files / problems / kissing-5d / compute / q5 / construct_more.json
{
"parts": {
"d7": {
"n": 13480,
"thresh": 49,
"n_types": 13,
"types": {
"(0, 0, 0, 7, 7)": 40,
"(0, 0, 1, 4, 9)": 480,
"(0, 0, 3, 5, 8)": 480,
"(0, 1, 5, 6, 6)": 960,
"(0, 2, 2, 3, 9)": 960,
"(0, 2, 3, 6, 7)": 1920,
"(0, 3, 3, 4, 8)": 960,
"(1, 1, 4, 4, 8)": 960,
"(1, 2, 2, 5, 8)": 1920,
"(1, 3, 4, 6, 6)": 1920,
"(1, 4, 4, 4, 7)": 640,
"(2, 2, 4, 5, 7)": 1920,
"(4, 4, 4, 5, 5)": 320
},
"support": {
"2": 40,
"3": 960,
"4": 4800,
"5": 7680
},
"comment": "n=13480 > 400; no full 41-clique B&B. Type-restrict below.",
"n_extras": 13440,
"d5_deg_hist": {
"30": 320,
"33": 1600,
"35": 8640,
"36": 1920,
"37": 960
},
"same_missed_highdeg": {
"n_groups": 2000,
"group_size_hist": {
"3": 960,
"6": 320,
"8": 480,
"12": 240
},
"best_total": 38,
"max_group_omega": 1,
"any_incomplete": false,
"found_41": false,
"comment": "same-missed extras are edgeless (omega=1) on these types"
},
"mixed_highdeg": {
"3": {
"k": 3,
"n1": 37,
"n_U": 80,
"tried": 80,
"best_extras": 1,
"best_total": 38,
"found_41": false,
"complete": true
},
"4": {
"k": 4,
"n1": 36,
"n_U": 3120,
"tried": 3120,
"best_extras": 1,
"best_total": 37,
"found_41": false,
"complete": true
},
"5": {
"k": 5,
"n1": 35,
"n_U": 57160,
"tried": 57160,
"best_extras": 2,
"best_total": 37,
"found_41": false,
"complete": true
}
},
"type_01566_axis": {
"n": 192,
"best": 12,
"found_41": false,
"nodes": 6723,
"complete": true,
"thresh": 49,
"type": "(0, 1, 5, 6, 6)",
"comment": "zero fixed in coordinate 0; 192 of the 960 type-(0,1,5,6,6) extras"
}
},
"d5_plus_typeB": {
"n": 680,
"skipped": true,
"reason": "subgraph of leftover 1480; other workers own that graph",
"best": null,
"found_41": false,
"complete": false
},
"C_orbit": {
"n": 640,
"skipped": true,
"reason": "type-C extras of leftover (1/4)Z^5; not re-searched",
"best": null,
"found_41": false,
"complete": false
},
"Qsqrt3": {
"orbit": {
"n": 80,
"best": 20,
"found_41": false,
"nodes": 21,
"complete": true,
"seed": "(sqrt(3), 1, 0, 0, 0)/sqrt(2)",
"field": "Q(sqrt(3))"
},
"d5_union": {
"n": 120,
"best": 40,
"found_41": false,
"nodes": 1,
"complete": true,
"seed": "D5 union (sqrt(3), 1, 0, 0, 0)/sqrt(2)",
"field": "Q(sqrt(3))",
"n_d5": 40,
"n_orbit": 80
},
"orbit_1110": {
"seed": "(sqrt(3), 1, 1, 1, 0)/sqrt(3)",
"field": "Q(sqrt(3))",
"n": 320,
"skipped": true,
"reason": "n=320 > 200; no 41-clique B&B",
"best": null,
"found_41": false,
"complete": false
},
"d5_union_1110_axis": {
"n": 104,
"best": 40,
"found_41": false,
"nodes": 1,
"complete": true,
"seed": "D5 union (sqrt(3),1,1,1,0)/sqrt(3) with first coord 0",
"n_orbit_slice": 64
},
"found_41": false,
"best": 40,
"complete": true
},
"cube_axes_holes": {
"weight3": {
"n": 122,
"best": 26,
"found_41": false,
"nodes": 8417,
"complete": true,
"parts": {
"axes": 10,
"cube": 32,
"weight3": 80
},
"hole": "(pm1,pm1,pm1,0,0)"
},
"weight4": {
"n": 122,
"parts": {
"axes": 10,
"cube": 32,
"weight4": 80
},
"hole": "(pm1,pm1,pm1,pm1,0)",
"best": 30,
"best_lb_nodes": 200001,
"best_lb_complete": false,
"found_41": false,
"complete": true,
"nodes": 983,
"comment": "best is a lower bound from a seed_best=0 search; complete is the 41-decision with seed_best=40"
},
"found_41": false,
"best": 30,
"complete": true
}
},
"found_41": false,
"best": 40,
"comment": "No exact 41-point spherical code in the pools that finished. d7 n=13480 is count-plus-type-restrict only; a skipped or incomplete search is residue, not a lower bound. Did not re-search the leftover 1480-point (1/4)Z^5 graph or the 355-point T^5 remainder. Did not claim tau_5=40."
}