With no wages on a W-2 that would result in you having more compensation than the Social Security wage base, $6,456 of net profit from self employment is the amount that would produce $456 as the deductible portion of self-employment taxes, leaving $6,000 available to support a Roth IRA contribution.
$6,456 - ($6,456 * 0.9235 * 0.153 / 2) = $6,000 (after rounding)
AGI is not the same as your compensation and is only used in determining if your total income is too much to make the Roth IRA contribution. To contribute to a Roth IRA you need to have enough compensation but not too much total income.
EIC is a tax credit. It reduces tax liability, not AGI.
I am largely baffled by California.
