Purple Mathematics: A Descriptive Account of a Visual Framework for Numerical Identity and an Interactive Explorer

Purple Mathematics is a visual framework that equips each positive integer with a structured identity derived from local operations on its neighbours, and arranges the integers along a bridge running from a Zero pole to an Infinity pole about a central dividing line. This paper gives a descriptive account of the framework and of an accompanying interactive visualization (a self-contained HTML explorer). It defines the bridge and its poles and the unit as a Balance Boundary; the dig operation, the reach, and the purple number, with the resulting Zero and Infinity domains; the wall of determination triangles built over the primes; the Determination Slope and the signal sensor placed on each apex, together with the signals the sensor receives; two signed identity calibrations, the Deviation ID and the Dig ID; a helix that coils around the dividing line and carries the integers; and an overlay of the nontrivial Riemann zeta zeros with associated rising frequency signals. It then describes the explorer’s six views, its controls, and its rendering conventions. The paper records definitions and describes components only; references are provided for the classical objects named. MSC 2020. 11A41 (primes); 11N25 (integers with special multiplicative structure); 00A66 (mathematics and visual arts / visualization); 11-04 (software, source code).