files / problems / hilbert16-limit-cycles / compute / q2 / p-harnack-recurrence / certs / core.json
{
"N_max": 50,
"n_pairs": 1225,
"Har_1_to_6": [
0,
1,
1,
4,
6,
11
],
"Har": {
"1": 0,
"2": 1,
"3": 1,
"4": 4,
"5": 6,
"6": 11,
"7": 15,
"8": 22,
"9": 28,
"10": 37,
"11": 45,
"12": 56,
"13": 66,
"14": 79,
"15": 91,
"16": 106,
"17": 120,
"18": 137,
"19": 153,
"20": 172,
"21": 190,
"22": 211,
"23": 231,
"24": 254,
"25": 276,
"26": 301,
"27": 325,
"28": 352,
"29": 378,
"30": 407,
"31": 435,
"32": 466,
"33": 496,
"34": 529,
"35": 561,
"36": 596,
"37": 630,
"38": 667,
"39": 703,
"40": 742,
"41": 780,
"42": 821,
"43": 861,
"44": 904,
"45": 946,
"46": 991,
"47": 1035,
"48": 1082,
"49": 1128,
"50": 1177
},
"L_pub": {
"1": 0,
"2": 4,
"3": 13,
"4": 28,
"5": 37,
"6": 53,
"7": 74,
"8": 96,
"9": 120,
"10": 142,
"11": 153,
"12": 157,
"13": 212,
"14": 252,
"15": 345,
"16": 351,
"17": 384,
"18": 372,
"19": 503,
"20": 509,
"21": 568,
"23": 833,
"24": 843,
"25": 870,
"26": 880,
"27": 1023,
"29": 1080,
"31": 1380,
"35": 1536,
"39": 2012,
"43": 2272
},
"n_beats_quoted_m_ge_2": 0,
"n_beats_closed_recorded": 0,
"n_beats_claimed": 0,
"m1_quoted_exceedances": [
{
"n": 17,
"m": 1,
"N": 18,
"lift": 384,
"L_pub_N": 372,
"L_pub_n": 384,
"Har_m": 0,
"increment_would_give": 385,
"is_dent": false
}
],
"H_K_5": 28,
"L_pub_4": 28,
"L_pub_5": 37,
"H_K_5_equals_L_pub_4": true,
"H_K_5_equals_9": false,
"H_K_5_beats_H_5": false,
"Har_1": 0,
"weaker_than_increment": true,
"four_chebyshev": {
"14": 252,
"29": 1080,
"31": 1380,
"39": 2012
},
"harnack_vs_four": {
"14": 212,
"29": 1024,
"31": 1081,
"39": 1540
},
"do_not_claim_252_1080_1380_2012_as_ours": true,
"do_not_claim_HK5_28_as_ours": true,
"best_harnack": {
"2": {
"lift": 0,
"n": 1,
"m": 1
},
"3": {
"lift": 4,
"n": 2,
"m": 1
},
"4": {
"lift": 13,
"n": 3,
"m": 1
},
"5": {
"lift": 28,
"n": 4,
"m": 1
},
"6": {
"lift": 37,
"n": 5,
"m": 1
},
"7": {
"lift": 53,
"n": 6,
"m": 1
},
"8": {
"lift": 74,
"n": 7,
"m": 1
},
"9": {
"lift": 96,
"n": 8,
"m": 1
},
"10": {
"lift": 120,
"n": 9,
"m": 1
},
"11": {
"lift": 142,
"n": 10,
"m": 1
},
"12": {
"lift": 153,
"n": 11,
"m": 1
},
"13": {
"lift": 157,
"n": 12,
"m": 1
},
"14": {
"lift": 212,
"n": 13,
"m": 1
},
"15": {
"lift": 252,
"n": 14,
"m": 1
},
"16": {
"lift": 345,
"n": 15,
"m": 1
},
"17": {
"lift": 351,
"n": 16,
"m": 1
},
"18": {
"lift": 384,
"n": 17,
"m": 1
},
"19": {
"lift": 385,
"n": 17,
"m": 2
},
"20": {
"lift": 503,
"n": 19,
"m": 1
},
"21": {
"lift": 509,
"n": 20,
"m": 1
},
"23": {
"lift": 569,
"n": 21,
"m": 2
},
"24": {
"lift": 833,
"n": 23,
"m": 1
},
"25": {
"lift": 843,
"n": 24,
"m": 1
},
"26": {
"lift": 870,
"n": 25,
"m": 1
},
"27": {
"lift": 880,
"n": 26,
"m": 1
},
"29": {
"lift": 1024,
"n": 27,
"m": 2
},
"31": {
"lift": 1081,
"n": 29,
"m": 2
},
"35": {
"lift": 1384,
"n": 31,
"m": 4
},
"39": {
"lift": 1540,
"n": 35,
"m": 4
},
"43": {
"lift": 2016,
"n": 39,
"m": 4
}
},
"example_H6_from_H2": 8,
"L_pub_6": 53,
"L_closed_18": 385
}