The Six-Decade Barrier for Understanding Cellular-Pulsating Burning of Energetic Materials: A Systematic Classification That Reveals New Research Horizons

Cellular-pulsating (hotspot) burning of energetic materials has resisted a unified theoretical explanation for over 6 decades, despite extensive experimental characterization across multiple materials and laboratories. The central question—why no prior theoretical approach has simultaneously accounted for all defining characteristics of this phenomenon—has never been addressed in systematic form. This study presents the first systematic classification of the complete theoretical corpus, comprising 73 key publications from 1942 to 2025, into six functional research classes, each rigorously assessed against three mandatory, mutually independent diagnostic criteria derived directly from the experimental record: spontaneous pattern formation on smooth, homogeneous burning surfaces (Criterion S); material-independent pressure scaling (Criterion U); and millisecond spatial coordination of cells across inter-cell distances of 10–20 mm (Criterion C). The analysis reveals that 0% of classified publications satisfy all three criteria simultaneously. Criterion C is structurally unreachable for all existing models, reflecting a four-orders-of-magnitude discrepancy (×40,000) between the thermal diffusion timescale (~1000 s) and the experimentally observed coordination timescale (20–40 ms). This systematic failure is traced to a single shared unstated axiom—that inter-cell information propagates exclusively via thermal diffusion and chemical kinetics—inherited from classical continuum combustion theory and never previously identified as such. The classification provides the first rigorous evaluation framework for unified combustion theories, derives three necessary physical constraints on any complete theory, and explains why the century-long Zel’dovich–Novozhilov tradition reached its logical limit without resolving the origin of cellular patterns.