Revealing an evolving corona around a prototypical intermediate-mass black hole

X-ray observations of accreting black holes reveal X-ray reverberation \citep{Uttley2014}, which is an effective approach to infer the geometrical arrangement of the disc-corona system \citep{Emmanoulopoulos2014} and the dynamics of the inner accretion flow \citep{Reynolds1999}. A promising scenario to explain rapid X-ray variations is that they are a consequence of both accretion rate and coronal height changes \citep{Parker2014Mrk335, Wilkins2015}. While supermassive black holes (SMBHs) \citep[e.g.][]{2009Natur.459..540F, Zoghbi2012NGC4151, Cackett2013, Kara2016FeKlag} mostly, and a handful of stellar mass black holes (sBHs) \citep[e.g.][]{Uttley2011, DeMarco2011, Wang2022, Uttley-Malzac2025} show reverberation, it is not often seen in the intermediate-mass black hole (IMBH) regime due to the low count rate from the inner disc, except for a few low mass objects, $M_{\rm BH}<3\times10^6~M_\odot$, showing soft X-ray lags \citep{Mallick2021}. Here we examine the closest prototypical IMBH, NGC\,4395, which has high X-ray flux variability, allowing it to be treated as an ideal proxy, in which iron-K reverberation lag is detected. We undertake two independent approaches in NGC\,4395: X-ray reverberation and reflection spectroscopy \citep{Reynolds2003} -- which relies on the full treatment of general relativistic (GR) ray-tracing calculations. The combined result of these approaches reveals an evolving corona that changes height from $1.65_{-0.75}^{+1.86}~R_{\rm g}$ ( $=GM_{\rm BH}/c^2$) to $26.66_{-4.77}^{+2.71}~R_{\rm g}$ with increasing luminosity. GR transfer function modelling of the reverberating iron-K line allows us to place constraints on the black hole mass of ($3.0_{-2.8}^{+3.7}\times10^5~M_{\odot}$) concurrently with the spin ($0.98_{-0.02}^{+0.01}$) and coronal height without inherent degeneracy. Furthermore, results for NGC\,4395 fit well with the scaled black hole mass versus iron-K lag \citep{Kara2016FeKlag}, and with the hypothesis that today's SMBHs are formed from rapidly spinning small mass black holes \citep{Volonteri2005, Sesana2014, Fiacconi2018}