Low-mass white dwarfs (LMWDs) are believed to be exclusive products of binary evolution, as the Universe is not yet old enough to produce them from single stars. Because of the strong tidal forces operating during the binary interaction phase, the remnant host systems observed today are expected to have negligible eccentricities. Here, we report on the first unambiguous identification of a LMWD in an eccentric (e=0.13) orbit with a millisecond pulsar, which directly contradicts this picture. We use our spectra and radio-timing solution (derived elsewhere) to infer the WD temperature T_eff = 8600 +/- 190 K) and 3D systemic velocity (179.5 kms). We also place model-independent constraints on the WD radius (R_WD = 0.024+/- 0.004/0.002 R_sun) and surface gravity (log g = 7.11 +/- 0.08/0.16 dex). The WD and kinematic properties are consistent with the expectations for low-mass X-ray binary evolution and disfavour a three-body formation channel. In the case of the high eccentricity being the result of a spontaneous phase transition, we infer a mass of 1.6 M_sun for the progenitor of the pulsar, which is too low for the quark-nova mechanism proposed by Jiang et al. (2015). Similarly, the scenario of Freire & Tauris (2014), in which a WD collapses onto a neutron star via an rotationally-delayed accretion-induced collapse, requires both a high-mass differentially rotating progenitor and a significant momentum kick at birth under our constraints. Contrarily, we find that eccentricity pumping via interaction with a transient circumbinary disk is consistent with all inferred properties. Finally, we report tentative evidence for pulsations which, if confirmed, would transform the star into an unprecedented laboratory for WD physics and stellar convection.
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