New lower bound instance showing α-core empty below 2.1508 in proportionally fair clustering, plus exact α_m* thresholds for m=3..6 in Droop quota cases via MILP search and direct proofs.
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Improved Lower Bounds for Proportionally Fair Clustering
New lower bound instance showing α-core empty below 2.1508 in proportionally fair clustering, plus exact α_m* thresholds for m=3..6 in Droop quota cases via MILP search and direct proofs.