A survey of current 4k displays seems to indicate that at least 2 HDMI or SDI connections are required to support the resolution. In the DVI-D world, 4 connections are required as with the Meridian 810.

It looks to me like a connection standard, not currently ratified, will be required for true 4k carriage over a single cable. This assumes that the data will not be compressed to fit inside current bandwidth delivery systems.

Meridian Advocate