The Flanked-5 Number System: Reconciling Decimal Milestones within a Symmetric Duodecimal Framework

Abstract We present a novel rearrangement of the base-12 (duodecimal) positional numeral system. By inserting two unique digits directly flanking the value 5, we shift the conventional positions of the remaining numbers. This configuration preserves the superior geometric divisibility of the duodecimal framework while anchoring the intuitive milestones of the base-10 system (5 and 10) at the critical 180-degree and 360-degree coordinates of a circular matrix. Furthermore, this structural shift forces all prime numbers greater than 3 to resolve into a perfectly symmetric, four-fold repeating digital root termination, mapping arithmetic progression directly onto geometric harmonic waves.