In a six-state lumpable Markov chain with T=P², the supremum determinant over all 3-partitions is strictly less than the relaxed sup det(U*TU).
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A Strict Gap Between Relaxed and Partition-Constrained Spectral Compression in a Six-State Lumpable Markov Chain
In a six-state lumpable Markov chain with T=P², the supremum determinant over all 3-partitions is strictly less than the relaxed sup det(U*TU).