files / problems / ramsey-r55 / compute / q1 / certs / q1_summary.json
{
"any_43_graph": false,
"any_cayley_hit": false,
"aut_mckay": {
"aut_histogram": {
"1": 424,
"2": 232
},
"n_capped": 0,
"n_graphs": 656,
"n_has_7cycle": 0,
"n_has_involution": 232,
"n_nontrivial": 232,
"n_trivial": 424,
"seconds": 0.513
},
"c7_n14": {
"edges": 56,
"n": 14,
"nclauses": 4004,
"nvars": 13,
"ok_55": true,
"solve_sec": 0.0,
"status": "SAT",
"time_limit_hint": 180,
"total_sec": 0.044,
"use_card": false
},
"c7_n42": {
"n": 42,
"nclauses_card": 1725498,
"nclauses_slim": 1701336,
"note": "Cadical195 timeout 180s (card) and 300s (slim). Isolated SAT timeout is not a bound. Encoder self-test on n=7 agrees; n=14 is SAT and (5,5).",
"nvars_card": 6273,
"nvars_slim": 123,
"status": "UNKNOWN",
"time_limit_sec": [
180,
300
],
"use_card": [
true,
false
]
},
"c7_n43": {
"n": 43,
"nclauses_slim": 1925196,
"note": "Cadical195 timeout 300s on the slim C7 encoding (one fixed vertex, six 7-orbits). Isolated SAT timeout is not a bound.",
"nvars_slim": 129,
"status": "UNKNOWN",
"time_limit_sec": 300,
"use_card": false
},
"c7_selftest": {
"agree": true,
"brute_55": [
false,
true,
true,
true,
true,
true,
true,
false
],
"n": 7,
"n_55": 6,
"sat": [
false,
true,
true,
true,
true,
true,
true,
false
]
},
"cayley": {
"c11c4": {
"done": "DONE group=c11c4 n=44 scanned=294262 hits=0 pruned=591004 sec=2.774",
"hits": 0,
"n": 44,
"pruned": 591004,
"scanned": 294262,
"sec": 2.774
},
"c2c22": {
"done": "DONE group=c2c22 n=44 scanned=625004 hits=0 pruned=359690 sec=5.157",
"hits": 0,
"n": 44,
"pruned": 359690,
"scanned": 625004,
"sec": 5.157
},
"c3c15": {
"done": "DONE group=c3c15 n=45 scanned=93976 hits=0 pruned=271560 sec=0.923",
"hits": 0,
"n": 45,
"pruned": 271560,
"scanned": 93976,
"sec": 0.923
},
"d22": {
"done": "DONE group=d22 n=44 scanned=469925806 hits=0 pruned=349496800 sec=406.695",
"hits": 0,
"n": 44,
"pruned": 349496800,
"scanned": 469925806,
"sec": 406.695
}
},
"circulant44": {
"done": "DONE n=44 ndist=22 deg=[19,24] scanned=1704794 legal_deg=1704794 hits=0 sec=1.288",
"hits": 0,
"legal_deg": 1704794,
"n": 44,
"ndist": 22,
"scanned": 1704794,
"sec": 1.288
},
"circulant45": {
"done": "DONE n=45 ndist=22 deg=[20,24] scanned=1704794 legal_deg=1704794 hits=0 sec=0.946",
"hits": 0,
"legal_deg": 1704794,
"n": 45,
"ndist": 22,
"scanned": 1704794,
"sec": 0.946
},
"extend_flips": {
"done": "DONE graphs_pairs=328 tried=564816 flip_ok=4080 extensions=0 sec=183.310",
"extensions": 0,
"flip_ok": 4080,
"graphs_pairs": 328,
"sec": 183.31,
"tried": 564816
},
"group_laws": {
"all_ok": true,
"rows": [
{
"n": 44,
"name": "C2xC22",
"ninv": 3,
"ok": true
},
{
"n": 44,
"name": "D22",
"ninv": 23,
"ok": true
},
{
"n": 44,
"name": "C11rtimesC4",
"ninv": 1,
"ok": true
},
{
"n": 45,
"name": "C3xC15",
"ninv": 0,
"ok": true
},
{
"n": 45,
"name": "C3xC3xC5",
"ninv": 0,
"ok": true
}
]
},
"interval_moved": false,
"note": "A HIT Cayley graph of order 44 or 45, or an extend_flips extension, would be a certified new (5,5)-graph and a dent. Isolated SAT timeouts are UNKNOWN, not a bound.",
"py_c11c4": {
"group": "c11c4",
"hits": 0,
"n": 44,
"ninv": 1,
"npairs": 21,
"pruned": 591004,
"scanned": 294262,
"seconds": 142.876
},
"py_c3c15": {
"group": "c3c15",
"hits": 0,
"n": 45,
"ninv": 0,
"npairs": 22,
"pruned": 271560,
"scanned": 93976,
"seconds": 33.359
},
"srg43": {
"degree_window": [
18,
24
],
"n": 43,
"n_integral": 0,
"note": "No integral parameter set in the legal degree window. 43 \u2262 1 (mod 4), so there is also no conference graph. Every SRG is either a conference graph or has integer eigenvalues, so there is no strongly regular graph on 43 vertices with degree in [18,24]. That excludes an SRG (5,5,43)-graph. It is not a bound on R(5,5).",
"params": []
},
"two_flip": {
"n_graphs": 656,
"n_known_types": 2,
"n_radius1": 4080,
"n_radius2": 22000,
"n_radius2_new_type": 0,
"new_sample": [],
"note": "Radius-2 walks of legal 1-flips. The 1-WL key is the colour-class-size histogram: Aut=1 (42 singletons) vs Aut=2 (21 pairs). Not an isomorphism test. 1-flip graphs do not extend (extend_flips.c).",
"seconds": 19.539
}
}