What is the maximum display resolution on the Intel HD Graphics 4000 chipset on a Lenovo t430?

For a Lenovo T430 Maximum external resolution:

• 2560x1600@60Hz (DisplayPort via optional Mini DP cable)
• 1920x1200@60Hz (single-link DVI-I via optional Mini DP cable)
• 2048x1536@75Hz (VGA)

Detailed Specifications - ThinkPad T430, T430i

Is 3840x2160@25hz (with reduced blanking).

xrandr --newmode "3840x2160x24.99"  218.500000  3840 3888 3920 4000  2160 2163 2167 2186  +HSync -VSync

xrandr --addmode HDMI1 "3840x2160x24.99"

Then apply this setting with your favorite "Display Settings" utility.

Intel HD Graphics 4000 supports resolution up to 1920×1200 through HDMI and 2560×1600 through DisplayPort. You should be safe.

Your Lenovo T430 has Mini DisplayPort connector on left side, so you can even reach for 30" or 32" displays with 2560×1600 (like Dell UltraSharp series).

I'm writing this answer from Lenovo with HD Graphics 4000 connected through HDMI to 1920×1200px LCD – so yeah, it definitely works.

It seems to be impossible to find specs document for HD 4000 directly at the Intel site (it was there before), but it is possible to find this information on many 3rd-party sites. Or check specifications of your laptop, it could be there. This is the best what can be found at Intel but specs are only partial there.

Additional note: 16:10 screen ratio is a good choice for productivity, I definitely recommend it over 16:9.