Log-Distance Integrability for Dissipative Flows: BV Selections on Fractal Attractors

We establish a BV chain rule for log-Lipschitz nearest-point projections onto compact attractors of dissipative dynamical systems. The main result provides conditions under which the time derivative of the log-distance functional d(u(t), A) remains integrable along trajectories, yielding BV regularity of the projected trajectory. DRAFT version. Subject to revisions. The Navier–Stokes transfer remains conditional and should be read as a selection-regularity framework, not as an unconditional 3D Navier–Stokes regularity theorem. Two sufficient routes to LDI are identified: bounded variation of the log-distance and power-law sublevel-time control. The v1.5 release publishes bibliographic source corrections; the…