Krapivin-Block-Tracker

We present the Krapivin-Block-Tracker (KBT) v2, a self-calibrating hybrid data structure combining Elastic Hashing / Funnel Hashing (Farach-Colton, Krapivin, Kuszmaul 2025, arXiv:2501.02305) with an adaptive hysteresis tracker in L1-cache. Three distinct metrics are reported: M1 (user-visible speedup): KBT directs every insertion to a guaranteed-free block, reducing probes per insertion from O(log δ⁻¹) to exactly 1.00. Net speedup over Krapivin without tracker: 3–48× depending on load regime. M2 (internal tracker efficiency): the hysteresis buffer reduces tracker update frequency by up to 307,838× compared to a naive single-bit marker. This measures internal overhead, not the user-visible speedup. M3 (tracker overhead): tracker cost as a fraction of total insertion cost is < 0.001% in all tested regimes. Version 2 adds adaptive hysteresis buffer h (EMA-based, empirically fitted f(h) = 1.04·h⁻³, stability limit α < 0.333) and adaptive threshold τ_H (hybrid rule: analytical optimum for p ≥ 0.52, static otherwise). The static critical point δ* = 0.20 is eliminated in v2. Includes Python simulation scripts and charts.