Phenomenal Velocity: A Step by Step Solution; Reasoning for the Method

This paper illustrates how Mathematica is omitting a solution to this equation. There is a third solution to this equation that is logically deducible, namely: Undefined. It is ignored by Mathematica to this present day, though they have been notified of this solution on numerous occassions. When dealing with equations of this form, be warned: There is at least one alternative interpretation/solution to v: Undefined. This is posted to notify anyone analyzing or using these forms of equations that the undefined solution is an existential reality and to proceed with caution.

Abstract:

 The following solution to phenomenological velocity is algebraically deductive and essentially demonstrates how a mathematician can exploit an algebraic, "push-out," operation that makes 1 go to an existential v implicitly. This is the essence of the method used for solving phenomenological velocity as demonstrated in this paper. However, it should be noted that Mathematica continues to miss the fact that there is a 3 rd solution to phenomenological velocity, which ought not be ignored (no pun intended), namely that v can be demonstrated as undefined with only the facts available within the original architecture of the initial formulation of the base equation. Our investigation demonstrates that phenomenological velocity is appropriately named, for the solution method demonstrated suspends the knowledge of the undefined expression for establishing a formal architecture of oneness, which is essentially a form of bracketing, or, "phenomenological reduction." Thus, as the oneness expression is then capable of being factored out within the square roots and interchangeable with the v-curvature expression herein. The complex field is not explicitly required for the phenomenological velocity solution method I demonstrate, but complex solutions are implied for variables in the system of equations. For background, Phenomenological Velocity exists as an optional interpretable real space, "hidden dimension," that forms a complete field with instantaneous (derivative) velocity via a trigonometric identity (Conditional Integral of Phenomenological Velocity, Emmerson 2023). Even though you can cancel out the Lorentz coefficient, and that is entirely agreed upon by the algebraic community, we can still solve for v implicitly by a modus ponens expression for one, and this is what is demonstrated in this paper. The paper is important, because it points out a missing solution that Mathematica has overlooked. Ignoring this solution could send an FTL spaceship vastly off course or into danger of the event horizon.