**Abstract** : Physics parameters in a near quadratic structural form demonstrates invariance in respect to the
symmetry of the Monster group across a slight vacuum energy change. Five parameters needed in
the structure are the Planck mass, the electron mass the charged pion mass, the gravitational
coupling constant and the electromagnetic fine structure constant. The gravitational coupling
constant along with the electromagnetic fine structure constant are reduced to a near unity value,
which responds to changing gravitational and vacuum energy conditions thus reflecting the
amount of space-time curvature. The entire parameter set changes are invariant due to an overall
symmetry as the special case of a baryonic star system or vacuum field changing from a near
Minkowski like space-time to a more extremal space-time curvature of a neutron star or black hole.
This involves the quark flavor change in a baryon of going from uud to udd, which is the isospin
symmetry action of the SU(2) group on the strong force dynamics of the proton-neutron nuclear
fields. In addition, a number theoretic equivalent of the structural form shows nearly the same
dimensionless ratio values on a one to one basis to the physics form. The number theoretic forms
are based on computer constructions of closed forms utilizing constants involving the complex
plane and suppressions of powers of pi and e. The number theoretic formula values for
dimensionless mass ratios nearly match the Codata 2014 set. That the structural features of the
physics forms and number theoretic forms match suggests that the main structural form has a
nontrivial solution(s) consisting of the Standard Model physics forms and possibly its dual number
theoretic forms. The near quadratic form using a near unity value to produce an integer is not a
simple encoding machine.