files / problems / kissing-5d / compute / q5 / n1_partcount.json
{
"n_groups": 240,
"n_four": 160,
"n_six": 80,
"n_stars": 10,
"time_limit_s": 30.0,
"solver": "scipy.optimize.milp / HiGHS",
"replay_star_free_small": {
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],
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}
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"status": "skipped",
"empty_by_part_count": false
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},
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"U": [
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"star_free": {
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"n1": 17,
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"star_free": true,
"max_ns": null,
"incumbent": null,
"status": "skipped",
"empty_by_part_count": false
}
},
"24": {
"k": 24,
"n1": 16,
"need": 25,
"unrestricted_construction": {
"verified_ns": 48,
"promising_witness": true,
"U": [
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},
"unrestricted": {
"k": 24,
"n1": 16,
"need": 25,
"star_free": false,
"max_ns": null,
"incumbent": null,
"status": "skipped",
"empty_by_part_count": false
},
"star_free_construction": {
"verified_ns": 44,
"promising_witness": true,
"U": [
0,
1,
2,
3,
4,
5,
6,
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10,
12,
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16,
17,
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19,
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22,
24,
26,
28,
31,
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]
},
"star_free": {
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"n1": 16,
"need": 25,
"star_free": true,
"max_ns": null,
"incumbent": null,
"status": "skipped",
"empty_by_part_count": false
}
}
},
"comment": "HiGHS MILP, leftover |U|=k in {19,20,21}; 22..24 only if cheap. max_ns is the proven maximum (null on cutoff). incumbent / verified_ns is an independently recounted contained-seed count for the solver's U. empty_by_part_count is true only on a proven max_ns < k+1 or an infeasible family. Cutoff is not a proof of the maximum and not a proof of emptiness. A promising_witness (verified_ns >= k+1) shows the slice is not empty by part-count. Star-free facts are not an unrestricted bound and do not move 40 <= tau5 <= 44.",
"skipped_22_24_milp": "not cheap: a leftover solve hit cutoff or used most of the 30s budget; 22..24 recorded by greedy construction only",
"by_k": {
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"incumbent": 42,
"status": "cutoff",
"empty_by_part_count": false,
"construction_ns": 32,
"promising_witness": true
},
"star_free": {
"max_ns": null,
"incumbent": 36,
"status": "cutoff",
"empty_by_part_count": false,
"construction_ns": 14,
"promising_witness": true
}
},
"20": {
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"incumbent": 47,
"status": "cutoff",
"empty_by_part_count": false,
"construction_ns": 32,
"promising_witness": true
},
"star_free": {
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"incumbent": 38,
"status": "cutoff",
"empty_by_part_count": false,
"construction_ns": 20,
"promising_witness": true
}
},
"21": {
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"incumbent": 50,
"status": "cutoff",
"empty_by_part_count": false,
"construction_ns": 32,
"promising_witness": true
},
"star_free": {
"max_ns": null,
"incumbent": 40,
"status": "cutoff",
"empty_by_part_count": false,
"construction_ns": 29,
"promising_witness": true
}
},
"22": {
"unrestricted": {
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"incumbent": null,
"status": "skipped",
"empty_by_part_count": false,
"construction_ns": 36,
"promising_witness": true
},
"star_free": {
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"status": "skipped",
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"construction_ns": 33,
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}
},
"23": {
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"status": "skipped",
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"construction_ns": 40,
"promising_witness": true
},
"star_free": {
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"status": "skipped",
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"construction_ns": 44,
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}
},
"24": {
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"status": "skipped",
"empty_by_part_count": false,
"construction_ns": 48,
"promising_witness": true
},
"star_free": {
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"incumbent": null,
"status": "skipped",
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"construction_ns": 44,
"promising_witness": true
}
}
}
}