file: tree_K4_N7.jsonl  N=7 K=4
order-feasible patterns per K-subset: 6
nodes=30 branching=30 solution_nodes=0 continued=29 refuted=151
nodes per depth: {0: 1, 1: 6, 2: 9, 3: 12, 4: 2}
certificates: max entry denominator=13, max lcm of denominators=13, nonzero entries 1..6
explicit multipliers computed and identity re-checked for 151 certificates
Table 2 of the note: 30 rows compared, 0 discrepancies
example node 3 case 0: relations [(-1, -1, -1, 0, 0, 1, 0), (-1, -1, 1, 0, 0, 0, 0), (0, 0, -1, 0, -1, -1, 1), (-1, -1, 0, -1, 0, 0, 1)]
  y = ['4/7', '2/7', '0', '0', '1/7', '0', '0']  v = ['2/7', '2/7', '0', '-1/7', '1/7', '0', '0']  lambda = ['-1/7', '-2/7', '-1/7', '1/7']
  note's multipliers (-1/7,-2/7,-1/7,1/7) reproduce v: True
VERDICT: CLOSED
