Charles St Pierre
My essay actually agrees with the well supported idea that the phenomenological universe is not centered at zero, but rather possesses a non-zero potential (Higgs ground state) as an inherent asymmetry and baseline complexity. Your example of matter and anti-matter annihilating into a non-zero energy is good evidence for that.
However, I suggest that the non-zero asymmetry we see in physical phenomena emerges from an even more fundamental geometric symmetry/neutrality which is centered at zero, just as complex number rotation is centered about the origin in a mathematical sense as a base-4 cycle or its more versatile and efficient cousin, the base-12 cycle. When the base-12 number cycle is in turn viewed in its simplest form as a cycle of four prime number positions symmetrically placed around the circle (at 1, 5, 7, 11), these four further simplify to two net vectors at positions 7 and 11 which are no longer symmetric (interestingly, creating a 2:1 asymmetry much like the Boltzmann and Schrodinger solutions you mention or the +2/3:-1/3 charges of the fermions). This is how I suggest that non-zero phenomena can emerge from zero-centered neutral geometry.
However, we see that this inherent neutrality is still preserved in natural phenomena when we take a broader view. Returning to your example of matter and anti-matter, they actually do represent the neutrality of zero in terms of equal and opposite charge or in terms of equal and opposite states of energy (matter versus annihilation energy). I also believe that classical logic not only applies to real number systems but also complex numbers when imaginary numbers are viewed as circular potentials not yet manifested onto the real number line. In this perspective, neutrality precedes symmetry which in turn precedes polarized phenomena. Thanks for the comments and feedback.