Personal income may not match adjusted gross income (AGI). For instance, non-taxable income would be included in personal Income but not in AGI. Non-taxable income can come from things like state bond interest or non-taxable social security benefits.
Capital gain income may be reduced by capital loss carryovers from previous years. So, the amount appearing on your form 1040, line 7(a) may differ from the amount reported on your Forms 1099-B. Also, you have to deduct investment losses from investment gains to arrive at net capital gains. Furthermore, all investment sales may not appear on Form 1099-B, they can also be reported on Form 1099-DIV and some may not be reported at all.
I'm not sure what you mean by "UI total directly additive." I would help if you could clarify that better, especially the meaning of "UI", as it normally means unearned income, but could also mean untaxed income.
Adjusted gross income is listed on line 11(a) on form 1040. You can see the sources of it from lines 1 to 10 listed on form 1040. You would have to trace backwards from the entries on Form 1040 to the source documents to verify the accuracy of the amounts on Form 1040 that make up AGI.
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