31": 116,
"32": 112
},
"common_N_of_C": 0,
"common_N_in_outsiders": 0,
"other_published_outside_C": {
"D5": 8,
"Q5": 14,
"R5": 10
},
"outsider_clique": {
"best": 26,
"nodes": 2000001,
"complete": false,
"found_target": false,
"seed_best": 14
},
"outsider_independence": {
"best": 24,
"nodes": 162,
"complete": true,
"found_target": false,
"seed_best": 0
},
"sample_N_hist": {
"0": 1006,
"1": 763,
"2": 1499,
"3": 809,
"4": 1414,
"5": 707,
"6": 1040,
"7": 458,
"8": 646,
"9": 335,
"10": 378,
"11": 196,
"12": 197,
"13": 136,
"14": 115,
"15": 75,
"16": 56,
"17": 44,
"18": 23,
"19": 28,
"20": 23,
"21": 11,
"22": 10,
"23": 7,
"24": 7,
"25": 1,
"26": 7,
"27": 1,
"28": 4,
"30": 2,
"32": 1,
"34": 1
},
"n_N_ge_13": 552,
"n_N_ge_13_rate": 0.0552,
"n_searched_13": 552,
"n_search_complete": 552,
"n_search_incomplete": 0,
"best_clique_in_N": 7,
"found_13_clique": false,
"need": 13
},
"Q5": {
"n_outsiders_deg_ge_23": 320,
"n_outsiders_deg_ge_22": 320,
"n_outsiders_deg_ge_21": 320,
"max_dC": 32,
"degC_hist": {
"28": 21,
"29": 22,
"30": 79,
"31": 98,
"32": 100
},
"common_N_of_C": 0,
"common_N_in_outsiders": 0,
"other_published_outside_C": {
"D5": 10,
"L5": 14,
"R5": 4
},
"outsider_clique": {
"best": 25,
"nodes": 2000001,
"complete": false,
"found_target": false,
"seed_best": 14
},
"outsider_independence": {
"best": 24,
"nodes": 100,
"complete": true,
"found_target": false,
"seed_best": 0
},
"sample_N_hist": {
"0": 865,
"1": 1111,
"2": 1443,
"3": 1265,
"4": 1126,
"5": 1015,
"6": 793,
"7": 645,
"8": 460,
"9": 357,
"10": 241,
"11": 221,
"12": 126,
"13": 106,
"14": 75,
"15": 47,
"16": 26,
"17": 21,
"18": 17,
"19": 14,
"20": 4,
"21": 2,
"22": 8,
"23": 1,
"24": 1,
"25": 4,
"26": 1,
"27": 1,
"28": 1,
"29": 2,
"37": 1
},
"n_N_ge_13": 332,
"n_N_ge_13_rate": 0.0332,
"n_searched_13": 332,
"n_search_complete": 332,
"n_search_incomplete": 0,
"best_clique_in_N": 7,
"found_13_clique": false,
"need": 13
},
"R5": {
"n_outsiders_deg_ge_23": 320,
"n_outsiders_deg_ge_22": 320,
"n_outsiders_deg_ge_21": 320,
"max_dC": 32,
"degC_hist": {
"26": 2,
"27": 1,
"28": 22,
"29": 26,
"30": 57,
"31": 141,
"32": 71
},
"common_N_of_C": 0,
"common_N_in_outsiders": 0,
"other_published_outside_C": {
"D5": 14,
"L5": 10,
"Q5": 4
},
"outsider_clique": {
"best": 27,
"nodes": 2000001,
"complete": false,
"found_target": false,
"seed_best": 14
},
"outsider_independence": {
"best": 24,
"nodes": 100,
"complete": true,
"found_target": false,
"seed_best": 0
},
"sample_N_hist": {
"0": 1322,
"1": 1287,
"2": 1544,
"3": 1210,
"4": 1098,
"5": 913,
"6": 743,
"7": 514,
"8": 389,
"9": 302,
"10": 199,
"11": 159,
"12": 89,
"13": 67,
"14": 42,
"15": 30,
"16": 29,
"17": 23,
"18": 10,
"19": 7,
"20": 7,
"21": 3,
"22": 3,
"23": 2,
"24": 3,
"25": 1,
"27": 2,
"28": 1,
"30": 1
},
"n_N_ge_13": 231,
"n_N_ge_13_rate": 0.0231,
"n_searched_13": 231,
"n_search_complete": 231,
"n_search_incomplete": 0,
"best_clique_in_N": 7,
"found_13_clique": false,
"need": 13
}
},
"comment": "Census of share-23 neighbourhoods, not an emptiness proof. C(35,12) is not enumerated. Outsider clique / independence figures are hints at node_limit 2000000. Incomplete search is residue. A 36-clique, if one exists, shares at most 23 with each published 35. This does not move 40 <= tau_5 <= 44."
}