Okay, we have from shinra's PR math that PS4 + XB1 was 384K, along with confirmation.
We have the below inequality equations.
XB1 + 360 < PS4
XB1 + WiU < PS4 + PS3
From that we assume
XB1 + WIU > PS4
WIU was calculated to be ~81K.
We also have confirmation that the GAF Aggregate Predictions were "good" and that PS4 is #1.
NeoGAF Aggregate Predictions - Jul-2014
1. PS4 - 221K
2. XB1 - 131K
3. 3DS - 108K
4. WIU - 90K
5. 360 - 48K
6. PS3 - 34K
Let's assume the aggregate numbers are perfect after replacing WIU with 81K. Does that fit the above equations?
XB1 (131K) + 360 (48K) < PS4 (221K)
true
XB1 (131K) + WIU (81K) < PS4 (221K) + PS3 (34K)
true
(assumed) XB1 (131K) + WIU (81K) > PS4 (221K)
false
XB1 (131K) + PS4 (221K) = 384K
false
Okay, not perfect, but a start. We are assuming that the difference between PS4 and XB1 is < WIU, so let's go with that and see what we get.
(assumed) PS4 - XB1 < 81K
(guess) PS4 - XB1 = 80K
PS4 + XB1 = 384K
Two equations, two unknowns ... PS4 would be 232K and XB1 would be 152K. That's the min XB1 number. Highest?
(assumed) PS4 - XB1 < 81K
(guess) PS4 - XB1 = 2K (since the total is an even number, the diff has to be an even number)
PS4 + XB1 = 384K
Two equations, two unknowns ... PS4 would be 193K and XB1 would be 191K.
PS4 between 193K and 232K (probably near high end of range)
XB1 between 152K and 191K (probably near low end of range or else the PR would be different)
So let's go with PS4 ~222K and XB1 ~162K. Does that now works with the above equations?
XB1 (162K) + 360 (48K) < PS4 (222K)
true
XB1 (162K) + WIU (81K) < PS4 (222K) + PS3 (34K)
true
(assumed) XB1 (162K) + WIU (81K) > PS4 (222K)
true
XB1 (162K) + PS4 (222K) = 384K
true
Okay, so that works, so let's see how that lays out.
Back-of-the-envelope Guesses, except for Wii U
1. PS4 - 222K
2. XB1 - 162K
3. 3DS - 108K
4. Wii U - 81K
5. 360 - 48K
6. PS3 - 34K
Hey, it's something! :lol
Edit:
Oh, yeah, Vita is confirmed < 17K, too.
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Part of OP below, but it was wrong. Just keeping it for reference.
Didn't work, and in fact, none of the ranges work with the above PS360 hardware values. Therefore, the PS360 hardware values would seem to be in error. In fact, we'd have to have PS3 > 360 to make the above work, so let's try switching the PS3 and 360 numbers and using the min XB1 range.
XB1 (152K) + 360 (34K) < PS4 (232K)
true
XB1 (152K) + 360 (34K) + WIU (81K) < PS4 (232K) + PS3 (48K)
true
(assumed) XB1 (152K) + 360 (34K) + WIU (81K) > PS4 (232K)
true
XB1 (152K) + PS4 (2321K) = 384K
true
That at least fits everything, so let's try working off that.