A novel theoretical framework formulated for information discovery from number system and Collatz conjecture data

Newly discovered fundamental theories (metamathematics) of integer numbers may be used to formalise and formulate a new theoretical number system from which other formal analytical frameworks may be discovered, primed and developed. The proposed number system, as well as its most general framework which is based on the modelling results derived from an investigation of the Collatz conjecture (i.e., the 3x+1 problem), has emerged as an effective exploratory tool for visualising, mining and extracting new knowledge about quite a number of mathematical theorems and conjectures, including the Collatz conjecture. Here, we introduce and demonstrate many known applications of this prime framework and show the subsequent results of further analyses as new evidences to justify the claimed fascinating capabilities of the proposed framework in computational mathematics, including number theory and discrete mathematics.