How many cube inputs are needed for stable Matrix Lab work in DSP?

TL;DR: Do the math.

All the following values assume infinite supply; obviously if you're producing them slower than that, there's your bottleneck.

Look at a single research lab. Unfortunately, the game doesn't tell you the exact amount of time it takes to process a cube (and that is going to depend on how many upgrades you've researched), but looking at my own stack and keeping a stopwatch to hand it processes 10 cubes in about thirty seconds - so three seconds per cube, so 1/3 cube per second.

UPDATE: You can get some hard numbers by looking at your production screen:Production overview - research section.

I've got two full stacks and at maximum activity they consume a total of 1200 cubes per minute, or 20 per second, so 10 per second per stack or 2/3 of a cube per second per individual lab.

A single T3 belt can supply 30 units per second; a fully upgraded T3 sorter traverses 6 grid units per second with a stack of six. Counting round trips, that means that a belt right alongside the lab can get served three times per second (one grid unit either way, 6/2=3), meaning a single sorter can supply 18 cubes per second to your lab stack.

What this means is that a single T3 belt can precisely supply three full lab stacks, and if the belt is directly adjacent to the stack a single max-upgraded T3 sorter can easily keep a single stack supplied.

I'll try and do a couple of research upgrades tomorrow or this weekend and see if that alters the equations significantly.

Conclusion: Assuming sufficient supply, a single fully upgraded sorter is perfectly capable of keeping up with the demands of a maximum height lab stack. If you're really having trouble and it's not because you've got a cube deficit, consider upgrading your sorter cargo stacking capability to max (not a bad idea in any event because it will help with everything).

Evidence: Two maximum size stacks of research labs being fed by a single sorter. Both stacks are fully lit up and processing.

Both of those towers are running on full stacks with a single sorter per tower, and they're doing fine and have been doing for several thousand cubes.