Spherical Time-Atlas Mapping for Impact-Spectrum Waveforms: A Consequence-Preserving Visualization Method for Time-Series Data

The waveform and impact score are mapped onto a spherical surface, where waveform amplitude is represented as radial deformation and consequence is represented as a brightness or color field. The sphere can also be flattened into a two-dimensional atlas that preserves time ordering through labeled longitude, latitude, shell, or wrap bands. This allows consequence regions, hidden consequence zones, loud-but-shallow regions, event wakes, transition ridges, wave-impact contrast, and consequence-preserving compression to be defined and measured. The framework is presented as a visualization and diagnostic tool for time-series data. It does not claim that time is physically spherical. Instead, it defines a reproducible mapping from waveform data to a consequence-preserving surface and flattened atlas. The method is intended to help identify where consequence is concentrated, especially when what matters is not the largest visible waveform event.