The Time Interval Only Set, Part 2

This paper is Part 2 continuing from investigation Part 1 from 2024. To recall, in Part 1, with the derivation of two theorems, defined is an axiomatic approach to the time interval only description. The time interval only set approach is an alternative to the usual one moment time description and the traditional tangent approach of change and differentiation. The two fundamental and nearly equivalent set theorems are the multiplication linearity theorem and the multiplication closure theorem. Both these theorems claim the multiplication of two time intervals results is a time interval. The present paper includes the construction of an overall simultaneous emission example surface for any approximation of spherical symmetric wave emission, applying a variation to a well known construction for indecomposable continua. Several comments and overall theorems are derived that evaluate the example surface construction. These include proof of two new theorems, emission theorem I and II, related to the identity transformation or mapping, which have value in their own right when considered as mathematical theorems. Emission theorem I and II depend on the ‘current parameter’ concept applying a multiple ‘dimensional domain definition’ within both the one moment time and time interval only description, new concepts defined applying set representation theory. Another part of the approach is the linear functional theorem. Within this approach defined is zero and non-zero equilibrium and simultaneous emission with ‘zero’ temperature to be a lowest bound temperature, resembling Boson type of simultaneous emission from collectives of multiple star sources. Finite time intervals being asymmetric this approach can be integrated in Curie’s principle for asymmetry. The current parameter allows for a comment on the fundamental theorem on polynomials. Assuming simultaneous emission internal interaction with em kinematic energy and gravitation energy provides several overall results including introduction of a time interval only description gravitation constant.