I am looking for an intuitive, mathematical explanation of the Equity
Risk Premium.  There must be a relationship between risk ans return
that is not only empirical.

Background:

In finance theory, the Capital Asset Pricing Model ("CAPM") reduces to
ke=Rf+Beta.ERP

Where:
ke = cost of equity (required return on equity)
Rf = risk free rates (the lowest return required from any invetsment)
ERP = Equity risk premium (the excess return of the equity market for
addtional risk in excess of Rf)
Beta = A factor to adjust for the risk relative relative to the equity
market (var/covar)

In this context, we use "risk" interchangeably with "volatility". 
Once the implied cost of inflation (Rf) is adjusted out, CAPM implies
that the discount rate applied to an equity investment is a function
of its volatility.

Yet, if value were able to be infinately scaled (negative values were
permitted) then there is a neutral expectation in the next period. 
Theoretically, ERP should be zero.

We all know this is not the case; businesses fail.  But this alone
doesn't explain ERP.  There isn't say, a 15% chance that the average
business will fail in a year.  Therefore, it's a matter of the
certainty of the level of those future cashflows.

Then, ignoring business failure risk, what is the theoretical,
statistical model for ERP?

Not sure i correctly understand your question. Some points however.

Risk measured in the CAPM is not the risk of a business failing,
rather is it the uncertainty of returns.

In a world where the marginal utility of wealth is decreasing - which
is commonly assumed and makes sense for rational agents since going
from $0 to $1000 is much more valuable than going from $100,000 to
$100,100 - an uncertain return of 10% is less valuable than a certain
return of 10%.

The theoretical risk premium depends on the assumed utility function
of investors, but is always positive.