Impact-Spectrum Waveforms: A Shell-Weighted Method for Mapping Event Consequence Across Time-Series Data

This manuscript introduces impact-spectrum waveforms, a consequence-aware visualization and diagnostic framework for time-series and waveform data. Standard waveform plots usually show amplitude over time, but the largest visible feature in a signal is not always the most consequential feature. A small deviation may produce a persistent downstream change, while a large transient may leave little lasting effect. The proposed method preserves the original waveform (f(t)) while attaching a normalized impact-depth value (D(t)) to each point through a color map. The framework defines observer-shell impact vectors, shell-weighted combined impact, an (X)-weighted balance between local intensity and downstream consequence, event trace-back scores, counterfactual-corrected impact, static three-dimensional waveform embeddings, and local cube-window observation frames. Proof-of-concept simulations demonstrate that the same waveform can be represented as a conventional two-dimensional graph, a color-coded impact-spectrum signal, a static three-dimensional curve, and a locally visible cube segment that projects back into the original waveform view. The framework is intended as a general graphing and diagnostic layer for identifying candidate consequential events in waveform-rich domains such as vehicle telemetry, mechanical failure analysis, biological signals, seismic data, sensor networks, and physics anomaly detection. The manuscript is presented as a theoretical and proof-of-concept framework.