nx_sketch_kmv.nx

sketch_kmv.nx -- KMV (K-Minimum-Values) sketch. Bar-Yossef et al. 2002 + Beyer 2007. Maintain the K smallest 32-bit hash values seen. Direct ancestor of DataSketches' Theta sketches; we ship the foundation primitive first then build Theta on top. CAPABILITIES (set-operation cardinality): - cardinality: (K-1) * 2^32 / kth_smallest when |set| > K total_inserted_unique when |set| <= K - union: K smallest across A.values ∪ B.values - Jaccard: |A.kmins ∩ B.kmins| / |A.kmins ∪ B.kmins| unbiased estimator of true Jaccard Error: rel_stddev ~ 1/sqrt(K-1) at 1-sigma. For K=4096: 1.56% stddev. For K=16384: 0.78%. COMPLEMENTS HLL: - HLL: better space per accuracy point for pure cardinality. - KMV: SAME sketch supports union AND intersection (Jaccard). The trade-off is well-studied; both ship in DataSketches (HLL.java and Theta.java) -- we ship the same axis pair. Hash domain: 32-bit (murmur3_32). We store hashes as i64 to keep arithmetic simple; the value space is [0, 2^32). Hash 0 is mapped to 1 (matches Cuckoo's empty-sentinel pattern; KMV uses the special "all-slots-filled-with-max" sentinel via the n_items counter instead, but mapping 0->1 avoids edge cases in the cardinality formula).