2 power supplies with ws2812b?

Hi all,
So after many hours reading and searching I would like a definitive answer for my simple(?) wiring set up please.
I have an Arduino UNO R3 with 2 x WS2812b strips of 30l/m.

I am making two arch strips with 86 leds each. Total = 172 leds
Each strip will be controlled separately (using Pin 12 and Pin 13).
My initial calculations are as follows and I am happy with this so far (with some more tweaking).

Full bright(256) = 60ma * 172 = 10.3 amps (I will not use all white so this is worse case...)

I will reduce brightness to 100 in my code, 100/256 * 60 *172 = 4.03amps

My issue is do I want them powered separately using 2 x 5volt 4amp power supplies, or just use one in the centre of my project. I would like to consider both wiring options please.

I know we need to tie the grounds, but do I just join ALL the ground wires to each other and the Arduino?
Does this interfere with the Data of the separate strips somehow?

My Diagram shows 2 power supplies - it is only my starting point.
Cheers,
DeXan

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I know we need to tie the grounds,

Then why isn't the top GND commoned?

I tried once and blew the first LED, so I was wondering if the Data line would be OK if I did this.

Is this (updated) diagram all we need to do to safely achieve this goal?

Thanks.

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I tried once and blew the first LED,

Then something else was wrong.

so I was wondering if the Data line would be OK if I did this.

No it is not.