Defining a Decidability Decider for the Halting Problem

When we understand that every potential halt decider must derive a formal mathematical proof from its inputs to its final states previously undiscovered semantic details emerge. When-so-ever the potential halt decider cannot derive a formal proof from its input strings to its final states of Halts or Loops, undecidability has been decided. The formal proof involves tracing the sequence of state transitions of the input TMD as syntactic logical consequence inference steps in the formal language of Turing Machine Descriptions.