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Richtmyer–Meshkov instability (RMI) at a single-mode interface separating an inert gas (N $_2$ ) and a reactive gas mixture (H $_2$ /O $_2$ /Xe) under reshock conditions is numerically investigated using a newly developed compressible reactive Navier–Stokes solver. The solver employs the Kéromnès mechanism (10 species, 21 reactions) for combustion modelling and a dual-flux algorithm to suppress numerical oscillations at material interfaces, demonstrating high accuracy across a wide range of benchmark tests. By systematically varying incident shock Mach numbers, we identify four distinct evolution regimes: an inert regime ( ${\textit{Ma}} \lt 1.80$ ), characterised by negligible combustion effects on interface evolution; a deflagration regime ( $1.80 \lt Ma \lt 1.86$ ), marked by strong coupling between interface dynamics and combustion through sustained interactions; a detonation regime ( $1.86 \lt Ma \lt 2.50$ ), where rapid transition to detonation leads to moderate coupling; and an immediate detonation regime ( ${\textit{Ma}} \gt 2.50$ ), where detonation occurs directly after incident shock impact, modifying interface evolution from the outset through intense heat release and pressure waves. Mixing width and mixing level are most significantly enhanced in the deflagration regime due to prolonged combustion-flow interactions, while cases with higher Mach numbers show reduced mixing due to rapid combustion completion. Heat release and enstrophy also display clear regime-dependent evolution behaviour: maximum heat release occurs in the detonation regime, while peak enstrophy is observed in the deflagration regime. A clear correlation is observed between the Damköhler number ( $Da$ ), which represents the ratio of hydrodynamic to chemical time scales, and the flow regimes: for ${\textit{Ma}} \lt 1.80$ , $Da \lt 1$ indicates negligible coupling; at ${\textit{Ma}} = 1.83$ , $Da \approx 1$ reflects sustained coupling; and for ${\textit{Ma}} \gt 2.00$ , $Da \gt 1$ denotes strong early coupling. This correlation provides a theoretical basis for interpreting the distinct regimes and guiding the modulation of reactive RMI.