Generalized non-commutative degeneration conjecture

In this paper we propose a generalization of the Kontsevich–Soibelman conjecture on the degeneration of Hochschild-to-cyclic spectral sequence for smooth and compact DG category. Our conjecture states identical vanishing of a certain map between bi-additive invariants of arbitrary small DG categories over a field of characteristic zero. We show that this generalized conjecture follows from the Kontsevich–Soibelman conjecture and the so–called conjecture on smooth categorical compactification.